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3 years ago

One of the skylights on the roof of Bianca’s building is in the shape of the solid below.

Mathematics

1 answer:

luda_lava [24]3 years ago

8 0

Answer:

588 sq. in.

Step-by-step explanation:

The total volume of air inside the skylight is in the shape of a pyramid, not the rectangular prism at the bottom.

So, if we look at the pyramid, it has a square base with dimensions 14 x 14. Its height is 11 - 2 = 9.

Formula for volume of a pyramid is:

V = 1/3 * Area of Base * height

Area of Base (since it is a square) = 14 * 14 = 196

Height is 9

plugging into the formula, we get:

$V=\frac{1}{3}*BaseArea*height\\=\frac{1}{3}*196*9\\=588$

Hence, volume is 588 sq. in.

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Solve for xxx in each of the figures below and mark the correct value.

Brums [2.3K]

Answer:

Picture 1:

12x+1=109

12x=108

x=9

Picture 2:

2x-3=57

2x=60

x=30

Let me know if this helps!

7 0

2 years ago

How would you solve this?

tangare [24]

Answer:

The area of the black square is equal to the sum of the areas of the gray squares.

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3 years ago

Read 2 more answers

If g(x) = 5x2^2 - 10x + 9 and h(x) = -3x3^3+ 5x - 6, find g(x) - h(x)?

AnnZ [28]

Answer:

B) $g(x) - h(x) = 3x^3 - 5x^2 - 15x + 15$

Step-by-step explanation:

Here, the given functions are:

$g(x) = 5x^2- 10x + 9 \\h(x) = -3x^3+ 5x - 6$

Now, g(x) - h(x) is :

$(5x^2- 10x + 9) - ( -3x^3+ 5x - 6)\\= 5x^2- 10x + 9 + 3x^3 - 5x + 6\\= 3x ^3 + 5x ^2+ (-10 x - 5 x) + (9 + 6)\\= 3x^3 - 5x^2 - 15x + 15$

⇒ $(5x^2- 10x + 9) - ( -3x^3+ 5x - 6) = 3x^3 - 5x^2 - 15x + 15$

B) Hence, $g(x) - h(x) = 3x^3 - 5x^2 - 15x + 15$

3 0

2 years ago

Window design. A triangular window on Ross camp's new scary boat has two sides that measure 87 centimeters 64 centimeter, respec

krek1111 [17]

Since the perimeter must not exceed 291.
Let the third side be x.

x + 87 + 64 < 291
x + 151 < 291.
x < 291 -151.
x < 140. (First)

But for a triangle there is what is called the Triangle Inequality Theorem. That given the two sides of a tringle, the third side of the triangle must greater than the positive difference between the two sides and less than the sum of the two sides.

So for this case. 87 and 64.

x > ( 87 - 64). x > 23.
x < (87 + 64) x < 151. Combine both inequalities.

23 < x < 151 (second).

Combining First and second. Both must be satisfied.
So we have a more accurate answer as:

23 < x < 140. x is greater than 23 and x is less than 140.

x could be 24, 25, 26, 27, ......, 139. cm.

I hope this helps.

3 0

3 years ago

Read 2 more answers

Find the inverse of each function. Is the inverse a function? f(x)=x⁷

Luda [366]

The inverse of the function x^7 is x^-7 and it is also a function.

An inverse function or an anti function is defined as a function, which can reverse into another function.

A standard method to find inverse of a function is to set y=f(x)

let y= f(x)=x^7

thus

$\sqrt[7]{y}$ =x