Help on the last thx!

100 points!! Brainliest if correct!!

Elena-2011 [213]

surface area (S) of a right rectangular solid is:

S = 2*L*W + 2*L*H + 2*W*H (equation 1)

where:

L = length

W = width

H = height

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you have:

L = 7

W = a

H = 4

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formula becomes:

S = 2*7*a + 2*7*4 + 2*a*4

simplify:

S = 14*a + 56 + 8*a

combine like terms:

S = 22*a + 56

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answer is:

S = 22*a + 56 (equation 2)

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to prove, substitute any value for a in equation 2:

let a = 15

S = 22*a + 56 (equation 2)

S = 22*15 + 56

S = 330 + 56

S = 386

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since a = 15, then W = 15 because W = a

go back to equation 1 and substitute 15 for W:

S = 2*L*W + 2*L*H + 2*W*H (equation 1)

where:

L = length

W = width

H = height

-----

you have:

L = 7

W = 15

H = 4

-----

equation 1 becomes:

S = 2*7*15 + 2*7*4 + 2*15*4

perform indicated operations:

S = 210 + 56 + 120

S = 386

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surface area is the same using both equations so:

equations are good.

formula for surface area of right rectangle in terms of a is:

S = 22*a + 56

-----

8 0

3 years ago

Read 2 more answers

The volume of a right circular cone with both

Rufina [12.5K]

Question:

The volume of a right circular cone with both diameter and height equal to h is 250/7 cm³.

What is the value of h?

Answer:

A. 5

Step-by-step explanation:

Given

Solid Shape: Cone

Volume = 250/7

Diameter = Height

Required

Find the height of the cone

Provided that the diameter (D) and the height (h) are equal; This implies that

D = h ------ (1)

Also, Diameter (D) = 2 * Radius (r)

D = 2r

Substitute 2r for D in (1)

2r = h

Multiply both sides by ½

½ * 2r = ½ * h

r = ½h

Volume of a cone is calculated by;

Volume = ⅓πr²h

⅓πr²h = 250/7

Substitute ½h for r

$\frac{1}{3} * \pi * (\frac{1}{2}h)^2 * h = \frac{250}{7}$

Take π as 22/7, the expression becomes

$\frac{1}{3} * \frac{22}{7} * (\frac{1}{2}h)^2 * h = \frac{250}{7}$

Open the bracket

$\frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7}$

Multiply both sides by 7

$7 * \frac{1}{3} * \frac{22}{7} * \frac{1}{4}h^2 * h = \frac{250}{7} * 7$

$\frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250$

Multiply both sides by 3

$3 * \frac{1}{3} * 22 * \frac{1}{4}h^2 * h = 250 * 3$

$22 * \frac{1}{4}h^2 * h = 750$

Multiply both sides by 4

$4 * 22 * \frac{1}{4}h^2 * h = 750 * 4$

$22 * h^2 * h = 3000$

$22 * h^3 = 3000$

Divide both sides by 22

$h^3 = \frac{3000}{22}$

$h^3 = 136.36$

Take cube root of both sides

$h = \sqrt[3]{136.36}$

$h = 5.15$

$h = 5$ (Approximated)

6 0

3 years ago

How to solve for X in the triangle

Vikentia [17]

Answer:

22.6

Step-by-step explanation:

a^2+b^2=c^2

8^2+b^2=24^2

b^2=512

b=22.6

7 0

2 years ago

Read 2 more answers

The width of the rectangle is 5x-4. The length of the rectangle is 5

drek231 [11]

Answer:

The area of the rectangle A = 25x² - 20x

Step-by-step explanation:

Given

The width of the rectangle = w = 5x - 4

The length of a rectangle = l = 5x

To determine

The area of the rectangle = ?

Using the Formula to determine the area of the rectangle

$A = wl$

substitute w = 5x - 4 and l = 5x in the formula

$A = (5x-4) (5x)$

Apply distributive law: a(b-c) = ab - ac

$=\left(5x\right)\cdot \:5x-\left(5x\right)\cdot \:4$

$=5x\left(5x\right)-4\left(5x\right)$

as 5x(5x) = 25x² and 4(5x) = 20x, so

$=25x^2-20x$

Therefore, the area of the rectangle A = 25x² - 20x

3 0

3 years ago

Which of the following is the point and slope of the equation y + 5 = 3(x + 9)?

Tatiana [17]

Answer:

Option B, (-9, -5), 3

Step-by-step explanation:

<u>The point slope form in: y - y1 = m(x - x1)</u>

m is the slope

(x1, y1) is the point

<u>Step 1: Determine what the slope and point is their equation</u>

y + 5 = 3(x + 9)

3 is the slope

(-9, -5) is the point

Answer: Option B, (-9, -5), 3

3 0

3 years ago