Each cube represents 1 cubic inch. What is the volume if the prism?​

Answer:

Part A) [tex]A=1.25W^2[/tex]

Part B) Length: 17.5 feet and Width: 14 feet

Step-by-step explanation:

Part A) Create an equation to represent the area of the basketball section A, in terms of the width W.

Let

L ----> the length of the  rectangular basketball section

W ---> the width of the  rectangular basketball section

we know that

The area of the rectangular basketball section is equal to

[tex]A=LW[/tex] ----> equation A

The length of the section will be 1.25 times the width of the section

so

[tex]L=1.25W[/tex] ----> equation B

substitute equation B in equation A

[tex]A=(1.25W)W\\A=1.25W^2[/tex]

Part B) Jackson decides to make the area of the basketball section 245 square feet. What are the dimensions, in feet, of the basketball section?

we have

[tex]A=1.25W^2\\A=245\ ft^2[/tex]

so

[tex]245=1.25W^2[/tex]

solve for W

[tex]W^2=245/1.25\\W^2=196\\W=14\ ft[/tex]

Find the value of L

substitute the value of W in the equation B

[tex]L=1.25(14)=17.5\ ft[/tex]

therefore

The dimensions are :

Length: 17.5 feet

Width: 14 feet

The area equation for the basketball section is A = 1.25w². For an area of 245 square feet, the width, w, is approximately 14 feet, and the length, l, is approximately 17.5 feet.

Part A: Equation of the Area

To create an equation that represents the area, A, of the basketball section in terms of the width, w, we start with the fact that the length is 1.25 times the width. So, if l represents the length, then l = 1.25w. The area of a rectangle is found by multiplying the length by the width, hence the area A = l × w. Substituting l = 1.25w gives us the equation A = (1.25w) × w = 1.25w².

Part B: Dimensions of the Basketball Section

Given the area of the basketball section is 245 square feet, we can use the equation found in Part A to determine the width and subsequently the length. The equation A = 1.25w² becomes 245 = 1.25w². Solving for w, we take the square root of both sides after dividing by 1.25, which gives w = √(245/1.25) ≈ 14 feet. To find the length, l, we multiply the width by 1.25, resulting in l = 1.25 × 14 ≈ 17.5 feet. Therefore, the dimensions are approximately 14 feet in width and 17.5 feet in length.

The first number is 15 and the second number is 8.

Step-by-step explanation:

Let us assume,

Given :

Sum of four times a first number and a second number is 68.

⇒ 4x + y = 68

⇒ y = 68-4x

If the first number is decreased by twice the second number the result is -1.

⇒ x - 2y = -1

Substitute y = 68-4x in the above equation.

⇒ x - 2(68-4x) = -1

⇒ x-136+8x = -1

⇒ 9x - 136 = -1

⇒ 9x = -1+136

⇒ x = 135/9

⇒ x = 15

The first number is 15.

The second number is y = 68-4x.

⇒ y = 68 - 4(15)

⇒ y = 68-60

⇒ y = 8

The second number is 8.

Answer:

see explanation

Step-by-step explanation:

(1)

To obtain f(2) and f(3) substitute x = 2, x = 3 into f(x)

f(2) = 3([tex]2^{4}[/tex] ) - 12(2³) - 12(2²) + 30(2)

      = 48 - 96 - 48 + 60 = - 36

f(3) = 3([tex]3^{4}[/tex] ) - 12(3³) - 12(3²) + 30(3)

      = 243 - 324 - 108 + 90 = - 99

(2)

Given a polynomial with roots x  = a, x = b, then

(x - a), (x - b) are the factors

and the polynomial is the product of the factors

Here the roots are x = - 2, x = - 1, x = 3 and x = 4, thus the factors are

(x + 2), (x + 1), (x - 3) and (x - 4)

The polynomial is the product of the factors, thus

f(x) = (x + 2)(x + 1)(x - 3)(x - 4) ← expand in pairs using FOIL

     = (x² + 3x + 2)(x² - 7x + 12) ← distribute

     = [tex]x^{4}[/tex] - 7x³ + 12x² + 3x³ - 21x² + 36x + 2x² - 14x + 24 ← collect like terms

     = [tex]x^{4}[/tex] - 4x³ - 7x² + 22x + 24

Answer:

x=-5

Step-by-step explanation:

slope=m=11/4

(x, - 7) x1 =x, y1 =-7

(-1,4) x2=-1, y2 =4

m=(y2-y1) /(x2-x1)

m=(4-(-7))/(-1-x)

11/4=(4+7)/(-1-x)

11/4=11/(-1-x)

then 4=-1-x,

-x=4+1

-x=5

x=-5

Answer:

(52 - 4) * (13 - 7)

Step-by-step explanation:

Step 1:  Convert words into an expression

52 minus 4 times the difference of 13 and 7.

