The ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.
What is the scale factor?
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
Let h1 and h2 be the heights of the two similar prisms, and let A1 and A2 be the areas of their respective bases.
Also, let k be the scale factor that relates the smaller prism to the larger prism.
a. We know that the volumes of the two similar prisms are proportional to the cubes of their corresponding side lengths, so we have:
(kh1)³ / (kh2)³ = 135 / 5000
Simplifying this expression, we get:
h1³ / h2³ = 135 / 5000
Taking the cube root of both sides, we get:
[tex]h1 / h2 = (135 / 5000)^{(1/3)}[/tex]
Using a calculator, we find:
h1 / h2 ≈ 0.405
Therefore, the ratio of the heights of the two similar prisms is approximately 0.405 to 1.
b. The ratio of the areas of the bases of two similar prisms is equal to the square of the scale factor. That is:
A1 / A2 = k²
To find the scale factor k, we can use the fact that the volumes of the two prisms are proportional to k³. Therefore:
k³ = 5000 / 135
k ≈ 5.091
Using this value of k, we get:
A1 / A2 = k² = (5.091)² ≈ 26
Therefore, the ratio of the areas of the bases of the two similar prisms is approximately 26 to 1.
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Visual work of 44. 4 divided by 100 with decimal moves
By division rule of fraction, dividing 44.4 by 100 results to 0.444, that is shifts three decimal places (to right).
We can divide 44.4 by 100 using simple rule of division.
Rewriting 44.4 in fractional form we get,
44.4 = 444/10
Dividing 444/10 by 100 we can write it in fractional form as 444/10*100.
Therefore, 44.4 divided by 100 in fractional form can be written as 444/1000.
Applying division rule of fractions,
Dividend is 444 and divisor is 1000.
Since the denominator of the fraction has three zeros (in divisor 1000) by properties of fraction the decimal place of the numerator shifts three places to its right.
Also something divided by one is the same value as its initial value.
Thus as 444 shifts to three decimal places (on its right) it becomes 0.444 as the denominator is 1*1000.
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9 didvided by 5 and 1 /7th
Answer:
7/4
Step-by-step explanation:
i am sooo sure that the answer is 1.75
Please PLEASE HELP ME this is due in 7 minutes and it the last question PLEASE
Answer:
(3,0)
Step-by-step explanation:
the point (5,-5) a translation of 2 units left would be equivalent to x-2.
(5-2,-5)
5 units up is equivalent to y+5
therefore
(5-2,-5+5)
yields
(3,0)
What is 270% of 136ft?
Answer:
367.2
Step-by-step explanation:
Basically 270% is 2.7 so if you multiply 2.7 by 136 you will get 367.2
2 fractions with different denominators that add up to 6 1/3
The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.
First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.
Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.
Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:
1/2 = 3/6
x/6
Now we need to find the value of x that makes the sum of the fractions equal to 19/3:
3/6 + x/6 = 19/3
To solve for x, we can multiply both sides by 6:
3 + x = 38/3
Then, we can subtract 3 from both sides:
x = 29/3
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The scores on a test are normally distributed, with a mean of 82 and a standard deviation of 8. What percent of scores are less than 90? Explain your answer.
WILL GIVE BRAINLIST
By calculating the CDF of normal distribution, the percentage of scores that are greater than 90 are 14.6%.
The CDF function of a Normal distribution is calculated by translating the random variable to the Normal Standard, and then looking up a value from the precalculated "Phi" function (Φ), which is the cumulative density function of the normal standard. The Normal Standard, often written Z, is a Normal with mean 0 and variance 1. Thus, Z∼N(μ=0,σ²=1).
Let x1, x2, .... be the scores on the test.
X ~ N (82, 64)
P(90 < X < 100) = Φ(18/8) - Φ(1) = 0.146 (using norm.s.dist function in excel)
Step-by-step explanation:
cores Distribution and Percentile
The scores on a test are normally distributed, with a mean of 82 and a standard deviation of 8. What percent of scores are less than 90? Explain
To find the percentage of scores that are less than 90 in a normally distributed test with a mean of 82 and a standard deviation of 8, we can use the cumulative distribution function (CDF) of the normal distribution.
