15. *Free response. GCO2. After examining the following graph, Kate claims that WXYZ is translated

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

Pyramid A

$s = 4$ -- base sides

$V = 36$ -- Volume

Pyramid B

$s = 6$ --- base sides

Required

Determine the volume of pyramid B [Missing from the question]

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

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

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

$V = 81$

6 0

3 years ago

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To write the polynomial 3x3 + x2 − 8x5 + 2x3 − 4x in standard form, which terms should be combined? A. 3x3 and 2x3 B. 3x3, 2x3,

djyliett [7]

Answer:

Option A. is correct

Step-by-step explanation:

Like terms are those terms that have same variables of same powers. Terms that are not like terms are said to be unlike terms.

For example $2x^3,7x^3$ are like terms and $5x^2,9x^5$ are unlike terms.

Given polynomial is $3x^3+x^2-8x^5+2x^3-4x$

Like terms need to be combined to write the polynomial in standard form

Here, like terms are $3x^3,2x^3$

Option A. is correct.

5 0

4 years ago

True or false? postulates are accepted as true without proof. a. true b. false

zubka84 [21]

Correct answer would be A. True
hope this helped :D

4 0

3 years ago

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7 1/2 divided by 1 1/2 = 5 How to check the answer

Gnom [1K]

Answer:

We verified that the equation $7\frac{1}{2}\div1\frac{1}{2}=5$ has both sides equal.

Step-by-step explanation:

We need to solve and verify: $7\frac{1}{2}\div1\frac{1}{2}=5$

Solving:

$7\frac{1}{2}\div1\frac{1}{2}=5$

Converting into improper fractions

$\frac{15}{2}\div\frac{3}{2}=5$

Converting division sign into multiplication and reversing 3/2 i.e

$\frac{15}{2}\times\frac{2}{3}=5$

Now simplifying

$\frac{15}{3}=5 \\5=5$

So, We verified that the equation $7\frac{1}{2}\div1\frac{1}{2}=5$ has both sides equal.

7 0

3 years ago

What is the value of this expression 3*[(7+8)*2+6] A.64 B.87 C.96 D.108

Westkost [7]

D. 108
thats the answer

8 0

4 years ago

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