(52 - 4) * (13 - 7)

Answer:  (52 - 4) * (13 - 7)

If needed simplify

(52 - 4) * (13 - 7)

48 * 6

288

A prism would beat a sphere in a competition because a prism has more sides and angles to outmaneuver the sphere, which is a single-sided shape with no angles.

To understand the riddle, one must consider the properties of both a prism and a sphere. A prism is a polyhedron with two congruent and parallel faces (called bases), and its sides are parallelograms.

The number of sides a prism has depends on the shape of its base. For example, a triangular prism has five faces (two triangular bases and three rectangular sides), while a hexagonal prism has eight faces (two hexagonal bases and six rectangular sides).

On the other hand, a sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a ball (viz., the geometric object consisting of all points in three-dimensional space at a distance r from a central point). Unlike a prism, a sphere has no edges or vertices, and it has only one surface with no sides.

In a competition where maneuverability and the ability to approach from different angles are advantageous, a prism would have more options to outmaneuver a sphere. A prism can present multiple faces to the sphere, potentially confusing or disorienting it, while the sphere, being uniform in all directions, has no such advantage. The prism's angles and edges could also be used strategically to deflect or redirect the sphere, giving the prism a competitive edge.

Therefore, the riddle plays on the geometric properties of the two shapes to suggest that in a hypothetical competition, the prism's multiple faces and angles would allow it to outperform the sphere, which has a single continuous surface and no angles to leverage.

Answer:

Hello there!

So, your question is

"something + something = 48"

and

"something * something = -40"

Since you didn't really give that much specific details, and you could correct me on this later, I'd say for the first one it's

47 + 1 = 48

As for the second one, it could be

-5 * 8 = - 40

OR

5 * -8 = -40

both ways are correct.

Step-by-step explanation:

Hope this helps! If you have more instructions on this question, please let me know! Instructions are very important for MATH, cause even I mess up if the instructions are not clear. :)

- immaback2x

Answer:

Hi

Step-by-step explanation:

Answer:

960 in  (or 80 ft)

Step-by-step explanation:

First, we should convert all of the feet measurements to inches so we have equal units of measurements:

50 ft = 600 in

5 ft 4 in = 64 in

40 in = 40 in

Now we can solve this problem with a simple proportion:

h / 600   =   64 / 40

600 * 64 = 40h

38400 = 40h

960 in = h

***also h = 80 ft

By setting up a proportion of corresponding sides from similar triangles, we find that the flagpole's height is roughly 80 feet.

This is a problem of similar triangles. The flagpole and its shadow form one triangle, and the woman and her shadow form a smaller, similar triangle. Since the triangles are similar, the ratio of corresponding sides should be equal. In this case, we have:

height of the flagpole / shadow of the flagpole = height of the woman / shadow of the woman

We can plug the provided values into this equation:

height of the flagpole / 50 feet = 5.33 feet / 3.33 feet

To solve for the height of the flagpole, we cross-multiply and divide, giving us:

height of the flagpole = (5.33 feet / 3.33 feet) * 50 feet

Following that logic, the height of the flagpole is approximately 80 feet tall.

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The rational expression is given by:

[tex]E=\frac{2x^2-72}{5x^2-245} \\ \\ Factor \ out: \\ \\ E=\frac{2(x^2-36)}{5(x^2-49)} \\ \\ E=\frac{2(x-6)(x+36)}{5(x-7)(x+7)} : \ \ \ \ a^2-b^2=(a-b)(a+b)[/tex]

The denominator can't be zero, therefore:

[tex](x-7)(x+7)\neq 0 \\ \\ \\ Thus: \\ \\ \boxed{x\neq 7 \ and x \neq -7}[/tex]

Finally, the values of x that make the rational expression undefined are

x = 7 and x = -7

Answer:

x = 7 and x = -7

Step-by-step explanation:

Got it right on edge 2021

I got a 100.

