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Flauer [41]
3 years ago
13

The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a heigh

t of 2 units, and the right cylinder has a height of 6 units. Which conclusion can be made from the given information?
A.) The volume of the triangular prism is half the volume of the cylinder. B.)The volume of the triangular prism is not equal to the volume of the cylinder.
C.)The volume of the triangular prism is twice the volume of the cylinder.
D.) The volume of the triangular prism is equal to the volume of the cylinder.
Mathematics
1 answer:
Lina20 [59]3 years ago
5 0

Answer:

B.)The volume of the triangular prism is not equal to the volume of the cylinder.

Step-by-step explanation:

Let A be the cross-sectional area of both congruent right triangular prism and right cylinder.

Since the prism has height 2 units, its volume V₁ = 2A.

Since the cylinder has height 6 units, its volume is V₂ = 6A

Dividing V₁/V₂ = 2A/6A =1/3

V₁ = V₂/3.

The volume of the prism is one-third the volume of the cylinder.

So, since the volume of the prism is neither double nor half of the volume of the cylinder nor is it equal to the volume of the cylinder, B is the correct answer.

So, the volume of the triangular prism is not equal to the volume of the cylinder.

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If alpha and beta are the zeroes of the polynomial f(x)= xsquare -8x +gamma such that alpha - beta = 2 find the value of gamma.
Komok [63]

Answer:

Γ = 15

Step-by-step explanation:

Given

f(x) = x² - 8x + Γ

with a = 1, b = - 8 and c = Γ , then

sum of zeros α + β = - \frac{b}{a} = - \frac{-8}{1} = 8

product of zeros = αβ = \frac{c}{a} = Γ

Given α - β = 2 , then

(α - β)² = 2²

α² - 2αβ + β² = 4 → (1)

and

(α + β)² = 8²

α² + 2αβ + β² = 64 → (2)

Add (1) and (2) term by term

2α² + 2β² = 68 ( divide through by 2 )

α² +β² = 34

Substitute α² + β² = 34 into (1)

34 - 2αβ = 4 ( subtract 34 from both sides )

- 2αβ = - 30 ( divide both sides by - 2 )

αβ = 15

Now

αβ = Γ = 15

Thus

f(x) = x² - 8x + 15

4 0
3 years ago
The slope of a line is 2 and the point (1, 1) lies on the line. What is the y-intercept of this line? (0, -1) (0, 5) (-2, 0)
artcher [175]

Answer:

(0, -1)

Step-by-step explanation:

It's helpful if we think of slope in the context of rise over run.

Since the point (1, 1) lies on the line, because of the slope 2, if we subtract x by 1 to get to x = 0, then we'll be subtracting y by 2.

By that logic, the answer must be (0, -1).

4 0
2 years ago
If a = 7 and b = 3 find the value of 2a + b
weeeeeb [17]
Answer is 17.

Both values are given where:
a = 7 and b = 3

Substitute the values into the given expression.

( 2 x 7 ) + 3

14 + 3 = 17

Hope it helps :]
5 0
2 years ago
Read 2 more answers
6(x + 3) - 2 < 8(x + 5)
stira [4]

The answer is x>-12

First you must use distributive property to simplify.

6x+18-2

Then, you must subtract 18 on both sides

6x-2

Next, add 2 on both sides

6x

Then, subtract 8x on both sides

-2x

Finally, Divide both sides by -2. Don't forget to switch the equality sign because the variable was changed to a positive using division.

x>-12

4 0
3 years ago
Read 2 more answers
Given x = 2^p and y = 2^q, express in terms of x and/or y
vampirchik [111]

Answer:

<h2>|||)</h2><h2>2^ (p + q) = 2^p • 2^q because you'd add the exponents, so xy</h2><h2>2^ 2q = 2^(q + q) = 2^q • 2^q as above, so y^2</h2><h2>2^ (p-1) = 2^p / 2^1 because you subtract exponents when dividing, so x/2</h2>

<h2>If xy = 32 then x = 32/y</h2><h2>so 2xy^2 would = 2(32/y)•y^2 = 64y = 32 so y = 1/2</h2><h2>making x = 64 since xy = 32</h2>

<h2>so 64 = 2^p; p = 6</h2><h2>1/2 = 2^q; q = -1</h2>

7 0
2 years ago
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