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seraphim [82]
3 years ago
10

What is the equation of the line that is perpendicular to the given line and has an x-intercept of -3?

Mathematics
1 answer:
Anvisha [2.4K]3 years ago
3 0

Answer:

y=-\frac{3}{2}x-\frac{9}{2}

Step-by-step explanation:

Let the equation of the perpendicular line is,

y = mx + b

where m = slope of the line

b = y-intercept

From the graph, slope of the line passing through (0, -1) and (3, 1),

m' = \frac{y_2-y_1}{x_2-x_1}

m' = \frac{1+1}{3-0}

m' = \frac{2}{3}

To get the slope (m) of this line we will use the property of perpendicular lines,

m × m' = (-1)

m × \frac{2}{3} = -1

m = -\frac{3}{2}

Equation of the perpendicular line will be,

y=-\frac{3}{2}x+b

x-intercept of the line is (-3) therefore, point on the line is (-3, 0)

0 = -\frac{3}{2}(-3)+b

b = -\frac{9}{2}=-4.5

Equation of the line will be,

y=-\frac{3}{2}x-\frac{9}{2}

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Marizza181 [45]

9514 1404 393

Answer:

  ∠Q = 89°

  ∠R = 123°

  ∠S = 91°

Step-by-step explanation:

It seems easiest to start by finding the measures of each of the arcs. The measure of an arc is double the measure of the inscribed angle it subtends.

  arc QRS = 2·∠P = 114°

So, ...

  arc QR = arc QRS - arc RS = 114° -41° = 73°

The total of the arcs around the circle is 360°, so ...

  arc PQ = 360° -arc PS -arc QRS

  arc PQ = 360° -137° -114° = 109°

__

  ∠Q = (1/2)(arc RS + arc PS) = (1/2)(41° +137°)

  ∠Q = 89°

__

  ∠R = (1/2)(arc PS +arc PQ) = (1/2)(137° +109°)

  ∠R = 123°

__

  ∠S = (1/2)(arc PQ +arc QR) = (1/2)(109° +73°)

  ∠S = 91°

7 0
3 years ago
Iwould like the answer and the details on a paper
PilotLPTM [1.2K]
I can't download the picture, you will have to type it out so I can explain it

5 0
3 years ago
Jamey says she only has 30% of her book to go before she finishes it. she has read 147 pages so far
Lubov Fominskaja [6]
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"Of" is always equaling to multiplication (×)

Now, it would be easier to simplify 

30% (147)
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Type the integer that makes the following addition sentence true: –88 + = –10
zhenek [66]

Answer:

78

Step-by-step explanation:

6 0
2 years ago
The graph of f(x)=2x^3+x^2-4x-2 is shown. How many of the roots of f(x) are rational
Alexeev081 [22]

We can one theorem to help us find rational roots of this polynomial.

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-2  + 1 + 4 - 2

There are 2 sign changes, so we know there will be 2 negative roots.

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7 0
3 years ago
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