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2 years ago

Which equation represents the line that is perpendicular to and passes through (-12,6)?.

Mathematics

1 answer:

Evgesh-ka [11]2 years ago

7 0

The equation that represents the line that is perpendicular is

3y + 5x = -42

The standard equation of a line in point-slope form is expressed as:

$y-y_1=m(x-x_1)$

m is the slope of the lne

(x1, y1) is any point on the line.

Given the equation y = 3/2x + 1, the slope of the line is 3/5

The s<u>lope of the line perpendicular</u> is -5/3

Substitute the point (-12, 6) and the slope m = -5/3 into the equation above to have:

$y-6=-5/3(x-(-12))\\3(y-6)=-5(x+12)\\3y-18=-5x-60\\3y = -5x - 60 + 18\\3y + 5x = -42\\$

Hence the equation that represents the line that is perpendicular is

3y + 5x = -42

Learn more on equation of a line here:brainly.com/question/19417700

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A road crew must repave a road that is 45 miles long. they can repave 120 miles each hour. how long will it take the crew to rep

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45 miles ----------------------?? x hours

x= 45 / 120 = 0.375 hours

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3 years ago

during one semester, the time elaine spent doing homework or participating in extracurricular activities was 20 percent less tha

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Answer:

963 hours

Step-by-step explanation:

I subtracted 20 from the 981

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1 year ago

In front of a store, there is a row of parking spaces. Cars park parallel to one another, with the front of each car facing the

Gelneren [198K]

The width used for the car spaces are taken as a multiples of the width of

the compact car spaces.

Correct response:

The store owners are incorrect

<h3 /><h3>Methods used to obtain the above response</h3>

Let <em>x</em><em> </em>represent the width of the cars parked compact, and let a·x represent the width of cars parked in full size spaces.

We have;

Initial space occupied = 10·x + 12·(a·x) = x·(10 + 12·a)

New space design = 16·x + 9×(a·x) = x·(16 + 9·a)

When the dimensions of the initial and new arrangement are equal, we have;

10 + 12·a = 16 + 9·a

12·a - 9·a = 16 - 10 = 6

3·a = 6

a = 6 ÷ 3 = 2

a = 2

Whereby the factor <em>a</em> < 2, such that the width of the full size space is less than twice the width of the compact spaces, by testing, we have;

10 + 12·a < 16 + 9·a

Which gives;

x·(10 + 12·a) < x·(16 + 9·a)

Therefore;

The initial total car park space is less than the space required for 16

compact spaces and 9 full size spaces, therefore; the store owners are

incorrect.

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1 year ago

Solve the compound inequality 4x – 7 > 5 or 5x + 4 ≤ –6

bija089 [108]

Answer:

inequality form: x $\leq$ -2 or x > 3

interval notation form: (-∞,-2] ∪ (3,∞)

Step-by-step explanation:

I attached a picture that shows all the work. You begin by isolating then solving for x on both sides. Then form a solution using the information found out about x. For example, you can combine the found inequalities for x to solve that x must be GREATER than 3 while being LESS than -2. Using that you can form an line and make a line. Remember, when writing in interval notation form you always begin from the left to the right (in reference) to the number line.

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1 year ago

Julie makes and sells shirts for children and adults. She sells the shirts for $20 per unit. Material for

Alisiya [41]

Answer:

Julie need to sell at least 45 shirts to break even.

Step-by-step explanation:

The selling cost of each shirt = $ 20

Cost of each shirt = $6

The fixed cost per month = $420

Number of shirts she can make = 80

Hence, the <u>cost of making 80 shirts</u> = 80 x $6 = $480

So, her total capital investment of the month

= Cost of shirts made + Fixed cost = $420 + $480 = $900

Now, let us assume she sell k number of shirts.

⇒ $20 x k = $900

or, k = 900 / 20 = 45

or, k = 45

Hence, Julie need to sell at least 45 shirts to break even.

6 0

2 years ago