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3 years ago

A line has an x-intercept of -8 and a y-intercept of 3. What is the equation of the line?

1 answer:

5 0

The answer is G. Your intercepts are the only info given, so you must find the slope with these points. Remember that the slope is rise/run. You are traveling from left to right, and from down to up, so your slope must be positive. Starting from (-8,0), you rise up three spaces to reach y=3 (the height of the y-intercept), then you move right 8 spaces to land directly onto (0,3). You rise 3, so 3 is your numerator. You run 8, so 8 is your denominator. Now you have your slope. The y-intercept is always your start value, so this value is always going to be your "b" value in "y=mx+b". M is slope. B is the y-intercept, which in this case, is 3.

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Please help solve this, I’ve tried my best. My answers are a height of 6.7 using 30-60-90 as a last resort, and the glass volume

Neko [114]

Answer:

A) To ensure the correct and exact straight height

B) 15 inches

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Step-by-step explanation:

Hello! Lets start!

First, it asks us to explain why the two bases must be parallel. In order to measure the correct and exact height, we must be sure that the bases are parallel, or else there would be a range of heights; in order to ensure that you are measuring a straight distance, they must be parallel!

Second, it asks us to identify the height of cone. To do this, we must make a slope! We can see that, for every time we go down 5 inches, we lose 1 inch of our base! Our slope in this situation would be -5. So, lets continue to see how long before the cone reaches its tip, in which the base would be equal to 0. At 5 inches, our base is 2 inches. At 10 inches, our base is 1 inch. At 15 inches, we do not have a base, as it equals 0! So therefore, our cone height is 15 inches.

Third, it asks us to identify the volume of the cup, which is also called a <em>circular truncated cone. </em>To do so, we can use the formula:

₁ $V = \frac{1}{3} \pi (r_{1}^2 + r_{1}r_{2} + r_2^2)h$

Lets plug in our information!

$V = \frac{1}{3} \pi (1.5^{2} + (1.5)(1) + 1^{2}) (5)\\V = 24.87$

Hope this helps! Remember, math is fun!

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3 years ago