Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0

Answers

Answer 1

The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

We have to given that;

Find the equations which are true for x = - 2 and x = 2.

Now, We can simplify as;

⇒ x² - 4 = 0

⇒ x² = 4

⇒ x = ± 2

⇒ x² = - 4

⇒ x = ±2i

⇒ 3x² + 12 = 0

⇒ x² + 4 = 0

⇒ x = ±2i

⇒ 4x² = 16

⇒ x² = 4

⇒ x = ±2

⇒ 2 (x - 2)² = 0

⇒ (x - 2)² = 0

⇒ x = 2, 2

Thus, The correct equations for x = - 2 and x = 2 are,

⇒ x² - 4 = 0

⇒ 4x² = 16

Learn more about the quadratic equation visit:

brainly.com/question/1214333

#SPJ1


Related Questions

Ok so I cant figure out how to find the angle of measure "C" I got measure "A" and "B" but don't understand "C"

Answers

Answer: The answer is 84

The total of the angels of the triangle always equals 180. So 62+34=96 therefor 96-180=84.

show that 3x4 1 is o(x4∕2) and x4∕2 is o(3x4 1).

Answers

3[tex]x^4[/tex] + 1 is equivalent to [tex]x^{(4/2)}[/tex] in terms of asymptotic growth rate. The value of 3[tex]x^4[/tex] + 1 is O([tex]x^{(4/2)}[/tex]) and [tex]x^{(4/2)}[/tex] is O(3[tex]x^4[/tex] + 1).

To show that 3[tex]x^4[/tex] + 1 is O([tex]x^{(4/2)}[/tex]), we need to find a constant C and a value of x such that:

|3[tex]x^4[/tex] + 1| <= C|[tex]x^{(4/2)}[/tex]|

For x >= 1, we can say that:

3[tex]x^4[/tex] + 1 <= 4[tex]x^4[/tex]

Taking the square root of both sides, we get:

sqrt(3[tex]x^4[/tex] + 1) <= 2x²

Thus, we can choose C = 2 and x0 = 1, and we have:

|3[tex]x^4[/tex] + 1| <= 2|[tex]x^{(4/2)}[/tex]| for all x >= 1

Therefore, 3[tex]x^4[/tex] + 1 is O([tex]x^{(4/2)}[/tex]).

To show that [tex]x^{(4/2)}[/tex] is O(3[tex]x^4[/tex] + 1), we need to find a constant C and a value of x such that:

|[tex]x^{(4/2)}[/tex]| <= C|3[tex]x^4[/tex] + 1|

For x >= 1, we can say that:

[tex]x^{(4/2)}[/tex] <= x²

Thus, we can choose C = 1 and x0 = 1, and we have:

|[tex]x^{(4/2)}[/tex]| <= |3[tex]x^4[/tex] + 1| for all x >= 1

Therefore, [tex]x^{(4/2)}[/tex] is O(3[tex]x^4[/tex] + 1).

Since both 3[tex]x^4[/tex] + 1 is O([tex]x^{(4/2)}[/tex]) and [tex]x^{(4/2)}[/tex] is O(3[tex]x^4[/tex] + 1).

Learn more about asymptotic growth at

https://brainly.com/question/28918543

#SPJ4

Mason County plans to dig a rectangular landfill. The county has set aside a tract of land that measures 50 meters by 80 meters for the dig. How deep must the workers dig for the landfill to hold 250,000 cubic meters of garbage?

Answers

Answer:62.5

Step-by-step explanation:

A large number of coins are divided into four piles according to whether they are pennies, nickels, dimes or quarters. (a) How many ways are there to select 25 coins from the piles?(b) How many ways are there to select 25 coins if at least 5 of the chosen coins must be quarters?(c) Suppose the pile only has 10 quarters, so at most 10 quarters can be selected. How many ways are there to select 25 coins?

Answers

(a) To solve this problem, we need to apply the concept of combinations.  We can find the total number of combinations by using the formula:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we want to select.

Let's assume that we have x pennies, y nickels, z dimes, and w quarters. Since we want to select 25 coins, we can write the equation as x + y + z + w = 25

To find the number of ways to select 25 coins, we need to find the number of solutions to this equation. The total number of combinations is given by: (25 + 4 - 1)C(4 - 1) = 28C3

where we have 25 coins to select and four piles to choose from. Thus, the answer is 28C3.

