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3 years ago

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JK is formed by J(-12,3) and K(8,-5). If line r is the perpendicular bisector of JK, write an equation for r in slope-intercept

form.

1 answer:

dem82 [27]3 years ago

3 0

Answer:

y = 5/2x + 4

Step-by-step explanation:

<u>Midpoint of JK:</u>

x = (-12 + 8)/2 = -4/2 = -2
y = (3 - 5)/2 = -2/2 = -1

<u>Slope of the line JK:</u>

m = (-5 - 3)/(8 - (-12)) = -8/20 = -2/5

Perpendicular lines have negative reciprocal slopes.

So the line r has a slope 5/2 and passes through the point (-2, -1)

<u>Equation of r:</u>

y = 5/2x + b
-1 = 5/2(-2) + b
-1 = -5 + b
b = 5 - 1
b = 4

<u>So the equation is:</u>

y = 5/2x + 4

You might be interested in

Teacher raises A school system employs teachers at

Cerrena [4.2K]

By adding a constant value to every salary amount, the measures of

central tendency are increased by the amount, while the measures of

dispersion, remains the same

The correct responses are;

(a) <u>The shape of the data remains the same</u>

(b) <u>The mean and median are increased by $1,000</u>

(c) <u>The standard deviation and interquartile range remain the same</u>

Reasons:

The given parameters are;

Present teachers salary = Between $38,000 and $70,000

Amount of raise given to every teacher = $1,000

Required:

Effect of the raise on the following characteristics of the data

(a) Effect on the shape of distribution

The outline shape of the distribution will the same but higher by $1,000

(b) The mean of the data is given as follows;

$\overline x = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i}$

Therefore, following an increase of $1,000, we have;

$\overline x_{New} = \dfrac{\sum (f_i \cdot (x_i + 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i + f_i \cdot 1000))}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i}$

$\overline x_{New} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + \dfrac{\sum (f_i \cdot 1000)}{\sum f_i} = \dfrac{\sum (f_i \cdot x_i)}{\sum f_i} + 1000 = \overline x + 1000$

Therefore, the new mean, is equal to the initial mean increased by 1,000

Median;

Given that all salaries, $x_i$ , are increased by $1,000, the median salary, $x_{med}$ , is also increased by $1,000

Therefore;

The correct response is that the median is increased by $1,000

(c) The standard deviation, σ, is given by $\sigma =\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n}}$ ;

Where;

n = The number of teaches;

Given that, we have both a salary, $x_i$ , and the mean, $\overline x$ , increased by $1,000, we can write;

$\sigma_{new} =\sqrt{\dfrac{\sum \left ((x_i + 1000) -(\overline x + 1000)\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 -\overline x - 1000\right )^{2} }{n}} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}}$

$\sigma_{new} = \sqrt{\dfrac{\sum \left (x_i + 1000 - 1000 - \overline x\right )^{2} }{n}} =\sqrt{\dfrac{\sum \left (x_i-\overline x \right )^{2} }{n}} = \sigma$

Therefore;

$\sigma_{new} = \sigma$ ; <u>The standard deviation stays the same</u>

Interquartile range;

The interquartile range, IQR = Q₃ - Q₁

New interquartile range, IQR $_{new}$ = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR

Therefore;

<u>The interquartile range stays the same</u>

Learn more here:

brainly.com/question/9995782

6 0

2 years ago

The area of a circle is 4π ft². What is the circumference, in feet? Express your answer in terms of \piπ.

Gnesinka [82]

Answer:2 ft

Step-by-step explanation:

Area of circle = pi x r^2 = 4 pi

So r^2 = 4

r =2

7 0

3 years ago

Read 2 more answers

k0ka [10]

The formula for an exponential equation is y = a * b^x with a and b being a fixed value.

"a" would also be the Y intercept, which is where the graph touches or crosses the Y axis. In the given graph, the curved line touches the Y axis at 100, so the value of a would be 100.

Now we need to find b.

The blue dot at Y 50 is lined up with x = 1, so we can use the point (1,50)

Using the X and Y values we can solve for b:

format: y = a * b^x we replace the letters with the numbers above:

50 = 100 * b^1

b^1 = b so now we have:

50 = 100 *b

Divide both sides by 100 to get b by itself:

b = 50/100, which reduces to 1/2, so b = 1/2

So the equation of the graph becomes y = 100(1/2)^x

You may need to write the 1/2 as 0.5, not sure how you need to enter it.

6 0

3 years ago

Read 2 more answers

Factors of 42 <br> I need to know what factors make 42

vodomira [7]

<em>1 x 42</em>

<em>2 x 21</em>

<em>3 x 14</em>

<em>6 x 7</em>

Step-by-step explanation:

We need to find factors of 42.

Factors: <em>Two numbers when multiplied if give you the required number then those 2 numbers are factors o that number.</em>

So, Factors of 42 are:

<em>1 x 42</em>

<em>2 x 21</em>

<em>3 x 14</em>

<em>6 x 7</em>

Only these numbers when multiplied will give 42.

So, All these numbers are factors of 42

Keywords: factors of numbers

Learn more about factors of numbers at:

#learnwithBrainly

3 0

2 years ago

Can you guys please help its due tommorow. Please help the best you can,and enjoy your points.

gtnhenbr [62]

It’s kinda blurry I can barely even see it can you upload that worksheet again so I can do it.

4 0

2 years ago