Answer:

She will wash 24% windows in one hour

Step-by-step explanation:

If Ava washes 12% windows in half hour

Since 2 half hours makes one hour

Therefore, 2 × 12% will be washed in one hour

That is, Ava will wash 24% windows in one hour

Answer:

A. True

B. False

C. False

D. False

Step-by-step explanation:

Hence she used it correctly by making parts of it.

Answer: Its A my boy

Step-by-step explanation:

Answer:

$38.40 new price.   Usual coupons give 20% only off the sale price if this is the case for the backpack you would need to show both answers one of 50% if both coupons allowed. Second workings would be your answer 30% of $60 = $18 and 20% further =$3.60 $18+$3.60= $21.60 full 20% discount on store 30% discount.

Therefore you can see $60-21.60 = $38.40 new price.

This is $21.60 discount and appears to be 36.8%

Step-by-step explanation:

Answer:

They used 2.3 liters of red paint

Step-by-step explanation:

Henri and Talia are mixing paint for an art project.

They mixed amount of red paint = p liters

They mixed amount of blue paint = 0.6 liters

They mixed amount of white paint = p-0.4 liters

Total amount of paint = p +0.6 +p - 0.4 = 2p+0.2

They then divided the mixture  evenly into 2 jars.

Amount of paint in 1 jar = [tex]\frac{2p+0.2}{2}[/tex]

We are given that Each jar contains 2.4 liters of paint

So, [tex]\frac{2p+0.2}{2}=2.4[/tex]

[tex]2p+0.2=2.4 \times 2[/tex]

[tex]2p+0.2=4.8[/tex]

[tex]2p=4.8-0.2[/tex]

2p=4.6

[tex]p=\frac{4.6}{2}[/tex]

p=2.3

Hence They used 2.3 liters of red paint

The correct statement is the red paint they use is 2.3 liters.

It is a system of an equation in which the highest power of the variable is always 1. A one-dimension figure that has no width. It is a combination of infinite points side by side.

Given

They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint.

They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint.

They mixed p liters of red paint, 0.6 liters of blue paint, and a p-0.4 liter of white paint. According to this, the total paint will be

The total paint in liters = p + 0.6 + p - 0.4

The total paint in liters = 2p + 0.2

They then divided the mixture evenly into 2 jars. If each jar contains 2.4 liters of paint. According to this,

[tex]\rm \dfrac{2p+0.2}{2} = 2.4[/tex]

On solving the equation, then p will be

[tex]\begin{aligned} \rm \dfrac{2p+0.2}{2} &= 2.4\\\rm 2p + 0.2 &= 4.8\\\rm 2p &= 4.6\\\rm p &= 2.3\end{aligned}[/tex]

Thus, 2.3 liters of red paint did they use.

More about the linear system link is given below.

Answer:

D. The mean for the 8th grade players is 3 times the mean for the 6th grade players. & E. The data set distribution for the 8th grade players is symmetric.

Answer:

He bought 12 oranges.

Step-by-step explanation:

Key words: "ALL the apples" "EACH orange."

7.75-2.35= 5.4

5.4/0.45= 12

Answer:

He bought 12 oranges.

Step-by-step explanation:

Keywords: "ALL the apples" and "EACH orange."

7.75-2.35= 5.4

5.4/0.45= 12

Step-by-step explanation:

Answer:

Your graph would look like lines going up and up and up

Step-by-step explanation:

Why you ask? Well, because the graph shown here is going by the factors of 6. And the factors of 6 are pretty high, which means it would be going up like a twisted line going right ot left depending which way you look at it. It would be going up and up because like 18 times 6 is 108 and 20 times 6 is 120.

To obtain j(x) = -3x²+5, we need to combine a linear function and a quadratic function. Three possible options are provided in the response.

The function j(x) = -3x²+5 is a quadratic function. To obtain this function by combining two other functions, we can use a linear function and a quadratic function added together. This means that one of the functions will have a degree of 1 and the other will have a degree of 2. Here are three options that could result in j(x):

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Answer:

  x = y = 250 mL

Step-by-step explanation:

The desired concentration of acid (20%) is exactly halfway between the concentrations of the available supplies (10%, 30%). So, the mix will be equal parts of each of those. x and y are both half the total quantity required:

  x = y = (500 mL)/2 = 250 mL

_____

If you need an equation to solve this, you can let x = 500 -y and write the equation for the acid volume in the final mix:

  10%(500 -y) +30%(y) = 20%(500)

  50 -0.1y +0.3y = 100 . . . . . eliminate parentheses

  0.2y = 50 . . . . . . . . . . . . . . subtract 50, collect terms

  y = 250 . . . . . . . . . . . . . . . multiply by 5 (equivalently, divide by 0.2)

  x = 500 -250 = 250

Option B: [tex]TU $\cong$ TS PU $\cong$ TU[/tex]

Option C: The length of line segment PR is 13 units.