(b) To solve this problem, we need to use the concept of counting with restrictions. Since we must select at least 5 quarters, we can assume that we have selected 5 quarters and we need to select the remaining 20 coins from the remaining piles. Let's assume that we have x pennies, y nickels, and z dimes. We can write it as x + y + z = 20

To find the number of ways to select 20 coins from the remaining piles, we can use the concept of combinations. The total number of combinations is (20 + 3 - 1)C(3 - 1) = 22C2

Thus, the total number of ways to select 25 coins with at least 5 quarters is given as 10C5 x 22C2

where we have selected 5 quarters from 10 quarters and 20 coins from the remaining piles.

(c)To solve this problem, we need to use the concept of counting with restrictions. Since we can select at most 10 quarters, we need to consider two cases:

(i) We select 10 quarters, and we need to select 15 coins from the remaining piles.

For case (i), we need to select 15 coins from the remaining piles. We can assume that we have x pennies, y nickels, and z dimes. We can write the equation as x + y + z = 15

The total number of ways to select 15 coins is (15 + 3 - 1)C(3 - 1) = 17C2

(ii) We select fewer than 10 quarters, and we need to select the remaining coins from the piles.

For case (ii), To calculate the number of ways, we can use the combination formula to select i quarters out of 10, where i can vary from 0 to 9, and select the remaining (25-i) coins from the remaining piles. We can then sum up the number of ways for all possible values of i to get the total number of ways to select 25 coins with at most 10 quarters.

To know more about Permutation and Combinations here

https://brainly.com/question/13387529

#SPJ4

A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads.
Part B: Flip a coin 14 times and record the frequency of each outcome. Be sure to include the frequency of each outcome in your answer. Then, determine the experimental probability of landing on heads and compare it to the theoretical probability.

Answers

The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

According to the given condition:

Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5.

Part B: Let's record the outcomes of flipping a coin 14 times and count the frequency of each outcome:

HHHHHHHHHHHHHH - 14 heads

TTTTTTTTTTTTTT - 14 tails

The frequency of heads is 14, and the frequency of tails is also 14.

To find the experimental probability of landing on heads, we divide the frequency of heads by the total number of flips:

experimental probability of heads = frequency of heads / total number of flips = 14 / 28 = 0.5

The experimental probability of landing on heads is the same as the theoretical probability. This is not surprising since the number of trials is large enough to approach the theoretical probability.

Therefore,The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. The experimental probability of landing on heads is also 0.5, which matches the theoretical probability.

To know more about probability visit :

brainly.com/question/13604758

#SPJ1

A rhombus has a diagonals of 6 inches and 8 inches. what is the perimeter and the area of the rhombus?

Answers

the perimeter of the rhombus is 20 inches, and the area is 24 square inches.

How to solve the question?

To find the perimeter of a rhombus, we need to know the length of one side. Fortunately, we can use the properties of a rhombus to find the length of the sides. A rhombus has two pairs of equal-length sides, so we can use the Pythagorean theorem to find the length of each side.

Let's label the diagonals of the rhombus as d1 and d2. The diagonals of a rhombus bisect each other at right angles, so we can draw a right triangle with half of each diagonal as the legs and a side of the rhombus as the hypotenuse. Using the Pythagorean theorem, we can find the length of the sides:

(1/2)d1 = 3 inches

(1/2)d2 = 4 inches

Side length = √((1/2)d1² + (1/2)d2²) = √(9 + 16) = 5 inches

Now that we know the length of the sides, we can find the perimeter:

Perimeter = 4 x side length = 4 x 5 = 20 inches

To find the area of the rhombus, we can use the formula:

Area = (diagonal 1 x diagonal 2) / 2

Area = (6 x 8) / 2 = 24 square inches

So the perimeter of the rhombus is 20 inches, and the area is 24 square inches.

To know more about rhombus visit :-

https://brainly.com/question/20627264

#SPJ1

Please answer asap
It would be helpful

Answers

The answer of the given question based on the cylinder is ,  the volume of the solid = 929.44  inch³ . , the mistake is student may have only calculated the volume of the inner cylinder.

What is Volume?

Volume is amount of three-dimensional space occupied by object or substance. It is a physical quantity that is measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). The volume of an object can be calculated by measuring its dimensions and using a mathematical formula specific to its shape.

To find volume of  solid, we need to subtract  volume of  inner cylinder from  volume of outer cylinder.

