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3 years ago

Are the following angle relationships possible? Explain.

Mathematics

1 answer:

mel-nik [20]3 years ago

7 0

Answer:

Step-by-step explanation:

The 5x+30 is the supplementary angle of the interior one:

180 - 5x - 30 = -5x + 150

Then they have to add up to 180:

4x-9 + 2x+3 -5x + 150 = 180

which simplifies to x = 36

So the angles would be 135, 75 and -30, which is impossible!

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3 years ago

8) through: (-3, -2), perp. to y = x – 1 A) y=-5x – 1 B) y=-4x – 5 C) y=-x – 5 D) y=-5x – 4

nexus9112 [7]

Answer:

The equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.

Solution:

Given, line equation is y = x – 1 ⇒ x – y – 1 = 0. And a point is (-3, -2)

We have to find the line equation which is perpendicular to above given line and passing through the given point.

Now, let us find the slope of the given line equation.

$\text { Slope }=\frac{-x \text { coefficient }}{y \text { coefficient }}=\frac{-1}{-1}=1$

We know that, product of slopes of perpendicular lines is -1.

So, 1 $\times$ slope of perpendicular line = -1

slope of perpendicular line = -1

Now let us write point slope form for our required line.

$\mathrm{y}-\mathrm{y}_{1}=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_{1}\right)$

y – (-2) = -1(x – (-3))

y + 2 = -1(x + 3)

y + 2 = -x – 3

x + y + 2 + 3 = 0

x + y + 5 = 0

y = -x -5

Hence the equation through (-3, -2) and perpendicular to y = x – 1 is y = -x -5 and option c is correct.

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