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3 years ago

What is the equation that represents the line that passes through the points (9, -2) and (12, -5)?

Mathematics

1 answer:

garik1379 [7]3 years ago

8 0

Hi there!

$\large\boxed{y = -x + 7}$

To begin, we must use the slope formula to calculate the slope of the line:

$m = \frac{y_2-y_1}{x_2-x_1}$

Plug in the coordinates:

$m = \frac{-5-(-2)}{12-9}$

Simplify:

$m = \frac{-3}{3} =-1$

Recall that the equation for a line in point-slope form is:

y - y1 = m(x - x1)

Plug in coordinates into the equation along with the slope:

y - (-2) = -1(x - 9)

Simplify:

y + 2 = -x + 9

y = -x + 7

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48÷3=16

Step-by-step explanation:

In the expression, 96 divided by 8 = a , the quotient a =12

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3 years ago

Read 2 more answers

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

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3 years ago

Last years sales at the drive in movie theater totol 144.600. This year's sales should increase by 1/3. how much should sales in

KATRIN_1 [288]

A] Given that the last years's sales was $144,600 and this years sales should increase by 1/3. Then:
i] Amount the sales should increased by will be:
(last year's sales)*(increase)
=144,600*(1/3)
=48,200

ii] The sales in the new year will be:
(last year's sales)+(increase)
=144600+48600
=$192, 800

2] Given that the sales of hifi which included 6% tax was 205,000. The actual sales was:
Actual percentage sales=100%
percentage sales after taxation=100-6=94%
thus the actual sales was:
(100)/(94)*205,000
=218, 085.1064

3]Given that the rate per $100 is $0.83, and the insurance was for 90000, the insurance premium will be:
(total insurance) *(unit rate)/(number of units)
plugging the values we obtain:
90000*0.83/100
$747

6 0

3 years ago

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Simplify the square root of 7+2<br> So 7+2 is inside the quare root

serious [3.7K]

Answer:

Step-by-step explanation:

$\sqrt{7+2}=\sqrt{9}=\sqrt{3^2}=\boxed{3}$