the endpoint of ab are a(-7, -6) and b(5,6) what are the coordinates of point c on ab that is 1/3 the distance from point a to point b

Answers

Answer 1

Answer:

The coordinates of c are (-3,-2)

Step-by-step explanation:

We have the coordinates of a=(-7,-6) and b=(5,6). We need to find the coordinates of a point c=(x,y) such that:

[tex]d_{ac}=1/3 d_{ab}[/tex]

The coordinates x and y have the same relation as the distance:

[tex]x_{ac}=1/3x_{ab}[/tex]

Or, equivalently:

[tex]x_a-x=\frac{1}{3}(x_a-x_b)[/tex]

Multiplying by 3:

[tex]3x_a-3x=x_a-x_b[/tex]

Operating:

[tex]3x_a-x_a+x_b=3x[/tex]

[tex]2x_a+x_b=3x[/tex]

Dividing by 3:

[tex]x=\frac{2x_a+x_b}{3}[/tex]

Similarly:

[tex]y=\frac{2y_a+y_b}{3}[/tex]

Substituting:

[tex]x=\frac{2*(-7)+5}{3}=-3[/tex]

[tex]y=\frac{2*(-6)+6}{3}=-2[/tex]

The coordinates of c are (-3,-2)


Related Questions

if you earn $35 in 5 hours, how much money will you earn in 17 hours? how much will you earn in 1 hour?

Answers

Answer:

$119, $7.

Step-by-step explanation:

First, we need to find the unit rate of pay, in dollars.

Divide $35 by 5 to get $7 per hour.

Now, we multiply the unit rate of pay by 17 to find out how much money is made in the 17 hours that were worked.

By doing this, we get the answer: $119.

Hope this helps! Let me know.

109 is 63% of what? Thx.

Answers

Answer:

109 is 63% of 173.02

Step-by-step explanation:

Let 109 = 63% of x

Thus;

63/100 * x = 109

63x = 10900

x = 10,900/63

x = 173.02

Reasoning How can you find the slope of the
line that passes through the points (0, 0) and
(2, 4)? Explain.

Answers

use the equation y2-y1/x2-x1 so you would do 4-0/2-0= 4/2= 2 so your slope is 2


What is the slope, y-intercept, and equation of a line given the points (-4, 0) and (1, 5)?

Slope:

y-intercept:

Equation:


Answers

Answer:

[tex]Slope: 1\\y-Intercept: 4\\Equation: y = x + 4[/tex]

Step-by-step explanation:

Given two points, we can find the equation of the line between them with the following:

[tex]y = mx + b\\m = \frac{y_2-y_1}{x_2-x_1}[/tex]

First, we can calculate m, or slope

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{5-0}{1-(-4)} = \frac{5}{5} = 1[/tex]

Next we can use the top equation and solve for b, the y-intercept

[tex]y = mx + b\\y = x + b\\5 = (1) + b\\b = 4\\\\y = x + 4[/tex]

[tex]Slope: 1\\y-Intercept: 4\\Equation: y = x + 4[/tex]

D'Andrea and Eden had a sit-up contest. D'Andrea did 176 sit-ups in 4 minutes. Eden did 215 sit-ups in 5 minutes. Which athlete did the most sit-ups per minute?

Answers

Answer:

Eden

Step-by-step explanation:

Answer:

it has D'Andrea

Step-by-step explanation:

Because here we are using direct variation and the formula is y=kx and k=y/x. I used k=y/x You divide 176 by 4 and you'll get 44 that's D'Andrea and the you divide 215 by 5 and you get 43 for Eden. you can see you does more sit up

Freida earns $5.25 per hour and time-and-a-half for overtime for all hours over 40 hours. How much did she earn the week she worked 48 hours?

Answers

Answer:

Total earned= $273

Step-by-step explanation:

Giving the following information:

Regular labor hours= $5.25

Overtime labor hours= $5.25*1.5= $7.875

To calculate the total earned, we need to use the following formula:

Regular labor hours= 40*5.25= 210

Overtime labor hours= 8*7.875= 63

Total earned= 210 + 63

Total earned= $273

Write this statement as a conditional statement in the form “if p, then q.”

A ray divides an angle into two congruent angles. So, the ray is an angle bisector.

Answers

Answer:

if a ray divides an angle into two congruent angles, then the ray is an angle bisector.

Step-by-step explanation:

if p statement is before the comma, called the hypothesis of the conditional statement.

then q statement is after the comma and it is called the conclusion of the conditional statement.

if a plot of land contains a rectangular array of 102 strawberries plants, how many rows are in the array if there are 34 plants in each row?