Volume of the outer cylinder = πr²h

where r = radius of the outer cylinder = 4 inches (diameter is given as 8 inches)

h = height of the outer cylinder = 23 inches

Volume of the outer cylinder = π(4)²(23) = 368π in³

Volume of the inner cylinder = πr²h

where r = radius of the inner cylinder = 2 inches

h = height of the inner cylinder = 18 inches

Volume of the inner cylinder = π(2)²(18) = 72π in³

So, the volume of the solid = Volume of the outer cylinder - Volume of the inner cylinder

= 368π - 72π

= 296π

= 929.44  inch³

The student's answer of 988.05 in³ is significantly higher than the correct answer, suggesting that the student may have only calculated the volume of the inner cylinder instead of subtracting it from the volume of the outer cylinder. This mistake may have arisen due to misreading the problem or misunderstanding the instructions.

To know more about Radius visit:

https://brainly.com/question/12922563

#SPJ1

2. A carnival game uses a fair spinner with 16 sections. There are 2 white sections, 4 red sections, and 10 blue sections on the spinner. Part A Find the probability of each event. Express your answer as a fraction in simplest form. P(blue) = = P(green) = P(red) =​

Answers

The probability of landing on a blue section on the spinner is 10/16, which simplifies to 5/8.

The probability of landing on a green section is 0/16, which simplifies to 0.

The probability of landing on a red section is 4/16, which simplifies to 1/4.

What is probability?

The probability of any event occurring is calculated by finding the total number of possible outcomes that would result in that event occurring, and then dividing that number by the total number of possible outcomes.

In this case, the total number of possible outcomes is 16, since there are 16 sections on the spinner.

The total number of outcomes that would result in a blue section being chosen is 10, since there are 10 blue sections on the spinner.

Dividing 10 by 16 gives us the probability of landing on a blue section, which is 5/8.

The same process is used to calculate the probabilities for green and red sections, with the only difference being that the number of sections for each color is different.

Since there are no green sections, the probability of landing on a green section is 0.

There are 4 red sections, so the probability of landing on a red section is 4/16, which simplifies to 1/4.

For more questions related to event

https://brainly.com/question/29782219

#SPJ1

25% off original price! The original price of a trampoline is $68. What is the sale price?

Answers

sale price=$51

25% of $68= 17
$68-$17=$51

Answer: To find the sale price of the trampoline, you have to subtract 25% or a quarter of the original price ($68) from the original price ($68)

Step-by-step explanation:

To find a quarter of 68, you can simply divide this by 4 and now you have a quarter of the original price, $68. 68/4 = 17

Then you subtract a quarter of the original price from the original price.
68-17= sales price

68-17= 51

Sales Price = $51

Hope this helps :D

The Central Limit Theorem is an important tool that provides the information you will need to use ___ to make ___ about a population mean

Answers

The Central Limit Theorem is an important tool that provides the information you will need to use sample means to make inferences about a population mean.

The Central Limit Theorem (CLT) is a fundamental theorem in statistics that states that if we take repeated random samples of size n from any population with a finite mean and variance, then the distribution of sample means approaches a normal distribution as the sample size increases, regardless of the shape of the original population distribution.

This means that if we take a large enough sample size from a population, the distribution of the sample means will be approximately normal, even if the population distribution is not normal. This is important because the normal distribution is well understood and has many useful properties that make it easier to work with in statistical analyses.

Learn more about Central Limit Theorem here

brainly.com/question/18403552

#SPJ4

The table shows items sold at a food stand during a basketball game.
Sports Drink Bottled Water No Drink Total
5
175
35
145
10
80
50
400
Hot Dog
Candy
No Food
Total
0.0875
What is the probability that a person who buys candy at the food stand will not get a drink?

Answers

Answer:

c

Step-by-step explanation:

Answer:

0.0875

Step-by-step explanation:

The number of people who will get candy and no drink is 35 people.

and we know that there are 400 people in total.

So it should be 35/400 = 0.0875

In March in Austin, Texas, the temperatures for 7 consecutive days were 20°C, 22°C, 20°C, 24°C, 21°C, 26°C, and 23°C. What was the median of the temperatures for these days?

Answers

Answer:

21.5

Step-by-step explanation:

1. Line the numbers from least to greatest:

20, 20, 21, 22, 23, 26

2. cross off one from one side then the other

(ex: 20, 20, 21, 22, 23, 26 --> 20, 21, 22, 23 --> 21, 22)

3. the number left is the median, but if there are 2 numbers left do step 4 and 5

4. find the middle of the 2 numbers (ex: 21 and 22's middle is 21.5)

5. The middle of the those 2 numbers is the median (which in this case is 21.5)

what is different about P3(x)=x^4-21x+20x? what interceps would you predict for its graph?

