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3 years ago

Find area of shaded region

Mathematics

1 answer:

Leona [35]3 years ago

3 0

Answer:

ayyyy i go to RSM too? Which location r u at? ANyways the answer is

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Write an equation of the perpendicular bisector of the segment with endpoints Q(−2,0)

olga nikolaevna [1]

The equation of perpendicular bisector of QR is:

$y = -\frac{2}{3}x+\frac{22}{3}$

Step-by-step explanation:

Given points are:

$Q(-2,0)\ and\ R(6,12)$

First of all, we have to find the slope of the given line

So,

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

Here

(x1,y1) = (-2,0)

(x2,y2) = (6,12)

Let m1 be the slope of QR:

Then

$m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}$

Let m2 be the slope of perpendicular bisector

We know that the product of slopes of two perpendicular lines is -1

$m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}$

The bisector will pass through the mid-point of QR

$M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)$

Slope-intercept form of equation is:

$y = m_2x+b$

Putting the value of slope

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

Putting (2,6) in the equation

$6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}$

So,

$y = -\frac{2}{3}x+\frac{22}{3}$

Hence,

The equation of perpendicular bisector of QR is:

$y = -\frac{2}{3}x+\frac{22}{3}$

Keywords: Mid-point, equation of line

Learn more about equation of line at:

#LearnwithBrainly

3 0

3 years ago

Please help with these questions

AveGali [126]

5 ft.................

8 0

3 years ago

Read 2 more answers

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.

NeX [460]

Answer:

0.674

Step-by-step explanation:

If the random variable X is exponentially distributed and X has an average value of 25 minutes, then its probability density function (PDF) is

$\bf f(x)=\frac{1}{25}e^{-x/25}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/25}$

So, <em>the probability that X is less than 28 minutes is </em>

$\bf P(X\leq 28)=1-e^{-28/25}=1-e^{-1.12}=0.674$

8 0

3 years ago

Four equivalent expressions for 3(6m+3)

TEA [102]

There's an infinite number of equivalent expressions for 3(6m + 3), for example:

3 * 6m + 3 * 3
6 (3m + 1.5)
9 + 18m
1/2 (18 + 36m)

I hope it will help you :)

8 0

4 years ago

Find f(x)=x^2-x^3,find f(-10)

Elanso [62]

Answer:

Value of f(-10) is 1100

Step-by-step explanation:

Given that f(x) = x² - x³

Here we need to find f(-10).

f(-10) = (-10)² - (-10)³

f(-10) = 100 - (-1000)

f(-10) = 100 + 1000

f(-10) = 1100

Value of f(-10) is 1100

3 0

2 years ago