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4 years ago

Can someone help me plz

Mathematics

1 answer:

viva [34]4 years ago

4 0

The side length of the square base is 18 inches and the height of the pyramid is 9 inches.

Step-by-step explanation:

Step 1:

The volume of a square pyramid is calculated by multiplying the square of the base edge with the height of the pyramid and $\frac{1}{3}$ .

The volume of a square pyramid, $V = a^{2} \frac{h}{3}.$

Step 2:

From the given diagram, the base edge is the length of the four base edges which is x inches in this pyramid. a = x inches.

The height of the pyramid is from the base to the top, h = $\frac{x}{2}$ inches .

The volume of a square pyramid, $V = 972.$

Substituting the known values, we get

$972 = (x)^{2} (\frac{x}{2}) (\frac{1}{3} ) = \frac{x^{3} }{6} .$

$x^{3} = 6(972) = 5,832. x = \sqrt[3]{5,832} = 18.$

So x is 18 inches long.

The side length $= x = 18$ inches.

The height of the pyramid $= \frac{x}{2} = \frac{18}{2} = 9$ inches.

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3 years ago

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bulgar [2K]

Answer:

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Step-by-step explanation:

Let

x ----> the number of miles

y ----> the total cost for rent a car

we know that

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$y=mx+b$

where

m is the slope or unit rate

b is the y-intercept or initial value

<u><em>Prestige car rentals</em></u>

we have that

The slope is equal to $m=\$0.06\ per\ mile$

The y-intercept is $b=\$44$

therefore

$y=0.06x+44$ -----> equation A

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we have that

The slope is equal to $m=\$0.09\ per\ mile$

The y-intercept is $b=\$35$

therefore

$y=0.09x+35$ -----> equation B

For what number of miles both companies charge the same price>

Equate equation A and equation B

$0.09x+35=0.06x+44$

solve for x

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3 years ago

Find the unit rate for each brand. Round to the nearest cent (hundredth).

Natasha_Volkova [10]

The unit rate of each of the brands are:

Brand A's unit rate = 37 cents per ounce.

Brand B's unit rate = 31 cents per ounce.

The unit rate of each brand is simply how much a brand of tomatoes will cost per ounce.

To find the unit rate of each brand, do the following:

Brand A's unit rate = 2.99/8 = $0.37 per ounce = 37 cents per ounce.

Brand B's unit rate = 4.99/16 = $0.31 per ounce = 31 cents per ounce.

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2 years ago

An open box is constructed of 3500 cm2 of cardboard. The box is a cuboid, with height hcm and square base of side xcm. What is t

erica [24]

Answer:

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Step-by-step explanation:

side of square base = x

height = h

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Area = x² + 4xh = 3500

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h = (3500 - x²)/4x

Volume = Area of base x height

V = x² h

V = x² (3500 - x²)/4x

V = (3500 x - x³) / 4

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4 years ago

2. Quadrilateral ABCD was dilated with the origin as the center of dilation to create quadrilateral A'B'C'D. Which rule best rep

Virty [35]

Answer:

$(x,y) => (2.5x,2.5y)$

Step-by-step explanation:

Given

See attachment for ABCD and A'B'C'D'

Required

Determine the dilation rule

Using AB and A'B' as points of references;

$AB = (-1,2)\ to\ (2,1)$

$A'B' = (-2.5,5)\ to\ (5,2.5)$

The dilation factor (k) is calculated as:

$k = \frac{A'B'}{AB}$

This gives:

$k = \frac{(-2.5,5)}{(-1,2)} \ or\ k = \frac{(5,2.5)}{(2,1)}$

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$(x,y) => k(x,y)$

$(x,y) => 2.5(x,y)$

$(x,y) => (2.5x,2.5y)$

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3 years ago