The CDF of a normal distribution gives the probability that a random variable falls below a particular value. In this case, we want to find the probability that a score is less than 90.
The formula for the CDF of a normal distribution is:
CDF(x) = (1/2) * (1 + erf((x - μ) / (σ * sqrt(2))))
where erf is the error function, μ is the mean, σ is the standard deviation, and x is the value we want to find the cumulative probability for.
Plugging in the given values:
μ = 82
σ = 8
x = 90
We can calculate the cumulative probability using the formula:
CDF(90) = (1/2) * (1 + erf((90 - 82) / (8 * sqrt(2))))
Using a calculator or statistical software that provides the error function, we can find that erf(1.0) is approximately 0.6827.
Plugging this value back into the formula, we get:
CDF(90) = (1/2) * (1 + 0.6827) = 0.8414
So, the cumulative probability that a score is less than 90 is approximately 0.8414, or 84.14%.
Therefore, about 84.14% of the scores are less than 90 in this normally distributed test.
A deck of standard playing cards holds 52 unique cards.
36 of these cards are numbered cards (numbered 2-9), 4
of these cards are aces, and 12 of these cards are face
cards (jack, queen, and king). If you play a card game and
draw half of the face cards, one ace, and one fourth of the
numbered cards, how many cards do you have? How
many of each card type of card do you have? Cite
evidence from the problem.
PLS HELP
The total number of cards drawn is 16 and As a result, we have the following:
6 face cards, Aces 1, 9 numbered cards
How to determine the type of each card?Because there are 12 face cards, half of them are 6 face cards.
There are 4 aces, so we draw 1.
There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.
We draw a total of 6 + 1 + 9 = 16 cards.
We may use the information provided in the problem to determine how many of each card type we have. We chose:
6 face cards make up half of the deck.
1 ace: 1 ace
9 numbered cards are one-fourth of the numbered cards.
As a result, we have:
6 face cards
Aces: 1
9 numbered cards
We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)
There are 52 - 16 = 36 cards left.
This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.
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1. a national organization sets out to investigate the change in prevalence of hiv since the last census in 2010. a total of 4,706 participants were interviewed and a total of 468 responses were confirmed to be hiv positive. assume that the data from the census indicated that the prevalence of hiv in the particular population was 7.5%. a) is the sample size large enough to justify the use of the z formula? show your calculation to support your answer. (3 points)
Yes, the sample size of 4,706 is large enough to justify the use of the z formula.
To determine whether the sample size is large enough to justify the use of the z formula, we need to check whether the sample size is sufficiently large to meet the central limit theorem (CLT) conditions. The CLT states that the distribution of the sample mean of a sufficiently large sample size from any population, regardless of the distribution of the population, will be approximately normal.
One of the conditions for the CLT is that the sample size is large enough. There is no hard and fast rule for determining what is considered a "large" sample size, but a commonly used rule of thumb is that the sample size should be at least 30.
In this case, the sample size is 4,706, which is much larger than 30. Therefore, we can conclude that the sample size is large enough to justify the use of the z formula.
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PLEASE HELP SOSOSOSOSOS
Consider this system of equations
{10x + 13y + 15z = 4
{ 12x - 2y + 5z = - 8
{ 2x + 2y - 6z = 4
The system can be represented by the following matrix equation where A is a 3 x 3 matrix and ⇾b is a 3D vector
[ x
A [ y = ⇾b
[ z
Find A and ⇾b
The given system of equations can be represented in matrix form as:
| 10 13 15 | | x | | 4 |
| 12 -2 5 | x | y | = |-8 |
| 2 2 -6 | | z | | 4 |
Therefore, the matrix A is:
| 10 13 15 |
| 12 -2 5 |
| 2 2 -6 |
And the vector ⇾b is:
| 4 |
|-8 |
| 4 |
vic's favorite cookie recipe uses 250 250250 grams of flour for every 170 170170 grams of butter. imani made cookies using 750 750750 grams of flour for every 630 630630 grams of butter. what will vic think of the amount of butter in imani's cookies? choose 1 answer:
Vic would think that the amount of butter in Imani's cookies is appropriate since the ratio of flour to butter used in Imani's recipe is the same as the ratio used in Vic's favorite cookie recipe, which is 250:170 grams of flour to butter.
