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3 years ago

Write an equation for the line (in slope-intercept form) that passes through the given point with the slope m. (0, -7); m = -7

Mathematics

1 answer:

Alina [70]3 years ago

6 0

Answer:

y= -7x -7

Step-by-step explanation:

All line equations can be represented in the form y = mx + c where a is the gradient or slope and b is the y intercept. (letters used for m and c may vary)

You have been given the slope, = -7 which you can put into y=mx+c

y = -7x + c

The function of a line ^^ means that for any values of x, you multiply it by -7 and add -7. The given coordinates means that when x =0, y = -7. So you can plug these into y = -7x + c , -7 = -7(0) + c . Therefore c = -7

Alternatively, since the value for c is the y intercept, the coordinates immediately give you the answer c. x = 0 which means taht the line intercepts the y axis when y = -7. hence the y intercept = -7

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Which of the following is a solution of the inequality 0.75n + 1.5 < 59.25

mojhsa [17]

Answer:

b.77

Step-by-step explanation:

0.75n + 1.5 < 59.25

0.75n < 59.25 - 1.5

0.75n < 57.75

n < 57.75 / 0.75

n < 77

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3 years ago

Nine children (Andrew, Ben, Candy, David, Ella, Fiona, Gordon, Henry, Ivan) form a circle in alphabetical order, clockwise. To c

blondinia [14]

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2 years ago

What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)

8 0

3 years ago

Factor the expression using the GCF. 6x + 42

Nesterboy [21]

Answer: 6x + 42 +=78

Step-by-step explanation:

8 0

2 years ago

Write a real world problem that you would represent with the equation 4x+5=37.

AURORKA [14]

Bob was 5 feet off the ground. He travels 4 feet every single second. How long will it take for him to reach 37 feet?

4x + 5 = 37

4x + 5 (-5) = 37 (-5)

4x = 32

4x/4 = 32/4

x = 8

It will take Bob ~8 seconds to reach 37 feet*

*Problem & answer

hope this helps

3 0

3 years ago