Answers

3 rows. Sorry if I’m wrong

The track at Bronwyn’s school is ¼ mile around. If she can do 3 laps in 4 ½ minutes,

how fast is she running in miles per hour?

Answers

You start by figuring out how fast a lap is so you do
4.5 (4 1/2 miles)/3
=1.5 minutes

Which means it takes her 1.5 minutes to do 1/4 mile so you times that by four to get how long it takes her to run a mile
4x1.5
=6

This means it takes her 6 minutes to run a mile
To get this into miles per hour you divide 60 (because there’s 60 minutes in an hour) by 6 (her mile time)
60/6
=10

Therefore she is running 10 miles per hour

4.5x10^2 in standard notation

Answers

Answer:

450

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

Factorise x cube -2x square -5x plus 6

Answers

Answer:   {(x + 2), (x - 1), (x - 3)}

Step-by-step explanation:

Presented symbolically, we have:

x^3 - 2x^2 - 5x + 6

Synthetic division is very useful for determining roots of polynomials.  Once we have roots, we can easily write the corresponding factors.  

Write out possible factors of 6:  {±1, ±2, ±3, ±6}

Let's determine whether or not -2 is a root.  Set up synthetic division as follows:

-2   /   1   -2   -5   6

              -2     8   -6

     -----------------------

        1     -4      3    0

since the remainder is zero, we know for sure that -2 is a root and (x + 2) is a factor of the given polynomial.  The coefficients of the product of the remaining two factors are {1, -4, 3}.  This trinomial factors easily into {(x -1), (x - 3)}.

Thus, the three factors of the given polynomial are {(x + 2), (x - 1), (x - 3)}

triangle TCL is similar to triangle AEN. solve for x and y​

Answers

Answer:

y = 6.7

x = 8

Step-by-step explanation:

3^2 + 6*2 = y

√9 + 36 = y

6.7 = y

10^2 = 6^2 + x

100 = 36 + x

100 (-36) = 36 (-36) +x

√64 = x

8 = x

help plzzzzzz it should be easy

Answers

Answer:

uh

Step-by-step explanation:

l

Answer

1.<     2.>

Step-by-step explanation:

1. 9x4/5= 7.2<9

2. 4x6/5= 4.8>4

SOMEONE PLEASE HELP ME WITH THIS!!!!

Answers

Answer: B) 2(x + 3) - 1

Answer:

I think its answer b

Step-by-step explanation:

in not sure what the question is asking but b is the only answer equal to 2z+5. Im not sure if thats right though. check it on m a t h way.

38 marbles are shared between John, David and Paul so that John gets twice as many as David. Paul gets 5 only. How many marbles does john get?

Answers

Answer:

11

Step-by-step explanation:

The total number of marbles John gets is 22 and this can be determined by forming the linear equation with help of the given data.

Given :

38 marbles are shared between John, David, and Paul so that John gets twice as many as David. Paul gets 5 only.

The following steps can be used in order to determine the total number of marbles john gets:

Step 1 - Let the total number of marbles John have to be 'x', let the total number of marbles David have to be 'y', and let the total number of marbles Paul have to be 'z'.

Step 2 - So, the linear equation that represents the total number of marbles is:

x + y + z = 38    --- (1)

Step 3 - According to the given data, John gets twice as many as David, that is:

x = 2y  --- (2)

Step 4 - According to the given data, Paul gets only 5 marbles, that is:

z = 5  --- (3)

Step 5 - Substitute the value of x and z in equation (1).

2y + y + 5 = 38

Simplify the above equation.

3y + 5 = 38

3y = 33

y = 11

Step 6 - Substitute the value of y in equation (2).

x = 2(11)

x = 22

So, the total number of marbles John gets is 22.

For more information, refer to the link given below:

https://brainly.com/question/11897796

What is the solution to the equation 5x−2=2x+13

Answers

Answer:

X=5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5x-2=2x+13

-2x     -2x

3x-2=13

    +2   +2

3x=15

divide 15 by 3.

I WILL MARK AS BRAINLIEST!!!!

Answers

Answer:

1. 795, 23

2. 50, she will finish her candy on November 21 so she won't be able to share with her cousins

3. $276, 71 cars

Step-by-step explanation:

1. your equation: y = 35x + 235

plug in 16 to find how many pictures she will have on may 16: y = 35(16) + 235

you get y = 795

for the second part, you know are trying to find how long it will take to get to 1024 pictures, so you know your y, but you don't know your x

your equation: 1024 = 35x + 235

solve to get x = 22.54

this rounds up to 23, so your answer is 23

2. multiply 8 times 4 to get 32

subtract 32 from 82 to fin how many she has left

you get 50

for the second part, divide 82 by 4 to find how many day it will take to finish her candy

you get 20.5

so no, she will not have candy to share with her cousins, and she will finish her candy on November 21