Specifically, in Vic's recipe, there are approximately 1.47 grams of flour for every gram of butter (250/170), while in Imani's cookies, there are approximately ratio 1.19 grams of flour for every gram of butter (750/630). This means that there is relatively more butter in Imani's cookies compared to Vic's recipe. Based on this difference, Vic might expect Imani's cookies to have a richer, denser texture and a stronger buttery flavor than his favorite recipe.
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O is the center of the regular pentagon below. Find its area. Round to
the nearest tenth if necessary.
14
The area of the regular pentagon is 490 square units
How to determine the area of the pentagonThe formula used for calculating the area of a regular pentagon is expressed with the equation
A = 1/2 pa
Such that the parameters are;
A is the area of the pentagon.p is the perimeter of the pentagon.a is the apothem.From the information given, we have that;
Perimeter = 5s
Substitute the values,
Perimeter = 5(14)
multiply the values
Perimeter = 70 units
Now, substitute the value into the formula
Area = 1/2 × 70(14)
Area = 980/2
Divide the values
Area = 490 square units
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A ran a 20-mile race that she completed in 2.5 hours.
If A ran at a constant speed for the entire race,what was her speed in miles per hour?
SHOW YOUR WORK
Answer:
The answer for speed is 8 miles/hr
Step-by-step explanation:
speed =distance/time
s=20/2.6
s=8miles/hr
with a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.
This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.
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With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
With a simple random sample, each participant is selected at random from the population, ensuring that everyone has an equal chance of being selected.
This eliminates any potential bias or manipulation, as no one can control or influence the selection process. Additionally, the sample size can be increased to amplify the accuracy and representativeness of the data collected. Therefore, a simple random sample is a reliable method for gathering unbiased data.
With a simple random sample, nobody can game the system to purposefully amplify their answers over that of others because the selection process is random.
This means that each individual or element in the population has an equal chance of being chosen, ensuring unbiased and representative sample results.
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suppose that 8% of the patients tested in a clinic are infected with hiv. furthermore, suppose that when a blood test for hiv is given, 97% of the patients infected with hiv test positive and that 4% of the patients not infected with hiv test positive. what is the probability that a patient testing positive for hiv with this test is infected with hiv? (enter the value of the probability in decimal format and round the final answer to three decimal places.)
The likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4%
To illuminate this issue, we will utilize Bayes' hypothesis. Let's characterize the taking after occasions:
A: the persistent is contaminated with HIV
B: the persistent tests positive for HIV
We need to calculate P(A|B), the likelihood that an understanding is contaminated with HIV given that they tried positive for HIV.
By Bayes' hypothesis:
P(A|B) = P(B|A) * P(A) / P(B)
where
1. P(B|A) is the likelihood of testing positive for HIV given that the persistent is tainted with HIV (97%)
2. P(A) is the predominance of HIV within the clinic (8%)
3. P(B) is the likelihood of testing positive for HIV, which can be calculated utilizing the law of adding up to likelihood:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
where
1. P(B|A') is the likelihood of testing positive for HIV given that the persistent isn't tainted with HIV (4%)
2. P(A') is the complement of A, i.e., the likelihood of a quiet not being tainted with HIV (1 - 8% = 92%)
Substituting the values we have:
P(B) = 0.97 * 0.08 + 0.04 * 0.92 = 0.0736
P(B) = 0.0736
Hence,
P(A|B) = 0.97 * 0.08 / 0.0736 ≈ 0.104
P(A|B) = 0.104
So the likelihood that understanding testing positive for HIV with this test is tainted with HIV is almost 0.104 or 10.4% (adjusted to three decimal places).
