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Lostsunrise [7]
3 years ago
13

The lengths of the sides of the base of a right square pyramid are 3 feet, and its slant height is 8 feet. If the sides of the b

ase are increased to 9 feet, and the slant height is increased to 24 feet, by what factor is the surface area multiplied? A. 27 B. 9 C. 6 D. 3
Mathematics
1 answer:
8_murik_8 [283]3 years ago
5 0

Answer:

B. 9

Step-by-step explanation:

The base of a right square pyramid is a square, and we know that the lengths of the square are 3. We can calculate the original area of the base as: 3 * 3 = 9 ft squared.

The slant height is the height of the triangular sides of the pyramid. We know that it's 8 feet, and that the base of the triangle shares a side with the square, so b = 3. Knowing that h = 8 and b = 3, we can apply the triangle area formula: (b * h) / 2 = (8 * 3) / 2 = 24/2 = 12 ft squared. However, there are 4 triangles, so we multiply 12 by 4: 12 * 4 = 48 ft squared.

We add 48 to 9 to get the total original surface area: 48 + 9 = 57 ft squared.

Now, however, the sides of the base of the square are increased to 9 ft, so our new area is 9 * 9 = 81 ft squared.

The slant height becomes 24 ft, so our new triangle area is: (24 * 9)/2 = 216/2 = 108 ft squared. We multiply that by 4: 108 * 4 = 432 ft squared.

The new surface area is thus 81 + 432 = 513 ft squared.

To find the factor the original surface area is multiplied by, we divide 513 by 57: 513 / 57 = 9.

Thus, the answer is B, 9.

Hope this helps!

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Answer:

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Meaning: If the company sells -5 shirts, they would make a profit of -150 dollars. This interpretation of loss in the context of the problem

f(7) = -30

Meaning: If the company sells 7 shirts, they would make a profit of -30 dollars. This interpretation of loss in the context of the problem

f(10.5) = 5

Meaning: If the company sells 10.5 shirts, they would make a profit of 5 dollars. This interpretation of profit in the context of the problem

Step-by-step explanation:

Given

f(x) = 10x - 100

Required

Fill in the gap

f(-5) = 10 * -5 -100

f(-5) = -50 -100

f(-5) = -150

f(7) = 10 * 7 - 100

f(7) = 70 - 100

f(7) = -30

f(10.5) = 10 * 10.5 - 100

f(10.5) = 105 - 100

f(10.5) = 5

5 0
3 years ago
Write the slope intercept form of the equation of the line through the given point with the given slope through (-2,5),slope-3/2
hjlf
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6 0
3 years ago
Christy bought a 9- foot piece of lumber trim bookshelf. Altogether, she needs 100 inches of lumber. Did Christy buy enough lumb
a_sh-v [17]

Answer:

Yes.

Step-by-step explanation:

because 9 feet converted to inches equals 108 inches, we know this because we can convert feet to inches via multiplication. To do this, simply multiply the given number (9) by 12 to get your answer.

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irga5000 [103]

Answer:

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Step-by-step explanation:

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Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible. step 1 if a rectangle has dimensions
Veronika [31]


Please use the solution below:
Let P = perimeter, A = area
As provided above, a = xy and 
We know that the formula to solve for the perimeter of a rectangle is P = 2x + 2y. Using the given 112m, we can solve the perimeter using the formula:
112 = 2x + 2y
56 = x + y

x = 56-y or y = 56-x
Let's solve the perimeter in terms of y using the formula below:
A = (56-y)(y)
Find the derivative of A = 56-y^2 to get the value of y.
dA/dy = 56-2y = 0
y = 56/2
y = 28
To find X, substitute the value of y in the equation x = 56 - y. 
x = 56 - 28
Therefore, x = 28.
We can conclude that the figure is not a rectangle but a square.
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3 years ago
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