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3 years ago

Find an equation for the line that passes through the point (-4, 10) and (16, -2)

Mathematics

1 answer:

Crank3 years ago

3 0

Answer:

y = 3/5x + 62/5

Step-by-step explanation:

Equation of a line with two points is

m = y - y_1 / x - x _1

m = y_2 - y_1 / x_2 - x _1

Equating both

y - y_1 / x - x_1 = y_2 - y_1 / x_2 - x_1

Using what we are provided with

(-4 , 10)(16 , -2)

x_1 = -4

y_1 = 40

x_2 = 16

y_2 = -2

Imputing the values

10 - (-2) / 16 - (-4) = y - 10 / x - (-4)

10 + 2 /16 + 4 = y - 10 / x + 4

12 / 20 = y - 10 / x + 4

Lets cross multiply

12 ( x + 4) = 20(y - 10)

Open the brackets

12x + 48 = 20y - 200

12x + 48 + 200 = 20y

12x + 248 = 20y

Following this equation of line

y = mx + C

20y = 12x + 248

Let's divide through by 20 to get y.

20y / 20 = 12x + 248 / 20

y = 12x + 248 / 20

We can separate it by

y = 12x / 20 + 248 / 20

y = 3/5x + 62/5

Therefore, the equation of the line is

y = 3/5x + 62/5

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Answer:

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3 years ago

What is the answer to this?

Dennis_Churaev [7]

Answer:

Step-by-step explanation:

The angles (5x - 5)° and (6x + 31)° are supplementary angles.

Supplementary Angles add up to 180°.

Therefore we have the equation:

5x - 5 + 6x + 31 = 180 <em>combine like terms</em>

(5x + 6x) + (-5 + 31) = 180

11x + 26 = 180 <em>subtract 26 from both sides</em>

11x = 154 <em>divide both sides by 11</em>

x = 14

The angles (5x - 5)° and z° are vertical angles.

Vertical angles are congruent.

Therefore we have the equation:

z = 5x - 5 <em>put x = 14 to the equation</em>

z = 5(14) - 5

z = 70 - 5

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4 0

3 years ago

A board that is 4 1/2 feet long weighs 7 1/5 pounds. How much would one foot of the board

REY [17]

Answer:

A board that is 4 1/2 feet long weighs 7 1/5 pounds. How much would one foot of the board weigh? Write your answer as a mixed number

Step-by-step explanation:

8 0

3 years ago

One watering system needs about three times as long to complete a job as another warning system when both systems operate at the

algol13

Answer:

One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

Step-by-step explanation:

Given:

Both the system can complete the job = 9 minutes

We need find the time required by each system to do the job.

Solution:

Let the time required by another watering system to complete the job be 'x' mins.

Now given:

One watering system needs about three times as long to complete a job as another watering system.

Time required by one watering system = $3x$

Rate to complete the job by another watering system = $\frac{1}{x}\ job/min$

Rate to complete the job by One watering system = $\frac{1}{3x}\ job/min$

Rate at which both can complete the job = $\frac{1}{9}\ job/min$

So we can say that;

Rate at which both can complete the job is equal to sum of Rate to complete the job by another watering system and Rate to complete the job by One watering system.

framing in equation form we get;

$\frac{1}{x}+\frac{1}{3x}=\frac19$

Now taking LCM to make the denominator common we get;

$\frac{1\times3}{x\times 3}+\frac{1\times1}{3x\times1}=\frac19\\\\\frac{3}{3x}+\frac{1}{3x}=\frac19\\\\\frac{3+1}{3x}=\frac{1}{9}\\\\\frac{4}{3x}=\frac{1}{9}$

By Cross multiplication we get;

$4\times9 =3x\\\\3x =36$

Dividing both side by 3 we get;

$\frac{3x}{3}=\frac{36}{3}\\\\x=12\ min$

Time required by One watering system = $3x =3\times 12 =36\ min$

Hence One watering system requires 36 minutes to complete the job alone while another watering system requires 12 minutes to complete the job alone.

6 0

3 years ago

What is 3/4 x = 6 what is the value of x

olasank [31]

Answer:

Step-by-step explanation:

3/4x = 6 Multiply both sides by 4/3

4/3 * 3/4 x = 6*4/3 Combine

x = 6 * 4/3

x = 24/3

x = 8

6 0

4 years ago