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Darya [45]
3 years ago
12

a rectangular prism has a volume of 175 in3. The height of the prism is 7 in. The base is a square. What is the length of a side

of the base?
Mathematics
1 answer:
PIT_PIT [208]3 years ago
5 0
Vrect = base × height (h) = s^2×h
Vrect = 175 in^3, h = 7in.
s^2×h = 175
7s^2 = 175
7s^2/7 = 175/7
s^2 = 25
SR(s^2) = SR(25)
s = 5 in.
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Step-by-step explanation:

For this question, your friend is the point-slope form.

Point-slope form = y-y_1 = m(x-x_1)

The only variables you replace are m = slope, y1 = y of a given point, and x1 = x of a given point.

First, we need to find the slope that is perpendicular to the equation y=-\frac{3}{4}x+5

An equation that is perpendicular to another equation have to be negative reciprocals (negative inverse) of each other.

If the slope is 3, then the negative reciprocal of 3 is -\frac{1}{3}.

So, since the given slope is -3/4, the negative reciprocal is \frac{4}{3}.

We will use the negative reciprocal as m since we are trying to find the equation of line that includes (-3, -3) and is perpendicular to the other equation.

We will use point slope form using the (-3, -3) points and negative reciprocal as m.

y-y_1 = m(x-x_1)\\y-(-3) = \frac{4}{3} (x-(-3))\\y+3=\frac{4}{3}(x+3)

Now, we need to convert this into slope-intercept form. The reason why we need to do this is because y = mx + b, where b is the y-intercept. To do this, solve for y - or in other words, isolate y..

y+3=\frac{4}{3}(x+3)\\y+3=\frac{4x}{3}+4\\y+3-3=\frac{4x}{3}+4-3\\y=\frac{4}{3}x+1

The y-intercept of the line is 1.

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Step-by-step explanation:

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