Answers

There seems to be an error in the expression for P3(x). It appears to be missing an exponent for the second term.

Assuming that the correct expression is P3(x) = x^4 - 21x^2 + 20x, we can analyze its properties.

The degree of the polynomial P3(x) is 4, which means its graph will have at most 4 x-intercepts and at most 3 turning points.

To find the x-intercepts, we set P3(x) equal to zero and solve for x:

x^4 - 21x^2 + 20x = 0

x(x^3 - 21x + 20) = 0

Using the factor theorem or synthetic division, we can find that x = 0 is a root of the polynomial, so (x-0) is a factor. The remaining cubic factor can be factored as (x-1)(x-4)(x+5).

Therefore, the x-intercepts of the graph of P3(x) are x = 0, x = 1, x = 4, and x = -5.

What intercepts would you predict for its graph?

As for the y-intercept, we can find it by setting x = 0:

P3(0) = 0^4 - 21(0)^2 + 20(0) = 0

So the y-intercept is (0,0).

To determine the turning points, we can find the critical points by taking the derivative of P3(x) and setting it equal to zero:

P3'(x) = 4x^3 - 42x + 20

4x^3 - 42x + 20 = 0

Solving this equation yields three critical points: x ≈ -1.23, x ≈ 0.58, and x ≈ 2.65.

We can use the second derivative test to determine the nature of these critical points. The second derivative is:

P3''(x) = 12x^2 - 42

At x ≈ -1.23 and x ≈ 2.65, the second derivative is negative, indicating that these are local maxima. At x ≈ 0.58, the second derivative is positive, indicating that this is a local minimum.

Therefore, the graph of P3(x) has a local maximum at (approximately) (-1.23, P3(-1.23)), a local minimum at (approximately) (0.58, P3(0.58)), and a local maximum at (approximately) (2.65, P3(2.65)).

Learn more about graph from

https://brainly.com/question/13152891

Hey I need help with this can someone help me please.

Answers

The coordinates of point U are (-h, 0).

What is the coordinate of point U?

To find the coordinates of point U in the parallelogram RSTU, we can use the properties of parallelograms. In a parallelogram, opposite sides are parallel, and hence they have the same slope.

Given that point S is at (0, 0), we can calculate the slope of RS as follows:

Slope of RS = (y2 - y1) / (x2 - x1)

= (0 - g) / (0 - (-f)) (Substituting coordinates of R and S)

= g / f

Since RS and TU are opposite sides of the parallelogram, they must have the same slope. Thus, the slope of TU is also g / f.

Given that point T is at (h, 0), we can calculate the equation of the line TU in point-slope form using the slope we just found:

y - y1 = m(x - x1) (Point-slope form of a line)

where;

m is the slope of TU and (x1, y1) is the coordinates of point T.

Plugging in the values, we get:

y - 0 = (g / f)(x - h)

Simplifying, we get:

y = (g / f)x + gh / f

Now, we can substitute the coordinates of point U, which are (x, y), into the equation we just found:

y = (g / f)x + gh / f

y = (g / f)x + gh / f

Since U lies on the x-axis (i.e., y = 0), we can set y = 0 in the equation and solve for x:

0 = (g / f)x + gh / f

(g / f)x = -gh / f

x = -h

So, the x-coordinate of point U is -h.

Now, we can substitute the value of x = -h into the equation we found earlier to get the y-coordinate of point U:

y = (g / f)x + gh / f

y = (g / f)(-h) + gh / f

y = -gh / f + gh / f

y = 0

Learn more about coordinate points here: https://brainly.com/question/17206319

#SPJ1

What is the mean, median, mode, and range for 53, 13, 34, 41, 26, 61, 34, 13, 69

Answers

Answer:

Answers down below!

Step-by-step explanation:

Mean: 38.2

Median: 34

Range: 56

Mode: 13 and 34

Hope this helps!

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations of the inequality is

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

We have the inequality -3(2x - 5) < 5(2 - x)

Now, simplifying each side of inequality

-3(2x - 5) = -3(2x) + -3(-5)

-3(2x - 5) = - 6x + 15

and, 5(2 - x) = 5(2) + 5(-x)

5(2 - x) = 10 - 5x

So, - 6x + 15 < 10 - 5x

Now, Subtract 15 from both sides

- 6x < -5 - 5x

- x < - 5

x > 5

The correct statements are:

- 6x + 15 < 10 - 5x  and An open circle is at 5 and a bold line starts at 5 and is pointing to the right.

