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3 years ago

Write the equation of the line passing through the given pair of points. (-9, 7) and (-9, -1)

1 answer:

8 0

The first thing I should do with these two points is find the slope of the line.

m = (y2 - y1)/(x2 - x1)

m = (-1 - 7)/(-9 - -9)
m = -8/0

The slope is undefined. We cannot divide by 0. This makes sense because the points (-9, 7) and (-9, -1) would be right on top of each other. This is a vertical line that has an x-intercept at -9.

Your equation would be x = -9.

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$1.60.
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3 years ago

Delaware was the first state to enter the Union and Hawaii was the 50th. If we order the positions of entry for the rest of the

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Answer:

State A was the 12th state to enter the Union. State B was the 11th state to enter the Union.

Step-by-step explanation:

Let's call x to the order-of-entry of State B, therefore the order-of-entry of State A is x+1. Given that he product of their order-of-entry numbers is 132:

x*(x+1) = 132

x² + x - 132 = 0

Using quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 -4(a)(c)}}{2(a)}$

$x = \frac{-1 \pm \sqrt{1^2 -4(1)(-132)}}{2(1)}$

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$x_1 = \frac{-1 + 23}{2}$

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$x_2 = \frac{-1 - 23}{2}$

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The negative solution has no sense in the context of our problem, then the solution is x = 11.

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3 years ago

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Write the equation of the line that passes through the given point and is parallel to the given line.

romanna [79]

(Note: this answer is assuming that the equation has to be put in slope-intercept format.)

Answer:

$y = \frac{1}{2} x - \frac{5}{2}$

Step-by-step explanation:

1) Let's use the point-slope formula to determine what the answer would be. To do that though, we would need two things: the slope and a point that the equation would cross through. We already have the point it would cross through, (-3,-4), based on the given information. So, in the next step, let's find the slope.

2) We know that the slope has to be parallel to the given line, $y = \frac{1}{2}x - 8$ . Remember that slopes that are parallel have the same slope - so, let's simply take the slope from the given equation. Since it's already in slope-intercept form, we know that the slope then must be $\frac{1}{2}$ .

3) Finally, let's put the slope we found and the x and y values from (-3, -4) into the point-slope formula and solve:

$(y- (-4)) = \frac{1}{2} (x - (-3))\\y + 4 = \frac{1}{2} (x + 3))\\y + 4 = \frac{1}{2}x+ \frac{3}{2} \\y = \frac{1}{2}x + \frac{3}{2} - 4\\y = \frac{1}{2}x + \frac{3}{2} - \frac{8}{2} \\y = \frac{1}{2}x - \frac{5}{2}$

Therefore, $y = \frac{1}{2}x - \frac{5}{2}$ is our answer. If you have any questions, please do not hesitate to ask!

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3 years ago