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3 years ago

Determine the equation of the line with slope 3 that passes through the point M(1, 2).

Mathematics

1 answer:

Mandarinka [93]3 years ago

4 0

Answer:

Step-by-step explanation:

We are given the slope along with an (x, y) coordinate with which to write the equation. You could use this info in the slope-intercept form and solve for b, or you could use this info in the point-slope form and solve it for y. Trust me when I tell you that either one will get you the correct equation. Promise! I used the point-slope form, just because. ; )

y - 2 = 3(x - 1) and

y - 2 = 3x - 3 and

y = 3x - 1 OR in standard form, we will put the x and y terms on the same side of the equals sign, separated from the constant:

-3x + y = -1. But if we get picky and do not like to lead with negatives, we could change ALL the signs to their opposites (which is the same as multiplying the whole thing by a -1) to get

3x - y = 1 which is the third choice down.

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13) As they’ve given the zeros, you can use those to create factors. Since the zeros are x=-1, x=-3, and x=4, by making the right side 0 in each equation, you get the factors (x+1), (x+3), and (x-4). Then, you can multiply those factors using box method or FOIL or whichever method you prefer. By multiplying (x+1) and (x+3), I got x^2+4x+3. Then, I multiplied that by (x-4) to get x^3-13x-12, which is your final answer.

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15) x=1, x=1, x=2. These become the factors (x-1), (x-1), and (x-2). Then, by multiplying (x-1) and (x-1) you get x^2-2x+1. Multiply that by (x-2) to get your final answer, x^3-4x^2+5x-2.

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3 years ago

If the diameter of a youth baseball is 2. 8 inches and the diameter of an adult softball is 3. 8 inches, what is the approximate

Molodets [167]

The approximate difference in their volumes is 17.2 cubic inches

<h3>How to determine the difference in the volume?</h3>

The given parameters are:

Diameter, d = 2.8

Diameter, D = 3.8

The radii are the half of the diameter.

So, we have:

r = 1.4

R = 1.9

The volume of the balls is then calculated using:

$V = \frac{4}{3}\pi r^3$

The difference is then represented as:

$D = \frac{4}{3}\pi (R^3 - r^3)$

Substitute known values

$D = \frac{4}{3}* 3.14* (1.9^3 - 1.4^3)$

Evaluate

D = 17.2

Hence, the approximate difference in their volumes is 17.2 cubic inches