3. for this, you have a negative y intercept since you need to make $24 to start profiting

your equation: y = 6x - 24

plug in 50 to x: y = 6(50) - 24

you get y = 276

so you make $276 with 50 cars

for the second part, plug in 400 to y: 400 = 6x - 24

solve to get x = 70.66

this rounds up to 71, so your answer is 71

what is the solution for 2x-5=7​

Answers

Answer:

x = 12

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

1.  Add 5 to both sides.

2x = 7 + 5

2. Simplify  7+5 to 12.

2x = 12

3. Divide both sides by 22.

x = 12/2

4. Simplify 12/2 to 6

x = 6

On another day, Martin bought 123
5
pounds of grapes for a picnic. His friend bought 3
8
of that amount. Use compatible fractions to estimate how many pounds of grapes Martin’s friend bought.

123
5


3
8


Martin's friend bought about
pounds of grapes.

Answers

Answer:

The answer is 123

5

✔ 12 1/2

3

8

✔ 1/2

Martin's friend bought about  

✔ 6 ¼

pounds of grapes.

The number of pounds of grapes that are bought will be  [tex]4\frac{29}{40}[/tex]  pounds.

What is fraction?

Fractions are used to represent smaller pieces (or parts) of a whole.

Given the information that Martin bought 12 3/5 pounds of grapes for a picnic, while his friend bought 3/8 of that amount.

Therefore, the amount that his friend bought will be:

= 3/8 × 12 3/5

= 3/8 × 63/5

= 189/40

= [tex]4\frac{29}{40}[/tex]

Hence,  the number of pounds of grapes that are bought will be  [tex]4\frac{29}{40}[/tex]  pounds.

Learn more about fraction on:

brainly.com/question/9695343

#SPJ6

Ms. Geetha said that 60 of her total students will compete in the Math Olympics. If 60 is 20% of her students, how many total students does she have?

Answers

Answer:

300 students

Step-by-step explanation:

There are two ways to solve this question.

Way Number 1

60 is 20% of the total students

20÷100= 0.2

60÷0.2=300

Therefore there are 300 students

Way Number 2

60 is 20% of the total students

60/20 = x/100

x= 60*100÷20

x= 6000÷20

x= 300

Therefore there are 300 students.

Helppppppppmeeeeeeeeeeeeeeee

Answers

hahahhahahahahahhshahahahshhahxbcismc

Step-by-step explanation:

okay

Combine and simplify the following radical expression. 3^ square root 6 x 3^ square root 4​

Answers

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[tex] {3}^{ \sqrt{6} } \times {3}^{ \sqrt{4} } = [/tex]

[tex] {3}^{ \sqrt{6} } \times {3}^{2} = [/tex]

[tex] {3}^{ \sqrt{6} + 2 } = {3}^{2 + \sqrt{6} } [/tex]

♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️

Two numbers are opposites are 12 units apart. What are the two numbers? Answer smaller number, larger number

Answers

Answer:

-6, 6

Explanation:

-6 - 6 = -12

At the local pet store, zebra fish cost $2.00 each and neon tetras cost $1.90 each. If Ernesto bought 11 fish for a total cost of $21.50, not including tax, how many of each type of fish did he buy?

Answers

Answer:Break it into 2 shapes.

A rectangle: 8 x 7 = 56 square inches.

A triangle: 1/2 x 3 x 4 = 6 square inches.

Total: 56 + 6 = 62 square inches.

Step-by-step explanation:

please answerrr this is a college course im taking
Mrs. Hartley gave her students a choice
board with 16 projects in which they each
had to pick three. How many ways could a
student choose three projects?
A. 560
C. 2,304
D. 3,360
B. 48

Answers

Answer:

B) 48

Step-by-step explanation:

16 x 3 = 48

12/75=x/120 What is x?

Answers

Answer:

x = 18

Step-by-step explanation:

Answer:

19.2

Step-by-step explanation:

120/75=1.6

12 times 1.6=19.2

How can properties of operations be used to add expressions?

Answers

Use this. Hope it helps

can you help me solve this question? ​

Answers

The y- intercept is 4. M= 2/3

The y intercept is 4. M=2/3

Simplify the expression: 3(q + 11) - 4

Answers

Answer:

8

Step-by-step explanation:

Kelsey is a stock broker. She earns 11% commission each week.Last week she sold $7200 worth of stocks. How much did she make last week in commission? if she averages the same amount each week how much did she make in commission in 2011?

Answers

Answer:

$792 last week's commission.

$41,184 for 2011

Step-by-step explanation:

11% of 7200 is = $792

$792 times 52 weeks in a year is $41,184

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