Explanation:

Given that the circle is inscribed in triangle PRT. Points Q, S, and U of the circle are on the sides of the triangle. Point Q is on side P R, point S is on side R T, and point U is on side P T.

The length of RS is 5, the length of PU is 8 and the length of UT is 6.

Option A: The perimeter of the triangle is 19 units.

The perimeter of the triangle is given by

Perimeter of ΔPRT = PU + UT + TS + SR + RQ + QP

Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".

Thus, we have,

RS = RQ = 5

PU = PQ = 8 and

UT = TS = 6

Substituting the values in the perimeter of ΔPRT, we get,

Perimeter of ΔPRT = 8 + 6 + 6 + 5 + 5 + 8 =38 units

Thus, the perimeter of the triangle is 38 units.

Hence, Option A is not the correct answer.

Option B : [tex]TU $\cong$ TS PU $\cong$ TU[/tex]

Since, P, T and R are tangents to the circle and we know that "Tangents to a circle drawn to a point outside the circle are equal in length".

Then [tex]TU $\cong$ TS PU $\cong$ TU[/tex]

Hence, Option B is the correct answer.

Option C: The length of line segment PR is 13 units.

The length of PR is given by

PR = PQ + QR

Substituting the values RQ = 5 and PQ = 8, we get,

PR = 5 + 8 = 13 units

Thus, the length of line segment PR is 13 units.

Hence, Option C is the correct answer.

Option D: The length of line segment TR is 10 units.

The length of TR is given by

TR = TS + SR

Substituting the values TS = 6 and SR = 5, we get,

TR = 6 + 5 = 11 units

Thus, the length of line segment TR is 11 units

Hence, Option D is not the correct answer.

Answer: b and e

Step-by-step explanation:

Answer:

475 cm^2

Step-by-step explanation:

Base: 6 × 17 = 102

Left-most face: 6 × 11 = 66

Top face: 6 × 20 = 120

Front/Back faces: 11 × 17 = 187

Add: 102 + 66 + 120 + 187 = 475

To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine.

To find the measure of angle BAC in the given right triangle ABC, we can use the trigonometric function sine. The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we know that the length of the side opposite angle BAC is 6.9 centimeters and the length of the hypotenuse is 12 centimeters. Therefore, we can use the equation sin(BAC) = opposite/hypotenuse to find the measure of angle BAC.

sin(BAC) = 6.9/12

BAC ≈ sin-1(6.9/12)

Using a calculator, we can find that BAC ≈ 33.24°.

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Answer: it is important to keep both side of the equation balance while solving because, an equality sign is used which means, the right hand side is equal to the left hand side, and if the equation isn't balance we won't be able to get the correct answer for the missing variable.

We use greater than (>), less than (<) and greater than and equal to=> and less than and equal to <=

Step-by-step explanation:

Answer:

Step-by-step explanation:

8t - 32u = 8*t - 8*4*u

            = 8*(t - 4u) = 8(t -4u)

Answer:

y = -7x + 33

Step-by-step explanation:

Use the Point Slope Form:  (y - y1) = m(x - x1)

Step 1:  Find the Slope

Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

Slope = [tex]\frac{5 - (-2)}{4 - 5}[/tex]

Slope = [tex]\frac{5 + 2}{-1}[/tex]

Slope = [tex]\frac{7}{-1}[/tex]

Slope = -7

Step 2:  Plug into the point slope form

(y - 5) = -7(x - 4)

y - 5 + 5 = -7x + 28 + 5

y = -7x + 33

Answer:  y = -7x + 33

Answer:

56h+18

Distribute the 7 inside the paranthesis

Answer:

9.6 lb/acre

Step-by-step explanation:

This is a unit rate problem. You want to know the number of pounds used for one acre.

You divide 96 pounds by 10 acres to find the number of pounds per 1 acre.

(96 lb)/(10 acres) = 9.6 lb/acre

Answer: 9.6 lb/acre

To find how many pounds of seed are needed per acre, divide the total amount of seed used, which is 96 pounds, by the total area, 10 acres. The answer is 9.6 pounds per acre.