Learn more about Inequality here:

https://brainly.com/question/30228778

#SPJ1

Find the number of minutes between 17:53 and 7:26

Answers

There are 813 minutes in between 17:53 to 7.26 .

Time can be represented in two formats, that is in a twelve - hour format and in a twenty four - hour format.

Here the time 17:53 and 7:26 is represented in twenty four - hour format where the day is divided in twenty four hours and time runs from midnight and ends at midnight.

(If the time 17:53 and 7:26 was represented in twelve - hour format then it would have AM and PM to denote if the time is from midnight till noon or noon till midnight, which is clearly not the case.)

Thus, from 17:53 to 7.26 there is 13 hours and 33 minutes.

We know one hour has 60 minutes. Therefore by method of conversion of hours to minutes we get,

Number of minutes between 17:53 to 7.26 = {(13*60) + 33} = 780+33 = 813

To know more about  conversion of hours to minutes here

https://brainly.com/question/30775919

#SPJ4

A rectangle with width of 3. There is a vertical line that splits rectangle into two sections with different lengths. One length is x the other is 4. 3(x + 4) represents the area of the rectangle above. Which expression below is equivalent by the Distributive Property? (4 points) a 3x+12 b (3 + x) + 4 c (x + 4) ⋅ 3 d 3x + 4

Answers

The expression that is equivalent by the Distributive Property is A 3x+12

this is the only answer that actually uses the distributive property.

What is the Distributive Property?

The Distributive Property is a mathematical rule that applies to operations such as multiplication and addition or subtraction. It states that when you multiply a number by a sum or difference of two or more numbers, you can distribute the multiplication over each of the individual terms in the sum or difference.

3 can be multiplied by both x and 4 to get 3x+12 (which is using the distributive property)

Read more about the distributive property here:

https://brainly.com/question/2807928

#SPJ1

Mrs. Ades places tiles numbered 1 through 10 in a bag and assigns numbers 1-6 to Elias and tiles 7-10 to Maha. Each day, she draws a tile, and the person whose tile is drawn has to do chores. Is Mrs. Ades being fair? Explain.

Answers

Answer:

Mrs. Ades is not being fair. The probability of Elias and Maha getting chosen should be equal, but Elias has a 6/10 chance of being chosen, while Maha only has a 4/10 chance of being chosen. This is because Elias has 6 tiles assigned to him, while Maha only has 4 tiles assigned to her.

Explanation:

To make it fair, Mrs. Ades should assign each person an equal number of tiles, or draw from a bag with the tiles numbered 1 through 5 twice, assigning one to Elias and one to Maha each time, and then draw from a bag with tiles numbered 6 through 10 twice, assigning one to Elias and one to Maha each time.

which method would be best to compare the spread of the frequency distributions for the two groups? explain your reasoning. calculate and compare spread using this method.

Answers

Standard deviation is the best method for comparing the spread of frequency distributions for two groups, as it provides an accurate and sensitive measure of variability.

To compare the spread of the frequency distributions for two groups, we can use the measure of variability called the standard deviation. The standard deviation provides a measure of how much the data points are spread out around the mean.

A smaller standard deviation indicates that the data points are clustered closely around the mean, whereas a larger standard deviation indicates that the data points are more spread out from the mean.

The reason why standard deviation is a good measure of spread is that it is sensitive to the distance between data points and the mean. Therefore, it provides an accurate measure of how much the data is spread out, regardless of the shape of the distribution.

To calculate the standard deviation, we first need to calculate the mean of each group, and then the difference between each data point and the mean, squared.

We then take the average of these squared differences and take the square root to get the standard deviation.

For example, suppose we have two groups of test scores:

Group A: 75, 80, 85, 90, 95

Group B: 60, 70, 80, 90, 100

To calculate the standard deviation for Group A, we first calculate the mean:

(75 + 80 + 85 + 90 + 95) / 5 = 85

Then we calculate the difference between each data point and the mean, squared:

(75 - 85)² = 100

(80 - 85)² = 25

(85 - 85)² = 0

(90 - 85)² = 25

(95 - 85)² = 100

Next, we take the average of these squared differences:

(100 + 25 + 0 + 25 + 100) / 5 = 50

Finally, we take the square root of this average:

√(50) = 7.07

Therefore, the standard deviation for Group A is 7.07. We can repeat these steps for Group B and compare the two standard deviations to determine which group has a larger spread.

