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3 years ago

On a time crunch, please help ASAP!

Mathematics

1 answer:

grigory [225]3 years ago

7 0

Answer:

2x + 5y - 11 = 0

Step-by-step explanation:

(3,1) and (-2,3)

Slope: (3-1)/(-2-3) = - 2/5

y-intercept: 1 - (-2/5)(3) = 1 + 6/5 = 11/5

y = -2/5x + 11/5

Standard form: 2x +5y -11 = 0

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Please help, the question below

Licemer1 [7]

Answer:

$\sf R=\left(3, -\dfrac{5}{4}\right)$

Step-by-step explanation:

Given:

P = (1, 5)
Q = (-2, 3)
R = (a, b)
R lies on line x = 3
PR = QR

If point R lies on the line x = 3, then the x-value of point R is 3.

⇒ a = 3

<u />

<u>Distance between two points</u>

$\sf d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

(where (x₁, y₁) and (x₂, y₂) are the two points)

Use the <u>distance formula</u> to derive equations for PR and QR.

Let (x₁, y₁) = P = (1, 5)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf PR & =\sf \sqrt{(3-1)^2+(b-5)^2}\\ & = \sf \sqrt{4+(b-5)^2} \end{aligned}$

Let (x₁, y₁) = Q = (-2, 3)

Let (x₂, y₂) = R = (3, b)

$\begin{aligned} \sf QR & =\sf \sqrt{(3-(-2))^2+(b-3)^2}\\ & = \sf \sqrt{25+(b-3)^2} \end{aligned}$

As PR = QR, equate the derived equations and solve for b:

$\begin{aligned} \sf PR & = \sf QR \\\sf \sqrt{4+(b-5)^2} & = \sf \sqrt{25+(b-3)^2}\\\sf 4+(b-5)^2 & = \sf 25+(b-3)^2\\\sf 4+b^2-10b+25 & = \sf 25 + b^2-6b+9\\\sf b^2-10b+29 & = \sf b^2 -6b +34\\\sf -10b+29 & = \sf -6b + 34\\\sf -4b & = \sf 5\\\sf b & = -\dfrac{5}{4}\end{aligned}$

Substitute the found values of a and b to find the coordinates of R:

$\sf R=(a,b)=\left(3, -\dfrac{5}{4}\right)$

Learn more about the distance formula here:

brainly.com/question/28144723

8 0

2 years ago

Read 2 more answers

X−6 = 4(2−3x)−8x <br> _______________

atroni [7]

Answer:

Step-by-step explanation:

x−6 = 4(2−3x)−8x

Rearrange terms

x-6= 4(-3x+2)-8x

Distribute

x-6= -12x+8-8x

Combine Like Terms

x-6= -20x+8

21x-6= 8

Isolate x

21x= 8+6

21x=14

x= 14/21

Simplify

x=2/3

5 0

3 years ago

Read 2 more answers

You have $44000 in a savings account that pays 2% annual interestand the inflatation rate is 3.24%. How much buying power in dol

puteri [66]

At the end of the year ...
the price will be 44,000*1.0324 = 45,425.60
the bank balance will be 44,000*1.02 = 44,880.00

This is 545.60 fewer dollars than required to pay the price.

You lose $545.60 in current-year buying power.

4 0

3 years ago

A store is selling a hat at a 55 percent markup. The store originally paid $16 for the hat. What is the retail price of the hat?

AleksandrR [38]

Set up the proportion of $ on one side and percents on other. You can put x for the retail value of the hat and 16 on the bottom. Then on the other side put the percentage of the added markup plus 100% which is the original price on the top over 100%. It should be something like x/16 = 155/100. The cross multiply. (x)(100) = 100x and (16)(155) = 2480. Then divide 2480 by 100 to isolate the x. Your final answer will be x = 24.80 which is the retail price.

6 0

3 years ago

Read 2 more answers

ASSIGNMEN

saw5 [17]

Answer:

(-1,-8)

Step-by-step explanation:

8 0

3 years ago