The lengths of two sides of a triangle are shown.
Side 1: 3x² - 4x-1
Side 2: 4x-x² +5
The perimeter of the triangle is 5x³ - 2x² + 3x - 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work.
Part B: What is the length of the third side of the triangle? Show your work.
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.

The length of an American football field including end zones is 21600 inches.

To convert yards to inches, we multiply by 36, since there are 36 inches in one yard.

Therefore, a football field that is 120 yards long is equivalent to 120 x 36: = 4320 feet. To convert feet to inches, we multiply by 12, since there are 12 inches in one foot.

Therefore, a 120-yard football field is equivalent to 4320 x 12 = 51,840 inches. However, we must also take into account the two end zones, which are each 10 yards long, or 360 inches. Thus, the total length of an American football field including the end zones is 120 x 36 x 12 + 2 x 360 = 21,600 inches.

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use slope equation -5 - (-3)/(2-1) then solve

Gold costs less than platinum per ounce because the slope of the graph for gold is less steeper than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

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Answer:

y=3+2 to the power of x +1

Step-by-step explanation:

The variables are as follows:

x = 4

y = 4.8

The lengths of the sides of the kites are 4.5 and 6.8 units.

A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.

The non vertex angles are congruent.

Therefore,

x + 0.5 = 2x - 3.5

2x - x = 0.5 + 3.5

x = 4

y + 2 = 2y - 2.8

2y - y = 2 + 2.8

y = 4.8

Hence,

length of one pair = 4 + 0.5 = 4.5 units

length of the other pair = 4.8 + 2 = 6.8 units

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A line plot for the data is shown in the image attached below.

In Mathematics and Statistics, a line plot can be defined as a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

In this scenario and exercise, we would use an online graphing calculator to graphically represent the given data set on a line plot as shown in the image attached below.

In conclusion, we can reasonably infer and logically deduce that the mode of the data set is equal to 3.5 or 3 1/2 because it has the highest frequency of 5.

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Answer:

2) [tex](3x+2)^{2}[/tex]

3) [tex](2x+5)(2x-5)[/tex]

4) [tex](x^{2} +8)(x^{2} -8)[/tex]

Step-by-step explanation:

A method I was taught was the snowflake method whenever there were numbers in front of [tex]x^{2}[/tex] (ex [tex]4x^{2} and 9x^{2}[/tex]) picture shown below (you can search up some videos if you would like)

The snowflake method is really efficient and helps factor polynomials faster

For 3 and 4, you basically have to find the square root of the number without the [tex]x^{2}[/tex] and make sure (for example 25) one parenthesis had -5 and the other had +5. Number 4 had [tex]x^{4}[/tex], [tex]x^{2}*x^{2}[/tex] is  [tex]x^{4}[/tex] so you would include that in the equation. To double check, use foil.

The correct option are - A. x²  + (y – 3)²  = 36 and E. x²  + (y + 8)²  = 36 , for the equation of circle.

The standard form equation for just a circle, which is (x - s)² + (y - t)² = r², is used to formulate our equation if we assume a generic centre point like (s,t)and r is the radius of circle.

By simply expanding basic binomial squares in their regular form and merging like words, circles can likewise be presented in expanded form.

Now for the given data:

Put the values in the standard form of the circle:

(x - s)² + (y - t)² = r²,

(x - 0)² + (y - t)² = 6²,

x² + (y - t)² = 36

Where 't' can be any integer.

Thus, the options that satisfy the stated conditions are-

A. x²  + (y – 3)²  = 36 : here t = 3

and E. x²  + (y + 8)²  = 36 ; here t = - 8.

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Correct question:

Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis?

Select two options.

A. x²  + (y – 3)²  = 36

B. x²  + (y – 5)²  = 6

C. (x – 4)² + y² = 36

D. (x + 6)² + y² = 144

E. x²  + (y + 8)²  = 36

The transformation in words for picture 6 is a rotation of 90° counterclockwise or 90° counterclockwise rotation.

The algebraic rule for the above transformation is (x, y) → (-y, x).

The transformation in words for picture 7 is a reflection across the line x = -3.

The algebraic rule for the above transformation is [tex]Ref_{x=-3} \triangle ABC[/tex].

The transformation in words for picture 8 is a reflection across the x-axis.

The algebraic rule for the above transformation is (x, y) → (x, -y).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of quadrilateral RSTUVW, the coordinates of W of the image is as follows:

(x, y)                               →            (-y, x)

Ordered pair W  = (-1, 3) → Ordered pair R' = (-(3), -1) = (-3, -1).

In Mathematics and Geometry, a reflection over the x-axis is modeled by this transformation rule (x, y) → (x, -y). Therefore, a reflection over the x-axis would maintain the same x-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

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If the room is 12'x20' with 8' ceilings and the tile costs $4.75 per square foot,  the total cost is $1140.

To calculate the cost of replacing the tile in the kitchen, we need to first calculate the total area of the floor.

