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2 years ago

Find the equation of the line through the points (-3,-3) and (2,-1) using point-slope form. Then rewrite the

Mathematics

1 answer:

IrinaVladis [17]2 years ago

3 0

Answer: See below

Step-by-step explanation:

The point-slope equation is y-y₁=m(x-x₁). Since we don't know our slope, we can use the formula $m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$ to find the slope. All we have to do is use the coordinate we were given and plug it into the formula.

$m=\frac{-1-(-3)}{2-(-3)} =\frac{2}{5}$

Now that we have the slope, we can fill out the point-slope equation.

y-(-3)=2/5(x-(-3))

y+6=2/5(x+3)

This is the point-slope form.

Now, we can distribute and solve to get slope-intercept form.

y+6=2/5x+6/5

y=2/5x-24/5

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Unit 2 | Lesson 10

tiny-mole [99]

The answer is B. 14(m − 8)

m represent the weight of the boxes that Marco lifted.
d represent the weight of the boxes that Drew lifted.

The boxes that Drew lifted each weighed 8 lb less than the boxes Marco lifted:
d = m - 8

So the weight of one box that Drew lifted is (m - 8). Since he lifted boxes, the total number of pounds Drew lifted is 14(m - 8)

3 0

3 years ago

if 5 litres of water are drawn from a cylindrical container of internal diameter 56cm find the drop in the level of water in the

AlexFokin [52]

Answer:

the drop in the level of water in the container is 2.03 cm

Step-by-step explanation:

The volume of a cylinder can be written as;

$V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter$

the change in height when the volume changes can be derived by differentiating the equation.

$dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}$

substituting the given values;

$\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.$

$dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm$

the drop in the level of water in the container is 2.03 cm

4 0

3 years ago

Write the equation of the line shown

Vanyuwa [196]

Answer:

y = $\frac{1}{2}$ x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = $\frac{y_{2}-y_{1} }{x_{2}-x_{1} }$

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 1) ← 2 points on the line

m = $\frac{1-0}{0-(-2)}$ = $\frac{1}{0+2}$ = $\frac{1}{2}$

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = $\frac{1}{2}$ x + 1 ← equation of line

3 0

1 year ago

Read 2 more answers

A certain college graduate borrows 5510 dollars to buy a car. The lender charges interest at an annual rate of 17%. Assuming tha

Diano4ka-milaya [45]

Answer:

His annual payment rate required to pay off the loan in 7 years is $k = $2362.41$ a year.

He has to pay $11026.85 in interest

Step-by-step explanation:

The first step to solve this problem is find how much the student will have to pay for the car. So, we have to find how much the present value of the car(in $) will be worth in 7 years. This is a compound interest problem:

The compound interest formula is given by:

$A = P(1 + \frac{r}{n})^{nt}$

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this exercise, we have:

A = The value we want to find

P = The initial value = 5510

r = 0.17

n = 1

t = 7

$A = 5510(1 + \frac{0.17}{1})^{7}$

$A = $16536.85$

In a seven year period, he has to pay $16536.85. Per year, he has to pay a rate k of:

$k = \frac{16536.85}{7} = $2362.41$

His annual payment rate required to pay off the loan in 7 years is $k = $2362.41$

How much does he pay in interest?

His loan is $5510 and he has to pay $16536.85. So, in interest, he has to pay $16536.85 - 5510 = $11026.85$

5 0

2 years ago

Find the measure of angle A If Angle A = 2x+18 and angle C = 3x+12

tatyana61 [14]

Answer:

Below in bold.

Step-by-step explanation:

2x + 18 + 3x + 12 = 180 (property of a cyclic quadrilateral).

5x = 180 - 18 -12

5x = 150

x = 30

So m < A = 2(30)+18

= 78 degrees.

4 0

2 years ago