Find the distance between (3,4) and (4,-6).

Given:

JK is formed by J(-12, 3) and K(8,-5).

Line r is the perpendicular bisector of JK.

To find:

The equation of line r is slope intercept form.

Solution:

Line r is the perpendicular bisector of JK. So, it passes through the midpoint of J and K.

[tex]Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-12+8}{2},\dfrac{3+(-5)}{2}\right)[/tex]

[tex]Midpoint=\left(\dfrac{-4}{2},\dfrac{-2}{2}\right)[/tex]

[tex]Midpoint=\left(-2,-1\right)[/tex]

Slope of JK is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{-5-3}{8-(-12)}[/tex]

[tex]m=\dfrac{-8}{20}[/tex]

[tex]m=\dfrac{-2}{5}[/tex]

Product of slopes of two perpendicular lines is -1.

[tex]m_1\times m_2=-1[/tex]

[tex]-\dfrac{2}{5}\times m_2=-1[/tex]

[tex]m_2=\dfrac{5}{2}[/tex]

The slope of perpendicular line r is [tex]\dfrac{5}{2}[/tex] and it passes through (-2,-1). So, the equation of perpendicular line is

[tex]y-y_1=m(x-x_1)[/tex]

[tex]y-(-1)=\dfrac{5}{2}(x-(-2))[/tex]

[tex]y+1=\dfrac{5}{2}(x+2)[/tex]

[tex]y+1=\dfrac{5}{2}x+5[/tex]

[tex]y=\dfrac{5}{2}x+5-1[/tex]

[tex]y=\dfrac{5}{2}x+4[/tex]

Therefore, the equation of line r is [tex]y=\dfrac{5}{2}x+4[/tex].

The required equation of line "r" in slope-intercept form is y = 5/2x + 15

First, we need to find the equation of a line in slope-intercept form as

y = mx + b

m is the slope of the line

b is the y-intercept

Given the coordinate points  J(-12, 3) and K(8,-5)

Get the slope of the line

Slope  = -5-3/8+12

Slope = -8/20

Slope - -2/5

Slope of the line "r" perpendicular is 5/2

Get the y-intercept of line r

Substitute (8, -5) and m = 5/2 into y = mx + b

-5 = -5/2(8) + b

-5 = -20 + b

b = 15

Hence the required equation of line "r" in slope-intercept form is y = 5/2x + 15

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Answer:

B

Step-by-step explanation:

(6[tex]x^{5}[/tex]z)^3

6^3 is 226

*(x^2)^3=  x^6        (5*3= 15)

*when there are exponents being raised to a power, the exponents are multiplied

**(z^1)^3= z^3     (3*1= 3)

** all numbers are raised to the 1st power (unless otherwise noted x^2, 5^4 2^2, etc)

So the top would end up being 226x^6z^3

Now, since this number is over 4x^4z^2,  you need to divide 226x^15z^3 by 4x^4z^2

**divide like terms**

226/4= 54

***x^15/ x^4= x^x^11

*** when you divide exponents, you subtract the bottom number from the top, in this case:

15-4

that equalls 11

So x^11

you do the same for z:

z^3/z^2= z^1 or z      (3-2=1 )

You put it all together and you end up with

54x^11z

******** If there are any mistakes I'm really sorry!!******

Answer:

7 units

Step-by-step explanation:

Answer:

It is $2.79

Step-by-step explanation:

You take $8.37 and divide it by 3 then you get $2.79. So for 1 can its $2.79.

Answer:

3/10

Step-by-step explanation:

if you make 1/2 into 5/10 and 4/5 into 8/10 than 8/10 is 3/10 more than 5/10

Answer:

ohh this is little bit hard

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

600-775=125

25x5=125

Answer:7 team members

Step-by-step explanation:think of money... 25 cents times 4 is a dollar. So that means count from 600 by 25 until you get to 775

The Answer is : 20/40

Answer:c

Step-by-step explanation:

Answer: 4

Step-by-step explanation: you add 5 and 3, then you divide by the number of numbers which is 2.