Learn more about the frequency distributions at

https://brainly.com/question/14926605

#SPJ4

18. 12 cm 14 cm 12 cm 14 cm 8 cm Find the area of the rectangle and the triangle independently. What is the ratio comparing the area of the triangle to the area of the trapezoid (the entire figure put together)? (Must be in Reduced Form) ​

Answers

The ratio of the area of the triangle to the area of the trapezoid is 3:8.

How to calculate the ratio

Area of the rectangle will be:

= 14 cm x 12 cm

= 168 cm²

Height of the triangle

= 14 cm - 8 cm

= 6 cm

Area of the triangle will be:

= 1/2 x 12 cm x 6 cm

= 36 cm²

Area of the trapezoid will be:

= 1/2 x (base1 + base2) x height

= 1/2 x (12 cm + 12 cm) x 8 cm

= 96 cm²

Ratio will be:

Area of the triangle / Area of the trapezoid

= 36 cm² / 96 cm²

= 3/8

Learn more about area on

https://brainly.com/question/25292087

#SPJ1

can yall help me on this i have been stuck on it for a long time

Answers

The number of packs bought is given as follows: 60.The number of packs of buns is given as follows: 6.The number of hot dogs is given as follows: 5.

What is the least common multiple?

The least common multiple of two or more numbers is the smallest number that is a multiple of each of the given numbers. For example, the LCM of 2 and 3 is 6, because 6 is the smallest number that is a multiple of both 2 and 3.

For this problem, the number of packs bought is the least common multiple of 10 and 12, which is obtained by factoring them into prime numbers as follows:

10 - 12|2

5 - 6|2

5 - 3|3

5- 1|5

1 - 1

Hence:

lcm(10, 12) = 2² x 3 x 5 = 60.

Hence:

The number of packs of buns is given as follows: 6, as 60/10 = 6.The number of hot dogs is given as follows: 5, as 60/12 = 5.

More can be learned about the least common multiple at https://brainly.com/question/10749076

#SPJ1

Use the binomial theorem to expand (2x^2+5y)^5

Answers

The expanded form of (2x² + 5y)⁵ using the binomial theorem is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

Expand the expression using binomial theorem?

Given the expression in the question:

(2x² + 5y)⁵

To expand (2x² + 5y)⁵ using the binomial theorem, we need to apply the following formula:

(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + C(n, 2)a⁽ⁿ⁻²⁾ b² + ... + C(n, r)[tex]a^{(n-r)}[/tex] [tex]b^r[/tex] + ... + C(n, n)a⁰ bⁿ

Where C(n, r) is the binomial coefficient, which represents the number of ways to choose r items from a set of n distinct items.

(2x² + 5y)⁵

Here: a = 2x² and b = 5y, so we have:

Plug into the above formula

(2x² + 5y)⁵ = C(5, 0)(2x²)⁵ (5y)⁰ + C(5, 1)(2x²)⁴ (5y)¹ + C(5, 2)(2x²)³ (5y)² + C(5, 3)(2x²)² (5y)³ + C(5, 4)(2x²)¹ (5y)⁴ + C(5, 5)(2x²)⁰ (5y)⁵

Simplifying each term using the binomial coefficient formula C(n, r) = n! / (r! (n-r)!):

(2x² + 5y)⁵ = 1(32x¹⁰)1(1) + 5(16x⁸)1(5y)¹ + 10(8x⁶)2(25y²) + 10(4x⁴)3(125y³) + 5(2x²)4(625y⁴) + 1(1)5(3125y⁵)

Simplifying the coefficients and the exponents of x and y:

(2x² + 5y)⁵ = 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵

Therefore, the expanded form is 32x¹⁰ + 400x⁸ y + 2000x⁶ y² + 5000x⁴ y³ + 6250x² y⁴ + 3125y⁵.

Learn more about binomial theorem here: https://brainly.com/question/30100273

#SPJ1

6. Justin listed these items on his deposit slip: (bills) 8 one-hundreds, 27 fifties, 83 fives, 141 ones; (coins) 13 quarters, 117 nickels; (checks) $317.94, $57.89, $527.24, $77.49. He received cash back of 30 twenties and 11 tens. What total deposit did he make?​

Answers

Justin made a total deposit of $1985.66.

What is deposit?

A deposit is a sum of money that is added to an account or made available for use in a financial transaction. It can refer to money that is placed into a bank account, such as a savings or checking account, or to a payment made in advance for goods or services. Deposits are often required when b accounts, taking out loans, or making large purchases.

In the context of banking, deposits can earn interest, which can increase the amount of money in the account over time.

