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3 years ago

How can a triangular prism have a greater volume than a rectangular prism?

Mathematics

1 answer:

son4ous [18]3 years ago

3 0

Answer:

Step-by-step explanation:

Assume that the two prisms have bases of equal area.

Then the volume of the rectangular prism is V = (base area)(height).

The volume of the triangular prism is V = (1/3)(base area)(height)

We could compare the two volumes by creating the ratio inequality

(1/3) (base area)(t-height)

------------------------------------------

(base area)(r-height)

The triangular prism will have the greater volume for (1/3)((t-height) > r-height.

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QUESTION 9 1 POINT Find the equation of a line that contains the points (-2,-5) and (3, -1). Write the equation in slope-interce

svet-max [94.6K]

Answer:

If only slope:

$y = \frac{4}{5}x + b$

If slope and y-intercept:

$y = \frac{4}{5}x - 6.6\\or\\y = \frac{4}{5}x - 3.4$

*both are correct answers see steps below*

Step-by-step explanation:

The equation to find the slope is $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

The equation for slope-intercept form is $y = mx + b$ .

First, find the slope between two points.

$\frac{-1 - (-5)}{3 - (-2)} = \frac{4}{5}$

Keep the difference as a fraction if it can't be divided.

Next, plug in the slope value into the equation.

$y = \frac{4}{5}x + b$

If you also need to find what b is, pick a point; (-2, -5) OR (3, -1). Then fill in the equation with it's x and y values. (I'll do both points to show two different results).

Point (-2, -5):

$(-5) = \frac{4}{5}(-2) + b$

$(-5) = (-1.6) + b$

Add 1.6 on both sides to isolate the b. (since -1.6 is a negative, we need to cancel it out with its opposite)

$b = -6.6$

Point (3, -1):

$(-1) = \frac{4}{5}(3) + b$

$(-1) = (2.4) + b$

Subtract 2.4 on both sides to isolate the b. (since 2.4 is a positive, we need to cancel it out with its opposite)

$b = -3.4$

It does mean that both slopes have different y-intercepts but it overly depends on the point. These steps will ensure you to the correct answer.

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