Answer:

Average =  

Sum

Count

=  

8

2

=  

4

Step-by-step explanation:

Sum 8

Count 2

Median 4

Geometric Mean 3.8729833462074

Largest 5

Smallest 3

Range 2

Answer:

10%

Step-by-step explanation:

He had to payback 40 more than he borrowed.

440-400=40

40 is 10% of 400, what he borrowed.

400÷10=40

Answer:

10%

Step-by-step explanation:

That year, he paid $40 in interest, which is 10% of the original loan.

Answer:

The options as included in the attachment section are:

A. real numbers B.Cardinality C.element D.Set

The answer is D. Set

Step-by-step explanation:

In mathematics, a set is a group of well-defined objects that share common characteristics as rightly stated in this question. So in a mathematical calculation, the elements or objects collected as a group is called SET. The types of set include empty set, finite set, infinite set, universal set etc.

- Since set represents the whole collection or group, each object, which can be number, letter etc. in the group is an ELEMENT. Likewise, the cardinality of a set refers to the number of elements contained in a particular set.

Answer:

The answer is y = (x + 4)(x + 1)(2 – x)(3 – x)

Step-by-step explanation:

yw

Answer:

the answer is 2x^2 − x − 2

Answer:9 cups of red paint

Step-by-step explanation:1 batch = 3 cups of paint and you need to find the number of cups of paint for 3 batches so you multiply 3 x 3 and get 9. Hope this helped!!!:)

Answer:

I think its -2/3

Step-by-step explanation:

Step-by-step explanation:

2+8=10

-2-6=8

-4+7=2

6-9=-3

-5-5=-10

7-7=0

Part b.)

Yes. 8° with a rise of negative 7 would look like this 8+-7= 1.

I'm not familiar with the iniger game but here's my best take on the questions

1) no because a positive plus a positive is positive

2) yes, positive plus negative can be negative if the negative is bigger than the positive ex.(5-15=-10

3) yes, negative plus negative is negative

sorry if this took too long but tried my best to hurry

OKOKOKOKOKOKOKOK

When the table says that there has been a RISE, that means that you should ADD. When the table says there has been a FALL, that means you should SUBTRACT.

The second row and the second column is saying a RISE, meaning that you should ADD 8 and 2. 8 + 2 = 10. So the answer for that one would be 10 degrees celcius (third column, second row.) The numbers in bold are your equation for the second row and fourth column.

Here are the rest: AT MEANS AFTERNOON TEMPERATURE :)

3rd row: AT = -8 [degrees celcius] EQUATION: -2 - 6 = -8

4th row: AT = 3 [degrees celcius] EQUATION: -4 + 7 = 3

5th row: AT = -3 [degrees celcius] EQUATION: 6 - 9 = -3

6th row: AT = -10 [degrees celcius] EQUATION: -5 - 5 = -10

7th row: AT = 0 [degrees celcius] EQUATION: 7 - 7 = 0

Woohoo! We're done with that part now.

(b) So, as I said before, a RISE means you must ADD. If you have a rise in -7 degrees celcius, how would you write that mathematically? You would write it like this: + ( - 7 ). You are ADDING NEGATIVE SEVEN. I know it sounds weird, but it is what it is. NOW. Adding negative 7 IS THE EQUIVALENT of saying subtract seven. Here's an example:

10 + ( - 7 ) = 3 (this is true)

10 - 7 = 3 (this is also true)

Therefore, for b you would say that you agree because +(-7) is the equivalent of say 'minus 7'.

Hopefully, you can use what I explained to help you with number 2. If you need more help you can just comment on this post and I'll help you. :))

Answer:

142°

Step-by-step explanation:

Lines L and M are parallel and a line is transversal to them.