Let's start by adding up the bills:

Total amount of bills = 8 x 100 + 27 x 50 + 83 x 5 + 141 x 1

Total amount of bills = 800 + 1350 + 415 + 141

Total amount of bills = 1706

Next, let's add up the coins:

Total amount of coins = 13 x 0.25 + 117 x 0.05

Total amount of coins = 3.25 + 5.85

Total amount of coins = 9.10

Now, let's add up the checks:

Total amount of checks = 317.94 + 57.89 + 527.24 + 77.49

Total amount of checks = 980.56

Finally, let's add up the cash back:

Total amount of cash back = 30 x 20 + 11 x 10

Total amount of cash back = 600 + 110

Total amount of cash back = 710

To find the total deposit, we need to add up all the amounts:

Total deposit = Total amount of bills + Total amount of coins + Total amount of checks - Total amount of cash back

Total deposit = 1706 + 9.10 + 980.56 - 710

Total deposit = 1985.66

Therefore, Justin made a total deposit of $1985.66.

To know more about deposit visit:

https://brainly.com/question/1438257

#SPJ1

Read the following excerpt from Pointed Roofs by Dorothy Richardson. Then, respond to the question that follows. In a well-written paragraph of 5–7 sentences, explain how the author uses stream of consciousness and one other narrative technique to enhance her writing. Be sure to include specific textual evidence to support the narrative techniques you discuss in your response

Answers

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, in the given expert.

An excerpt is indeed a quotation from that other resource that the author introduces with fresh language in a sentence. This phrase is taken from Thomas Jefferson's 1801 inaugural speech: As he warned his audience, "I may often go wrong by defect of judgement," Jefferson admitted the fallibility of human nature. "I shall frequently err through lack of judgement" is the excerpt.

In "Pointed Roofs," Dorothy Richardson makes use of conversation and stream of consciousness to improve her writing. Using stream of consciousness, the author lets readers peek inside the protagonist, Miriam, to understand her feelings and thoughts as they happen. For instance, readers can feel Miriam's mild dizziness 

To know more about excerpt, here:

https://brainly.com/question/29708851

#SPJ1

Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.

Answers

If cash is  54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills, the total deposit is $454.00.

To find the total deposit, we need to add up the amounts from the checks and cash, and then subtract the cash received.

First, let's add up the amounts from the checks:

$152.54 + $147.46 = $300.00

Next, let's add up the amounts from the cash:

54 one-dollar bills = $54.00

12 five-dollar bills = $60.00

6 ten-dollar bills = $60.00

Total cash = $174.00

Finally, we need to subtract the cash received:

$174.00 - $20.00 = $154.00

Therefore, the total deposit is $300.00 + $154.00 = $454.00.

To learn more about deposit click on,

https://brainly.com/question/20022737

#SPJ1

Complete question is:

Find the total deposit if you have: Checks: $152.54 and $147.46: cash: 54 one-dollar bills, 12 five-dollar bills, and 6 ten -dollar bills; less $20.00 as cash received.

The top view of a plot of land is shown on a map, where each unit on the
coordinate grid represents 1 meter.
What is the area of this plot of land in square meters?
A 54 square meters
B92 square meters
C 112 square meters
D 120 square meters

Answers

The area of the plot of land that has a top view as shown on a map above is calculated as: C. 112 square meters

What is the Area of the Plot of Land?

The shape of the plot of land can be decomposed into two different triangles and 1 rectangle.

Area of triangle 1 = 1/2 * base * height

base = 8 m

height = 5 m

Area of triangle 1 = 1/2 * 8 * 5 = 20 square meters

Area of triangle 2 = 1/2 * base * height

base = 8 m

height = 7 m

Area of triangle 2 = 1/2 * 8 * 7 = 28 square meters

Area of the rectangle = length * width = 8 * 8

= 64 square meters.

Therefore, we have:

Area of the plot of land = 64 + 28 + 20

= 112 square meters.

Learn more about area on:

https://brainly.com/question/15901585

#SPJ1

Can someone give me a trig function with the following criteria

Answers

The trig function that meets the given criteria is determined as f(x) = 4sin(π/4x) + 9.4.

What is the trig function for the given criteria?

We can use the formula for a sinusoidal function of the form:

f(x) = Asin(Bx - C) + D

where:

A is the amplitudeB determines the period as T = 2π/BC determines the horizontal shiftD determines the vertical shift

We have A = 4 and K = 9.4, so we know that the midline of the function is at y = D = 9.4.

Since we don't have any information about the horizontal shift, we can assume that C = 0.