Area of the floor = Length x Width = 12 ft x 20 ft = 240 sq ft

Since we know the cost per square foot of tile, we can now multiply the total area of the floor by the cost per square foot to find the total cost:

Total cost = Area of the floor x Cost per square foot

Total cost = 240 sq ft x $4.75/sq ft

Total cost = $1140

Therefore, it will cost $1140 to replace the tile in the kitchen, assuming there are no additional costs such as labor or materials for removing the old tile.

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The truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as (-9, ∞)

Multiply both sides by -2 (and reversing the direction of the inequality because we are multiplying by a negative number) gives:

x > -2*(5/2 + 2)

x > -5 - 4

x > -9

Therefore, the truth set of the inequality is all values of x greater than -9. In interval notation, this can be written as:

(-9, ∞)

Below is the complete question:

Find the truth set of x*(-1/2) < 5/2 + 2

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There must be 46 chairs in each row and total number of chairs are 1058

To meet the given conditions, we need to find a number that has the following properties:

It should be divisible by 2, as there are an even number of chairs in each row.

It should be divisible by 23, as there are 23 rows of chairs.

It should be the same number in each row.

The smallest number that satisfies these conditions is 46, which is the least common multiple of 2 and 23.

So, we need to set up 46 chairs in each row.

The total number of chairs required will be:

Total number of chairs = 23 rows x 46 chairs per row = 1058 chairs

Hence, the total number of chairs are 1058

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The percent of the whole group are in the Navy is 27%.

Percent is a term used to express a fraction or a ratio out of 100. It is represented by the symbol "%". For example, if there are 20 red balls out of a total of 100 balls, we can say that the percentage of red balls is 20%.

To calculate the percentage, we can use the following formula:

Percentage = (Part / Whole) x 100

where "Part" is the value we want to express as a percentage, and "Whole" is the total value.

The percent of the whole group are in the Navy is:

= 135/500 × 100

= 27%.

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Answer:

27%

Step-by-step explanation:

135 of the 500 total members are in the Navy. Meaning that 135 out of 500 is 27%

From the calculation, g increases on the interval [-3, 6) and for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

To determine where g is increasing, we need to find where its derivative, g'(x), is positive. We can find g'(x) by differentiating g(x) with respect to x:

g'(x) = f(x)

Since f(x) is a piecewise-defined function, we need to consider each interval separately.

Therefore, g is increasing on the interval [-3, 6).

To justify this, note that g'(x) = 0 at x = 0 and x = 6, where g has local maxima. This means that g is increasing on the intervals (-3, 0) and (0, 6) and decreasing on (6, 9]. Since g is continuous, it cannot have any jumps, so it must be increasing or decreasing on each of these intervals. Since g(-3) = 0 and g(6) = 9, we know that g is increasing on the interval [-3, 6).

We can evaluate g(x) on the interval [0, 6] by integrating f(x) with respect to t from -2 to x:

g(x) = ∫_{-2}^{x} f(t) dt

On the interval [-3, 0), f(t) = 3, so we have:

g(x) = ∫_{-2}^{0} 3 dt + ∫_{0}^{x} (-t + 3) dt

Simplifying the integrals, we get:

g(x) = 6 - 1/2(x-2)^2, for 0 ≤ x ≤ 6

(Note that we can drop the "+C" since it's being evaluated at the limits of integration.)

Therefore, for 0 ≤ x ≤ 6, g(x) = 6 - 1/2(x-2)^2.

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Answer:

A

If u plug it into desmos u get a straight line

Answer:

the required answer is √5-√6

Answer: Jenny's score is no less than 5 points greater than 4/5 of Terrance's score.

Step-by-step explanation:

The inequality that represents the situation described is:

Jenny's score (denoted as "J") is no less than 5 points greater than 4/5 of Terrance's score (denoted as "T"):

J ≥ (4/5)T + 5

In this inequality, we are saying that Jenny's score "J" must be greater than or equal to 4/5 of Terrance's score "T", plus an additional 5 points. This reflects the condition that Jenny's score should be at least 5 points higher than 4/5 of Terrance's score.

For example, if Terrance's score "T" is 80, then 4/5 of Terrance's score is (4/5) * 80 = 64. Adding 5 points to this gives us 69. Therefore, Jenny's score "J" must be greater than or equal to 69 in this case, since it should be no less than 5 points greater than 4/5 of Terrance's score.

Answer:

Step-by-step explanation: 462 Divided by 24 = 19.25$

Proof: 19.25 x 24 = 462

Answer: 19.25$

Step-by-step explanation:

sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.

because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).

the confidence interval limits are

mean ± Z×sd/sqrt(n)

mean = mean value of the sample.

sd = standard deviation (either of - preferred - the entire population or of the sample)

n = number of data points (here 14).