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Erica wants to fill the bottom of a planter with 2 in. of rocks, then fill the rest of the planter with soil all the way to the top. She wants the volume of the soil to be exactly 640 in.³. What could be the shape of Erica's planter? 12 in. 0- 1 10 in. 10 in. 8 in. 8 in. 10 in. 8 in. 10 in. 12 in. 8 in. 8 in. 10 in.
Answer: b
Step-by-step explanation:
I didnt get it but thats the correct answer when i guessed on it
Answer:
The answer is the skin est one there
Step-by-step explanation:
I got the question wrong so I don't know how but this is the correct one
You invest $1000 in a certificate of deposit (CD) that earns 5% interest every year. If the function that represents growth of your money is f(x)=1.05x, in what year will your CD be at least worth $1,300
Answer: Year 6
Step-by-step explanation: The year my money would be at least $1300 is year 6.
In what year would the money be at least $1300?
The formula that can be used to determine the number of years that $100 would have a value of $1300 is:
Number of years = In(FV / PV) / r
Where:
FV = future value
PV = present value
r = interest rate
In(1300 / 1000) / 0.05
0.2623642645 / 0.05
= 5.2 years
Future value in 5 years = $1000(1.05^5) = $1276.28
Future value in 6 years = $1000(1.05^6) = $1340.10
Let h(x) be the number of hours it takes
a new factory to produce x engines. The
company's accountant determines that
the number of hours it takes depends on
the time it takes to set up the machinery
and the number of engines to be
completed. It takes 6.5 hours to set up
the machinery to make the engines and
about 5.25 hours to completely
manufacture one engine. The
relationship is modeled with the
function b(x)=6.5+5.25%
1. Determine the x and y-
intercepts of the function.
2. Is the function increasing or
decreasing?
Based on the information, the y-intercept is (0, 6.5).
The function is increasing.
How to calculate the interceptBased on the information, we can use the variable x. This will be:
0 = 6.5 + 5.25%x
-6.5 = 5.25%x
x = -6.5 / 5.25% ≈ -123.81
There's no x intercept due to the negative value which doesn't make sense in this scenario.
In order to find the y-intercept, we set x = 0 and evaluate b(x):
b(0) = 6.5 + 5.25% × 0 = 6.5
Therefore, the y-intercept is (0, 6.5).
The function b(x) is increasing since the coefficient of x is positive (5.25%). This means that as the number of engines produced (x) increases, the time it takes to manufacture the engines also increases.
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help pleasejhdfjg THIS ASSIGNMENT IS LIKE 2 WEEKS OVERDUE
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas (b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below. (c) The final total area is 2x² - 10x - 15.
What is an area model?An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
2x⁴ − 3x³ − 2x² − 4x − 1
+---------------------------------------
x | 2x⁵ -3x⁴ -2x³ -4x² -x
|
3 | 6x⁴ -9x³ -6x² -12x -3
+---------------------------------------
c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.
x + 8 x - 5
+--------------------
x | x² + 8x x² - 5x
|
-5 | -5x + -40 -5x + 25
+--------------------
The final total area can be found by adding up the areas of the smaller rectangles:
Total area = x² + 8x + x² - 5x - 5x - 40 + 25
= 2x² - 10x - 15
= 2x² - 10x - 15.