Then, the formula becomes:

f(x) = 4sin(Bx) + 9.4

Now, we need to find B so that the function has a period of 2π. Since the period is given by T = 2π/B, we have:

2π = TB = (13.4 - 5.4)B = 8B

Therefore, B = π/4. Finally, we can write the function as:

f(x) = 4sin(π/4x) + 9.4

This function has an amplitude of 4, a midline at y = 9.4, and a period of 2π.

Learn more about trig functions here: https://brainly.com/question/29615325

#SPJ1

How can you model an expression such as a − b?

Answers

By knowing what to do

100% of what number is 6​

Answers

The answer is 6 because 100% of a number is always just the number

Answer:

6

Step-by-step explanation:

Half of six is 3. That would be 50%. 6 at 100% is simply 6.

Other Questions
gibberellin stimulates the production of -amylase in germinating seeds, an enzyme that converts ______ into ______. what is 5x-9 and 3x+9 in which decade was the original safe drinking water act adopted as federal law in the united states What is the effect of the imagery in lines 13-27 of The Aeneid?A. It gives modern readers a deeper understanding ofthe speaker.B. It creates a sense of horrific yearning in readers.C. It uses old scare tactics to thrill modern readers.D. It forces readers to consider what their five sensestell them. A client with heart failure has a resting heart rate of 70 beats per minute. The client's stroke volume is 60 mL/beat. The client weighs 220 pounds. Calculate the client's cardiac output per minute. Record your answer in liters (L). Enter the numeral only. While considering a research question, a data analyst follows the SMART methodology. They limit their analysis to include data from July 2012 to August 2012. What component of the SMART framework describes this decision?A. TopicalB. TargetedC. ThoughtfulD. Time-bound in a printf, a backslash is printed by enclosing in quotesa. \b. \\c. /\d. // 9. What report lists the website pages where users first arrived?A. Events > PagesB. All PagesC. Exit PagesD. Landing Pages Choose the correct answers: 1. Our....... should be arriving soon. a. guests b.bests c.west 2. The chicken was dry and........ a.tasty b.taste c. tasteless 3. She has one of the most...... minds in the business. a. creative b. creativeness c. creativity 4. The..... certainly looks good on paper. a.survey b. design c.solve Who does the ghost name as being responsible for his death? Rust-colored sputum in a patient with pneumonia usually indicates: In England, the tax on soft drinks was recently introduced.Australians buy 1.29 billion litres of sugar-sweetened drinks perannum. Currently, the average price of these drinks is $1.7/litre.Assume that government wants to implement a sales tax (x% per litre) on soft drinks to reduce their sales (or demand) to 700 million litres. The price elasticity of demand for soft drinks is -0.89.a) How much sales tax should be imposed to achieve the demand target of 700 million litres? Hint: Find the value of x.b) How much additional revenue will be raised by this tax? Question 64Disease is considered the antithesis of health, defined as "a state of physical, mental and social well-being and ability to function, and not merely the absence of illness or infirmity."a. True b. False Guidelines:The Discussion Board provides a chance for you to present ideas and insights to your classmates and respond to your classmates' posts, as well. Take the opportunity to share your thoughts and opinions, your background knowledge and experience, or anything you may have learned in the course so far. Keep in mind that everyone in this class can read whatever you post. Keep your responses original and polite, and remember to use correct spelling and grammar. Also provide sources where appropriate.Remember that this is an academic Discussion Board, so stay on topic. If you are not sure how many posts you need to make, ask your instructor.Prompt:Consider the following questions:What do you think are the benefits of joining an organization that focuses on bringing interior designers together?What factors would you consider to be important if you had to choose to join one professional organization as a student? What is the time goal for initiation of fibrinolytic therapy in appropriate patients without contraindications after hospital arrival?a.30 minb.45 minc.35 mind.40 min Can someone help with this question???? What is the leading cause of death for persons with HIV infection worldwide? what do we mean by galaxy evolution? how do telescopic observations allow us to study galaxy evolution? how do theoretical models help us study galaxy formation? Please help with this question A circle is separated into eight sectors of equal area. These eight sectors are arranged to form a shape similar to a parallelogram.The area of the circle (r2) is equal to the area of the parallelogram (bh).Select from the drop-down lists to correctly complete each sentence.The height of the parallelogram is equal to the of the circle. The base of the parallelogram is equal to of the circle. Therefore, the area of the circle (r2) is equal to the , and the circumference of the circle is equal to . Question 11 Marks: 1 A deterioration in the ozone layer of the stratosphere can cause an increase in ultraviolet radiation reaching the earth.Choose one answer. a. True b. False