This problem is a simple division problem in Mathematics. We start by taking the total amount of seed that was used, which is 96 pounds. Then, we divide this by the total area, which in this case is 10 acres.

When we perform the calculation: 96 pounds ÷ 10 acres, the solution we get is 9.6 pounds per acre.

So, it requires 9.6 pounds of seed to plant one acre of the field. Remember, this is an average estimation. Actual seed requirement may vary depending on the type of seed and other factors such as soil and weather conditions.

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Answer:

Part A) [tex]W(t)=18.2(1.012)^t[/tex]

Part B) [tex]L(t)=28.5(1.008)^t[/tex]

Part C) [tex]A(t)=518.7(1.020096)^t[/tex]

Step-by-step explanation:

we know that

The equation of a exponential growth function is equal to

[tex]y=a(1+r)^x[/tex]

where

a is the initial value

r is the rate of change

Part A) Create functions to model :

The width of the island over time, w(t)

we have

[tex]W(t)=a(1+r)^t\\[/tex]

where

[tex]a=18.2\ km\\r=1.2\%=1.2/100=0.012[/tex]

substitute

[tex]W(t)=18.2(1+0.012)^t[/tex]

[tex]W(t)=18.2(1.012)^t[/tex]

Part B) Create functions to model :

The length of the island over time, l(t)

we have

[tex]L(t)=a(1+r)^t\\[/tex]

where

[tex]a=28.5\ km\\r=0.8\%=0.8/100=0.008[/tex]

substitute

[tex]L(t)=28.5(1+0.008)^t[/tex]

[tex]L(t)=28.5(1.008)^t[/tex]

Part C) Create functions to model :

The area of the island over time, a(t)

we have

[tex]W(t)=18.2(1.012)^t[/tex]

[tex]L(t)=28.5(1.008)^t[/tex]

Remember that the area of a rectangle is given by

[tex]A=LW[/tex]

substitute the given values

[tex]A(t)=(28.5(1.008)^t)(18.2(1.012)^t)[/tex]

[tex]A(t)=(28.5*18.2)(1.008*1.012)^t)[/tex]

[tex]A(t)=518.7(1.020096)^t[/tex]

Answer:

Here's the answer ;)

Answer:

it took Cyclone 6 hours in handing the bottles

Step-by-step explanation:

If cyclone had 10 bottles left after handing 40 bottles per hour = 250 - 10 = 240bottles

which means cyclone handed 240 bottles.

Therefore, if he handed 40bottle each hour and 240 bottles were handed all through. So the amount of hours cyclone used in handing the bottles will be 240 / 40 = 6 hours

Answer:

[tex]12.5 \ ft^2[/tex]

Step-by-step explanation:

Given that height is a quarter the sum of bases and that the height is 2.5ft.

The sum of bases is calculated as:

[tex]h=\frac{1}{4}\sum{b_i}=2.5\\\\\sum{b_i}=2.5\times 4\\\\\sum{b_i}=b_1+b_2=10\ ft[/tex]

#Having that (b1+b2=10 ft), we can now calculate the area using the given formula using the given figures:

[tex]A=\frac{1}{2}\times 2.5\times (b_1+b_2), b_1+b_2=10\\\\=\frac{1}{2}\times 2.5\times10\\\\=12.5[/tex]

Hence, the area of the trapezoid is 12.5 sq ft

*Using the h=2.5ft and the [tex]A=\frac{1}{2}h(b_1+b_2)[/tex]

Answer:The correct answer among the choices given is option 2. 

Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left. 

5x^2 + 27x + 13x = 14

5x^2 + 40x = 14

2. Make sure that the coefficient of the x^2 term is 1.

5(x^2 + 8x) = 14

3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.

5(x^2 + 8x + 16) = 14 + 80

5(x+4)^2=94

Step-by-step explanation:

The correct step is 5x2 + 40x = 14.

Completing the square is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)2 + k.

The most common application of completing the square is in solving a quadratic equation. This can be done by rearranging the expression obtained after completing the square: a(x + m)^2 + n, such that the left side is a perfect square trinomial. Completing the square method is useful in:

Given:

5x^2 + 27x = 14 - 13x

5x^2 + 27x + 13x = 14

5x^2 + 40x = 14

5(x^2 + 8x) = 14

Now,

Adding a term to both sides that will complete the square in the left side.

by dividing the coefficient of the x term by 2 and squaring it.

5(x^2 + 8x + 16) = 14 + 80

5(x+4)^2=94

Learn more about completing square method here:

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