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Sophie [7]
3 years ago
10

Write an Equation of the perpendicular bisector of the segment with endpoints Q(-2,0) and R(6,12).

Mathematics
1 answer:
iVinArrow [24]3 years ago
3 0

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:

  • brainly.com/question/774670
  • brainly.com/question/763150

#LearnwithBrainly

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adoni [48]

Answer:

1. 3/2

Domain =

-3, -2, 1, 4

Range =

-4, -2, 0, 3, 5

no it is not a function

Step-by-step explanation:

3 0
3 years ago
What is the annual compound interest rate for an investment account modeled by the function y=12⋅1.18t ?
NikAS [45]

Answer:

The interest rate for the given investment is 18%.

Step-by-step explanation:

We are given that,

The function representing the investment model is, y=12(1.18)^t.

It is required to find the interest rate for the investment.

Since, the function can be re-written as,

y=12(1.18)^t

i.e. y=12(1+0.18)^t

So, on comparing with the formula for compound interest i.e. A=P(1+r)^t, where 'r' is the interest rate.

We have that,

The interest rate for the given investment is 0.18 i.e. 18%.

7 0
2 years ago
A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test.
asambeis [7]
Building time :
4c + 6a < = 120

testing time :
4c + 4a < = 100

20 child bikes and 6 adult bikes...c = 20 and a = 6
sub into both equations
4c + 6a < = 120
4(20) + 6(6) < = 120
80 + 36 < = 120
116 < = 120 (correct)

4c + 4a < = 100
4(20) + 4(6) < = 100
80 + 24 < = 100
104 < = 100 (incorrect)

ur answer : No, because the bike order does not meet the restrictions of 4c + 6a < = 120 and 4c + 4a < = 100
6 0
3 years ago
You are preparing a chemical hazard label for a new product. you know that the product is flammable. what pictogram should be on
lilavasa [31]

A graphic logo that depicts the meaning of any warning or sign through pictorial illustrations is called a pictogram. It can be used in chemicals, laboratories, geography or tourism. The label should have: Flammable and Health Hazard!

<h3>What is a pictogram?</h3>

The pictogram can be explained as: According to the above description, the label sign should have a warning sign of flammable as it can catch and cause fire, a health hazard as it can cause corrosion, carcinogenic and irritation followed by an exclamation mark.

The flammable sign depicts that the substance can cause and catch fires also it can contain pyrophoric. It is cancer-causing, respiratory irritant and toxic hence is hazardous to health.

The exclamation mark is used at the end of the sentence for showing awareness and to convey the meaning of the sign.

Therefore, Flammable and Health Hazard! the sign should be used.

To learn more about pictograms follow the link:

brainly.com/question/14266873

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5 0
2 years ago
for events A and B, P(A)= 3/14 and P(B)= 1/5. Also, P(A and B)= 3/65. Are A and B independent events?
Lady_Fox [76]

No, A and B are not independent events

Step-by-step explanation:

Let us study the meaning independent probability  

  • Two events are independent if the result of the second event is not  affected by the result of the first event
  • If A and B are independent events, the probability of both events  is the product of the probabilities of the both events  P (A and B) = P(A) · P(B)

∵ P(A) = \frac{3}{14}

∵ P(B) = \frac{1}{5}

∴ P(A) . P(B) = \frac{3}{14} × \frac{1}{5}

∴ P(A) . P(B) = \frac{3(1)}{14(5)}

∴ P(A) . P(B) = \frac{3}{70}

∵ P(A and B) = \frac{3}{65}

∵ P(A) . P(B) = \frac{3}{70}

- The two answers are not equal

∴ P (A and B) ≠ P(A) · P(B)

- In independent events P (A and B) = P(A) · P(B)

∴ A and B are not independent events

No, A and B are not independent events

Learn more:

You can learn more about probability in brainly.com/question/13053309

#LearnwithBrainly

5 0
3 years ago
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