Chapter 3 solving equations

The endpoints of segment RS are R(-4, 3) and S(8, -5). Complete each statement using a fraction.

Ray Of Light [21]

Answer:

a. (-1 , 1) is the point at 1 : 3 of the way from R to S

b. (5 , -3) is the point at 3 : 1 of the way from R to S

Step-by-step explanation:

* Lets explain how to solve the problem

- If point (x , y) divide a line segment whose end points are

$(x_{1},y_{1})$ and $(x_{2},y_{2})$ , at ratio

$m_{1}:m_{2}$ from the first point, then

$x=\frac{x_{1}m_{2}+x_{2}m_{1}}{m_{1}+m_{2}}$ and

$y=\frac{y_{1}m_{2}+y_{2}m_{1}}{m_{1}+m_{2}}$

* Lets solve the problem

a.

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (-1 , 1) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $-1=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $(-1)m_{1}+(-1)m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $3m_{2}=9m_{1}$

- Divide both sides by 3

∴ $m_{2}=3m_{1}$

∴ $m_{1}=\frac{1}{3}m_{2}$

∴ (-1 , 1) is the point at 1 : 3 of the way from R to S

b.

∵ RS is a line segment whose end points are R (-4 , 3) and S (8 , -5)

∵ Point (5 , -3) divides it at ratio $m_{1}:m_{2}$ from R

- By using the rule above

∴ $5=\frac{-4m_{2}+8m_{1}}{m_{1}+m_{2}}$

- By using cross multiplication

∴ $5m_{1}+5m_{2}$ = $-4m_{2}+8m_{1}$

- By collecting $m_{1}$ in one side and $m_{2}$ in the

other side

∴ $9m_{2}=3m_{1}$

- Divide both sides by 3

∴ $3m_{2}=m_{1}$

∴ $\frac{m_{1}}{m_{2}}=3$

∴ (5 , -3) is the point at 3 : 1 of the way from R to S

8 0

4 years ago

Write the expression as a single term.<br> 3ln(x+2) - ln(x - 1)

Dafna1 [17]

Answer:

ln [(x + 2)^3 ]/(x-1)

Step-by-step explanation:

3ln(x+2) - ln(x - 1) = ln (x + 2)^3 - ln (x-1)

ln (x + 2)^3 - ln (x-1) = ln [(x + 2)^3 ]/(x-1)

7 0

3 years ago

For every 50 emails that Nick sent in a month, he received 30 emails. What is the ratio in simplest form of the number of emails

Anna35 [415]

The answer is D. Because, for every 50 emails dent he received 30 back in response. So, let 5 represent the emails he sent and let 3 represent the emails received... so your answer should be D: 5:3.

I hope this helps!!! Have a good day!!! :D

6 0

3 years ago

Read 2 more answers

Pls tell me least to greatest 4.5 and 3.9 and 4.258 and 3.75 and 4.256

Darya [45]

3.75, 3.9, 4.256, 4.258, 4.5

So how do you find out? It is really easy.

First you look the the number, we all know 3 is less then 4 so the 3s go first

Then you look the tenths, the choices are 3.75 and 3.9. The tenth 9 and 7, and we all know 7 is less then 9, so 3.75 is the first one, then 3.9.

Now let's look at the 4s. The choices are 4.5, 4.258, and 4.256. The tenths are 5, 2, and 2. 2 is less then 5 so they go before 4.5.

Then we look at the hundredth, the choices are 4.256 and 4.258. Since they have same hundreds, we look at the thousands. They are 6 and 8. 6 is less then 8 so 4.256 go before 4.258.

6 0

4 years ago

6. Michelle got a new job through the McCartney Employment Agency. The job pays $49,400 per year, and the agency fee is equal to

rjkz [21]

Answer:

$4, 116.66 times 35%=1,440.83 is the answer.

Step by step equation:

The agency fee is 35% of one months payment ($4,116.66) or ($1,440.83)

all you had to do is 49,400 divided by 12 months and you get $4,116.66 and then you times that by 35% and you get $1,440.83

8 0

3 years ago