Z = Z value of the standard normal distributing table for 99% (2.576).

here a little table for different confidence intervals :

Confidence Interval Z

80% 1.282

85% 1.440

90% 1.645

95% 1.960

99% 2.576

99.5% 2.807

99.9% 3.291

mean value = sum of all data points divided by the number of data points :

mean = 66.74/14 = 4.767142857...

sd = sqrt(sum((data point difference to mean)²)/n)

let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).

sd = 0.069941667...

the confidence interval limits are then

4.767142857... ± 2.576×0.069941667.../sqrt(14) =

= 4.767142857... ± 0.048152387...

upper limit = 4.815295244 ... ≈ 4.82

lower limit = 4.71899047 ... ≈ 4.72

that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.

in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.

The direct distance between Thom's house and his school, as the crow flies, is  7.21 miles.

To find the direct distance between Thom's house and his school, we can use the Law of Cosines.

The Law of Cosines is a formula used to find the length of one side of a triangle when the lengths of the other two sides and the angle between them are known. In this case, we have a triangle with sides of length 6 miles, 8 miles, and the angle between them is 60 degrees.

The Law of Cosines formula is:

c² = a² + b² - 2ab * cos(C)

where:

a and b are the lengths of the known sides of the triangle

C is the angle between those two sides

c is the length of the unknown side (the distance we want to find)

In this case:

a = 6 miles

b = 8 miles

C = 60 degrees

First, convert the angle from degrees to radians:

C (radians) = (60 degrees * π) / 180 = 1.047 radians

Now, apply the Law of Cosines:

c² = 6² + 8² - 2 x 6 x 8 x cos(1.047)

c² = 36 + 64 - 96 x cos(1.047)

c² ≈ 36 + 64 - 96 x 0.5

c² ≈ 36 + 64 - 48

c² = 52

Finally, find the square root to get the distance:

c = √52 = 7.21 miles

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1. Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.

2. Por lo tanto, el resultado de la expresión es -22.

3. Por lo tanto, el resultado de la expresión es 24.

4. Por lo tanto, el valor de x es 3.

5. Por lo tanto, el resultado de la expresión es 45.

1. Para sumar las dos expresiones, simplemente sumamos los términos semejantes:

(4x² + 8x +12) + (5x² − 3x + 6) = 9x² + 5x + 18

Por lo tanto, la suma de las dos expresiones es 9x² + 5x + 18.

2. Evaluando la expresión numérica:

5 - 21 + (-3) (2) = 5 - 21 + (-6)

Luego, sumamos los términos:

= -16 - 6 = -22

Por lo tanto, el resultado de la expresión es -22.

3. Evaluando la expresión numérica:

(-3) (-2) (-1) (4) = 24

Por lo tanto, el resultado de la expresión es 24.

4. Para encontrar el valor de x, debemos despejarlo de la ecuación:

18 + 3x = 27

Restando 18 de ambos lados, obtenemos:

3x = 9

Dividiendo ambos lados por 3, obtenemos:

x = 3

Por lo tanto, el valor de x es 3.

5. Evaluando la expresión numérica:

3² + 4 (3)² = 3² + 4 (9)

Primero elevamos al cuadrado 3, luego multiplicamos 4 por 9 y sumamos ambos términos:

= 9 + 36

Por lo tanto, el resultado de la expresión es 45.

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Answer:

D. Line O

Step-by-step explanation:

We can simply tell which one it is by looking at the picture. A tangent line is a line that intersects at one point only. Line L doesn't even touch the circle. Line M and N touch the circle in more than one place. If we look at O, we can see that it is "scraping" the edge of the circle, which is what pretty much every tangent line looks like.

Therefore, the answer is D.

Answer:

-31

Step-by-step explanation:

Answer:

x = 45 degrees

Step-by-step explanation:

All angles in a triangle will add up to 180 degrees.  So far we have 57 degree of 180.  We also see a supplementary angle, with one side being 102 degrees, so the other is 78 degrees, because it must add up to 180.  We see that the arrows in the bases show that the corners are even, so now we know two corners: one with 57 degrees and the other with 78.  

Now, follow this equation to find x:

57 + 78 + x = 180

135 + x = 180

-135        -135

x = 45

The volume of the fish tank is 408in³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

The volume of regular object is given as;

V = base area × height

base area = 13 × 6

= 78in²

The area of the cut out section = 1/2(a+b) h

= 1/2 × (3+6) × 6

= 9× 3 = 27in²

The actual area of the base shown = 78-27

= 51 in²

therefore the volume of the tank will be

V = 51 × 8

= 408in³

therefore the volume of the tank is 408in³

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The new mixture contains 34% peanuts.

Using a weighted average approach.

Let x be the percentage of peanuts in the new mixture. Then we can set up the following equation:

(0.16)(4) + (0.40)(12) = x(4 + 12)

simplifying the equation, we get:

0.64 + 4.8 = 16x

5.44 = 16x

x = 0.34 or 34%

Therefore, the new mixture contains 34% peanuts.

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Answer:

Yes it is a parallelogram because opposite sides of this quadrilateral are equal.