[tex]\therefore 38 \degree + m \angle7 = 180 \degree \\ (straight \: line \: \angle s) \\ \\ \therefore m \angle7 = 180 \degree - 38 \degree \\ \\ \huge \red { \boxed{\therefore m \angle7 = 142 \degree }}[/tex]

Answer:

y2 -y1 =4 - y  = 2      y has to = 2 because your slope m= - 2/7

x2-x1  =3-10 = -7

Step-by-step explanation:

( 10 , y )  (3 ,  4)

 x1   y1    x2  y2

We have that for the Question "(10, y) and (3, 4); m= -2/7 find missing value" it can be said that

The value of y is

y=8

From the question we are told

(10, y) and (3, 4); m= -2/7 find missing value

Generally the equation for the slope m  is mathematically given as

[tex]m=\frac{y2-y1}{x2-x1}\\\\Therefore\\\\m=\frac{y2-y1}{x2-x1}\\\\-2/7=\frac{4-y}{3-10}\\\\-2/7*-7=4-y\\\\y=4((-2/7)*-7)\\\\[/tex]

y=8

Therefore

The value of y is

y=8

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Answer:

see below

Step-by-step explanation:

Let f = number of friends

all but one friend got 6 pieces   and 1 friend got 2  for a total of 50 pieces

6(f-1) + 2 = 50

Subtract 2 from each side

6(f-1) +2-2 = 50-2

6(f-1) = 48

Divide by 6

6(f-1)/6 = 48/6

f-1 = 8

Add 1 to each side

f-1+1=8+1

f=9

Jack has 9 friends at the party

With Jack and his mom, there are 11 people

Answer: For I the answer is m=55, for J the answer is x=24

Step-by-step explanation:

I. Remote interior angles add up to exterior which means 30+80=2m which is 110=2m. Divide 110 by 2 gives you m=55

J. Same concept but this time it is 5x=120, divide 120 by 5 gives you 24.

Answer:

To find the perimeter, add together the lengths of the sides. Start at the top and work clockwise around the shape. Area of Polygon = (Area of A) + (Area of B) To find the area, divide the polygon into two separate, simpler regions.

Step-by-step explanation:

Answer:

168

Step-by-step explanation

Answer

191

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

An "additive inverse" refers to a number that when added to a specific number equals to "zero."

In the question above, the additive inverse of -7 is 7 because: -7 + 7 = 0

Other examples:

1. The additive inverse of 2 is -2 because: 2 + (-2) = 0

2. The additive inverse of -100 is 100 because: -100 + 100 = 0

3. The additive inverse of [tex]\frac{1}{2}[/tex] is -[tex]\frac{1}{2}[/tex] because: [tex]\frac{1}{2}[/tex] + -[tex]\frac{1}{2}[/tex] = 0

The additive inverse of -7 is equal to 7.

The additive inverse of a number is the number that, when added to the original number, gives a sum of zero.

To determine the additive inverse of -7, we need to find the number that, when added to -7, results in zero.

To do this, we can multiply -7 by -1, which is the multiplicative inverse of 1. Multiplying a number by its multiplicative inverse always gives the additive inverse of that number.

So, -7 multiplied by -1 is:

-7 x -1 = 7

Therefore, the additive inverse of -7 is 7.

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Answer:

c 60.5 ft x 2ft

Step-by-step explanation:

60.5 ft x 2 = 121 ft

The required possible side length of the tablecloth is 11ft x 11ft.

Given that,
Mrs. Sullivan wants to make a square tablecloth for her dining room table. She has 121 ft? of fabric. What are the possible side lengths of the tablecloth to be determined.

A square is for sided regular polygon, where the length of all sides is identical and the angle between the adjacent side is 90°.

Here,
She has 121 ft² of fabric.
She wants to make a square tablecloth for her dining room table.\

Area of the square = a²
121 = a²
a = √121
a = 11 ft

Thus, the required possible side length of the tablecloth is 11ft x 11ft.

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Answer:

Step-by-step explanation:

Multiply both sides by p to get:

xp = mn

Now divide both sides by n to get:

xp/n = m

Answer:

I think it is 17[tex]\sqrt{13\\\\[/tex]

Step-by-step explanation:

Answer:

17 root 13

Step-by-step explanation:

Answer:

-18 mat-way is good to use