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3 years ago

Consider the line y=-5/4x-5 find the equation of the line that is parallel to this line and passes through the point (-8,4)

Mathematics

1 answer:

gayaneshka [121]3 years ago

4 0

Answer:

y = -5/4x + 6

Step-by-step explanation:

Since the line we are supposed to find is parallel to y = -5/4x - 5 that means they are going to have the same slope. The line we are looking for is of the following type: y = -5/4 x + b

Since it passes through the point (-8,4):

4 = -5/4 * (-8) + b <=>

4 = -2 + b <=>

4 + 2 = b <=>

b = 6

Hence the line is going to be: y = -5/4x + 6

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2 years ago

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3 years ago

Which of the following correctly describes the domain of the function shown

labwork [276]

Option D:

$\{x: x \neq 1\}$ is the domain of the function.

Solution:

Given function is

$$r(x)=\frac{2 x}{x-1}$

<u>To find the domain of the function:</u>

Option A: $\{x: x \neq 0\}$

Substitute x = 0 in r(x).

$$r(0)=\frac{2 \times 0}{0-1}=0$

If x = 0, then r(0) = 0

So that x ≠ 0 is false.

So, $\{x: x \neq 0\}$ is not the domain of the function.

Option B: $\{x: x \neq \pm 1\}$

Substitute x = –1 in r(x).

$$r(-1)=\frac{2 \times (-1)}{-1-1}=1$

If x = –1, then r(–1) = 1

So that x = ± 1 is false.

So, $\{x: x \neq \pm 1\}$ is not the domain of the function.

Option C: $\{x: \text { all real numbers }\}$

Substitute x = 1 in r(x).

$$r(1)=\frac{2 \times 1}{1-1}=\frac{2}{0}$

It is indeterminate.

So, all real numbers are not the domain of the function.

Option D: $\{x: x \neq 1\}$

Substitute x = 1 in r(x).

$$r(1)=\frac{2 \times 1}{1-1}=\frac{2}{0}$

It is indeterminate.

So, $\{x: x \neq 1\}$ is the domain of the function.

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3 years ago