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Olenka [21]
3 years ago
13

Write the equation in slope-intercept form of the line that passes through

Mathematics
1 answer:
mixer [17]3 years ago
7 0

Answer:

We conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

where

  • m is the slope
  • b is the y-intercept

Given the line

y = -3/4x + 1

comparing with the slope-intercept form of the line equation

The slope = m = -3/4

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:  

slope = m = -3/4

Thus, the slope of the new perpendicular line = – 1/(-3/4) = 4/3

Using the point-slope form

y-y_1=m\left(x-x_1\right)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values of the slope = 4/3 and the point (12, 9)

y-y_1=m\left(x-x_1\right)

y-9=\frac{4}{3}\left(x-12\right)

Add 9 to both sides

y-9+9=\frac{4}{3}\left(x-12\right)+9

y=\frac{4}{3}x-16+9

y=\frac{4}{3}x-7

Therefore, we conclude that the equation in slope-intercept form of the line that passes through  (12,9) and is perpendicular to the graph of y = -3/4x + 1 will be:

  • y=\frac{4}{3}x-7
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2 cm
Novay_Z [31]

Answer:

Following are the solution to the given question:

Step-by-step explanation:

In question a:

\to 16= 4^2  is a perfect square.

\to 125 = 5^3 is not a perfect square

In question b:

\to 20 = 2 \times 2 \times 5, not a perfect square.

\to 25 = 5^2 is a perfect square .

\to 100 = 10^2 is a perfect square .

\to 125 is not a perfect square, its nearest perfect square is121 = 11^2 .

\to 144 = 12^2  is a perfect square .

\to 225 = 15^2  is a perfect square .

\to 10,000 = 100^2 is a perfect square .

5 0
3 years ago
Solve for w.<br> 6&gt;9+w.......
kramer

the answer is.... w<-3

7 0
3 years ago
During a school event, Noah is selling pizza at the food stand for $1.25 per slice.
Eddi Din [679]

Answer:

1. When he sold 20 slices of pizza at $1.25 each, he made $20

  When he sold 50 slices of pizza at $1.25 each, he made $62.5

2. 96 slices of pizza. You would get that by dividing 120 by 1.25, as he needs to make $120, and each slice costs $1.25

7 0
3 years ago
A scuba diving company currently charges $100per dive. On average, there are 30 customers per day. The company performed a study
Semenov [28]

A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write R=PC.

Per price increase is $20. So four price increase is $20*4=$80. Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4*2=8 customers are reduced. Hence, total customers is 30-8=22.

So Total Revenue is:

R=180*22=3960


B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

R=(100+2x)(30-2x)=-40x^{2}+400x+3000


C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as x=-\frac{b}{2a}, where a is the coefficient of x^{2} and b is the coefficient of x. So we have,

x=-\frac{b}{2a}=- \frac{400}{(2)(-40)}=5

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5*20=100. So the price that gives the greatest revenue is 100+100=200.

ANSWERS:

A. $3960

B. R=-40x^{2}+400x+3000

C. $200

4 0
3 years ago
Pls answer if you only know the correct answer! Thanks! :)
Aleonysh [2.5K]

Answer:

I would say it's -0.8

Step-by-step explanation:

Since 3 is pretty far, I'm assuming -2 is at the left end of the line, so -.8 seems like the most reasonable answer.

4 0
3 years ago
Read 2 more answers
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