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3 years ago

8

What is the slope of the line that passes through the points (12,-8) and (-9,-11)

1 answer:

Sauron [17]3 years ago

3 0

Answer: 1/7

Explanation:

1. Use the formula, y2-y1/x2-x1
Plug in the points, (12, -8) and (-9, -11) into the formula.
Point (12, -8): 12 is the X1 and -8 is the y1.
Point (-9, -11): -9 is the X2 and -11 is the y2
So, -11--8/-9-12

2. -11--8/-9-12= -3/-21= 1/7

I hope this helps!!

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3 years ago

The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?

S_A_V [24]

Step-by-step explanation:

Lets consider the unknown number as x

according to the question,

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2 years ago

2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

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Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

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2 years ago

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