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Find a possible solution to the equation cos(x+2)=sin(3x)
A.
x=0. 5 degrees
B.
x=1 degree
C.
x=22 degrees
D.
x=44 degrees
A possible solution to the equation cos(x+2)=sin(3x) is x = 22 degrees
The correct answer is an option (C)
Consider a trigonometric equation,
cos(x+2) = sin(3x)
For value x = 0.5 degrees,
cos(x + 2) = cos(2.5)
= 0.999
and sin(3x) = sin(1.5)
= 0.026
For x = 1 degree,
cos(x + 2) = cos(3)
=0.9986
sin(3x) = sin(3)
= 0.052
For x = 22 degrees
cos(x + 2) = cos(24)
= 0.913
sin(3x) = sin(66)
= 0.913
for x = 44 degrees,
cos(x + 2) = cos(46)
= 0.69
sin(3x) = sin(132)
= 0.743
Therefore, the solution to an equation cos(x+2) = sin(3x) is x = 22 degrees
The correct answer is an option (C)
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HELP i NEED to get my grades up
1. A cylinder has a radius and height of 2.0×10^7
feet and 4.0×10^5
feet respectively. What is the approximate volume of the solid? Leave your answer in terms of π
. Use scientific notation.
2. A cone has a diameter and length of 1.0×10^7
inches and 5.0×10^5
inches respectively. What is the approximate volume of the solid? Leave your answer in terms of π
. Use scientific notation. Round your significant figure to the nearest hundredth.
The approximate volume of the solid is 1.6 × 10^23 π cubic feet.
The approximate volume of the solid is 8.17 × 10^20 π cubic inches.
We have,
1.
The volume V of a cylinder is given by V = πr²h,
where r is the radius and h is the height.
Substituting r = 2.0 × 10^7 feet and h = 4.0 × 10^5 feet.
V = π (2.0 × 10^7)² (4.0 × 10^5)
Simplifying,
V = 1.6 × 10^23 π cubic feet (using scientific notation and leaving the answer in terms of π)
2.
The volume of a cone is given by V = 1/3πr²h,
where r is the radius, h is the height, and we are given the diameter (d = 2r).
Substituting,
d = 1.0 × 10^7 inches, r = d/2 = 5.0 × 10^6 inches, and
h = 5.0 × 10^5 inches, we get:
V = 1/3 π (5.0 × 10^6)² (5.0 × 10^5)
Simplifying,
V = 2.6 × 10^20 π cubic inches
(using scientific notation and leaving the answer in terms of π)
Rounding to the nearest hundredth,
V = 8.17 × 10^20 π cubic inches.
Thus,
The approximate volume of the solid is V = 1.6 × 10^23 π cubic feet.
The approximate volume of the solid is V = 8.17 × 10^20 π cubic inches.
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how many pattern block triangles would i need to make 4 hexagons
Answer:
4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles
Step-by-step explanation:
Pattern blocks are a set of geometric shapes commonly used in math education. The set typically includes six different shapes: triangle, rhombus, trapezoid, hexagon, square, and equilateral triangle. Each hexagon in a pattern block set is made up of six equilateral triangles.
To make 4 hexagons using pattern blocks, we would need to calculate the total number of equilateral triangles required. Since each hexagon is made up of 6 equilateral triangles, we can multiply the number of hexagons by 6 to get the total number of equilateral triangles needed.
4 hexagons * 6 equilateral triangles per hexagon = 24 equilateral triangles
So, you would need 24 pattern block triangles to make 4 hexagons using pattern blocks.
Answer:
Let's use pattern blocks to visualize the situation and say that a hexagon is 1 whole. Since 3 rhombuses make a hexagon, 1 rhombus represents and 2 rhombuses represent . We can see that 6 pairs of rhombuses make 4 hexagons, so there are 6 groups of in 4.
The selling price for peanut butter is $3. 79 and the cost is $2. 84
Answer: Profit = .95 or 95 cents
Step-by-step explanation:
What is the question here?
If it is profit then the answer is 3.79-2.84
How many planes of symmetry does a right pyramid with an isosceles triangle base have?
Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.
Hope this helps!
Write an equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞.
The equation using the parent function y = √x that has a domain of 3≤x<∞ and a range of -2≤y<∞ is y = √(x - 3) - 2.
What is equation?An equation is a mathematical statement that indicates the equality of two expressions. It typically contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields of mathematics, science, engineering, and economics. They can be written in various forms, such as standard form, slope-intercept form, point-slope form, and more.
