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3 years ago

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Randy buys gas at a store that charges $3 per gallon. Sarah buys gas at a different store. The table shown here gives the cost w

hen she buys 3, 4, and 5 gallons of gas.
Is gas more expensive at Randy’s store or Sarah’s store?

1 answer:

marin [14]3 years ago

5 0

Where is the table??

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Pyramid A has a triangular base where each side measures 4 units and a volume of 36 cubic units. Pyramid B has the same height,

omeli [17]

Answer:

The volume of pyramid B is 81 cubic units

Step-by-step explanation:

Given

<u>Pyramid A</u>

$s = 4$ -- base sides

$V = 36$ -- Volume

<u>Pyramid B</u>

$s = 6$ --- base sides

Required

Determine the volume of pyramid B <em>[Missing from the question]</em>

From the question, we understand that both pyramids are equilateral triangular pyramids.

The volume is calculated as:

$V = \frac{1}{3} * B * h$

Where B represents the area of the base equilateral triangle, and it is calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where s represents the side lengths

First, we calculate the height of pyramid A

For Pyramid A, the base area is:

$B = \frac{1}{2} * s^2 * sin(60)$

$B = \frac{1}{2} * 4^2 * \frac{\sqrt 3}{2}$

$B = \frac{1}{2} * 16 * \frac{\sqrt 3}{2}$

$B = 4\sqrt 3$

The height is calculated from:

$V = \frac{1}{3} * B * h$

This gives:

$36 = \frac{1}{3} * 4\sqrt 3 * h$

Make h the subject

$h = \frac{3 * 36}{4\sqrt 3}$

$h = \frac{3 * 9}{\sqrt 3}$

$h = \frac{27}{\sqrt 3}$

To calculate the volume of pyramid B, we make use of:

$V = \frac{1}{3} * B * h$

Since the heights of both pyramids are the same, we can make use of:

$h = \frac{27}{\sqrt 3}$

The base area B, is then calculated as:

$B = \frac{1}{2} * s^2 * sin(60)$

Where

$s = 6$

So:

$B = \frac{1}{2} * 6^2 * sin(60)$

$B = \frac{1}{2} * 36 * \frac{\sqrt 3}{2}$

$B = 9\sqrt 3$

So:

$V = \frac{1}{3} * B * h$

Where

$B = 9\sqrt 3$ and $h = \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9\sqrt 3 * \frac{27}{\sqrt 3}$

$V = \frac{1}{3} * 9 * 27$

$V = 81$

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3 years ago

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WILL MARK YOU BRAINLIEST ASAP

34kurt

Answer:

(-0.5, -1)

Step-by-step explanation:

To find the midpoint add the coordinates then divide by 2

x = (2 + -1)/2

x = 1/2 = 0.5

y = (3 + -5)/2

y = -1

(-0.5, -1)

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Steffen graphed two lines in order to find the solution to a given system of equations. What is the solution?

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check the picture below.

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Answer:

y = -3x + 6

Step-by-step explanation:

Equation of straight line is given by,

y = mx + b

m = slope of the line

b = y-intercept

From the graph attached,

m = $\frac{\text{Rise}}{\text{Run}}$

= $\frac{-6}{2}$

= -3

y intercept 'b' = 6

Therefore, equation of the line will be,

y = -3x + 6

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trasher [3.6K]

C. Prime
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