Here,
To shift the parent function y = √x to the right by 3 units and down by 2 units, we use the transformation:
y = √(x - 3) - 2
This equation has a domain of 3 ≤ x < ∞, since we subtract 3 from x inside the square root function. The range is -2 ≤ y < ∞, since we subtract 2 from the square root function.
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a variable needs to be eliminated to solve the system of equations below.
x-7y= -45 -x+8y=51
Eliminate x by adding the two equations, yielding [tex]y = 6[/tex]. Then, substitute y into either equation to solve for x, obtaining [tex]x = -3[/tex]. The solution is [tex](-3,6)[/tex].
What is equation?An equation is a mathematical statement that uses symbols, numbers, and variables to show that two expressions are equal, typically with an equal sign between them.
A variable is a quantity or symbol that can take on different values in a mathematical expression, equation, or formula, typically represented by a letter.
To eliminate a variable in a system of equations, we want to find a way to add or subtract the two equations so that one of the variables is eliminated.
In this case, we can eliminate the variable x by adding the two equations
[tex]x- 7y = -45[/tex]
[tex](-x +8y = 51)[/tex]
[tex]y = 6[/tex]
Now that we have found the value of y, we can substitute it into either of the original equations to solve for x. Let's use the first equation
[tex]x-7y = -45\\x- 7(6) = -45\\x = -45+42\\x = -3[/tex]
Therefore the solution to the system of equations is [tex]x= -3[/tex] and[tex]y= 6[/tex]
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the solution to the system of equations is (x, y) = (-3, 6).
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
To eliminate the variable x, we can add the two equations together. This will result in the x variable being eliminated, leaving us with an equation in terms of y:
(x - 7y) + (-x + 8y) = -45 + 51
Simplifying and solving for y, we get:
y = 6
Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Using the first equation:
x - 7(6) = -45
Simplifying and solving for x, we get:
x = -3
Therefore, the solution to the system of equations is (x, y) = (-3, 6).
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Change the function f(x)=2x^2+4x+3 into vertex form.
Answer:
f(x) = 2(x + 1)² + 1
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
given
f(x) = 2x² + 4x + 3 ← factor out 2 from the first two terms
= 2(x² + 2x) + 3
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 2x
f(x) = 2(x² + 2(1)x + 1 - 1) + 3
= 2(x + 1)² - 2(1) + 3
= 2(x + 1)² - 2 + 3
= 2(x + 1)² + 1 ← in vertex form
the model shows the fraction 2/4 A student uses the model to find 5/2 and 2/3
5/3 is greater than 1 (it's 1.67), and the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.
what is the fraction model?The area model, linear model, and set model are the three major types of fraction models. Evidence demonstrates that allowing pupils to deal with all three models is critical for establishing a conceptual knowledge of fractions.
The student is utilizing the model to calculate the product of 5/2 and 2/3, or (5/2) x (2/3).
To multiply fractions, simply multiply their numerators and then their denominators. So:
(5/2) x (2/3) = (5 x 2) / (2 x 3) = 10/6 = 5/3
Because 5/3 is greater than 1 (it's 1.67), the product will be located on a number line to the right of 2/3. As a result, "The product will be located to the right because is greater than 1." is correct.
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Complete question:
The price of a can of beans is raised from 64
cents to 74
cents.
Approximately what is the percent increase in the price of the can of beans?
Answer: 13%
Step-by-step explanation:
10/74 = 0.13513513513
(ASAP) Tell whether the transformation appears to be a rigid motion. Explain.
Yes, the transformation is a rigid motion because the angle measures and the distances between the vertices of the image are the same as the corresponding angle measures and distances in the preimage.
Why is the transformation a rigid motion?Since the shape and size are the same in both the preimage and the image, and only the position has changed, this transformation is considered a rigid motion. Rigid motions, such as translations, rotations, and reflections, preserve the shape and size of the original figure.
Assuming the shape has been bent, it means that the angle measures and distances between the vertices have been altered. But this is not the case.
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4PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
9.3 ft
Step-by-step explanation: