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GalinKa [24]
1 year ago
15

21. For the following exercises, use the descriptions of each pair of lines given below to find the slopes of Line 1 and Line 2.

Is each pair of lines parallel, perpendicular, or neither?
21. Line 1: Passes through (1, 7) and (5, 5)
Line 2: Passes through (−1, −3) and (1, 1)
Mathematics
1 answer:
dybincka [34]1 year ago
6 0

Answer:

The given lines are perpendicular.

Step-by-step explanation:

In the question, two lines are given as line 1 passes through (1,7) and (5,5). Whereas, line 2 passes through (-1,-3) and (1,1).

It is required to find the slope of given lines and figure out whether they are perpendicular, parallel or neither.

To solve this question, first find the slope of both lines. Check if their product is equal to -1, then they are perpendicular. If the slopes are equal the lines are parallel.

Step 1 of 2

Find the slope of first line.

$$\begin{aligned}m_{1} &=\frac{5-7}{5-1} \\m_{1} &=\frac{-2}{4} \\m_{1} &=-\frac{1}{2}\end{aligned}$$

Step 2 of 2

Find the slope of first line.

$$\begin{aligned}&m_{2}=\frac{1-(-3)}{1-(-1)} \\&m_{2}=\frac{4}{2} \\&m_{2}=2\end{aligned}$$

And

$$\begin{aligned}&m_{1} m_{2}=-\frac{1}{2}(2) \\&m_{1} m_{2}=-1\end{aligned}$$

Since, both slopes are reciprocal of each other.

Therefore, the lines are perpendicular.

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kaheart [24]

Answer:

-\frac{8}{45}

Step-by-step explanation:

Multiply the numerator by the reciprocal of the denominator.

4/5( −2/9)

7 0
3 years ago
1. m+ 10< 16
sleet_krkn [62]

Answer:

1.\ m

Step-by-step explanation:

1. Subtract 10 from both sides. Then:

m+ 10< 16\\ m+ 10-10< 16-10\\m

2. Divide both sides by -2. Notice that the direction of the symbol of the inequality will change. Then:

-2g\geq8\\\\\frac{-2g}{-2}\geq\frac{8}{-2}\\\\g\leq-4

3. Add 22 to both sides. Then:

y-22< 19\\ y-22+22

4. Divide both sides by -7. Notice that the direction of the symbol of the inequality will change. Then:

-7b>-28\\\\\frac{-7b}{-7}>\frac{-28}{-7}\\\\b

5. Subtract 30 from both sides. Then:

h+30

6. Divide both sides by -5. Notice that the direction of the symbol of the inequality will change. Then:

-5x

7. Subtract 13 from both sides. Then:

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8. Add 12 to both sides. Then:

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7 0
3 years ago
5y + 3 &gt; -7 + 13 how do i do this
ASHA 777 [7]
5y + 3 > -7 + 13

First add -7 + 13 = 6

5y + 3 > 6

Subtract 3 from both sides

5y + 3 -3 > 6 - 3

5y > 3

Divide both sides by 5

5y/5 > 3/5

y > 3/5
5 0
3 years ago
Suppose you want to study the relationship between smoking and cancer. You assume that smoking is a cause of cancer. Studies hav
finlep [7]

Answer:

The correct answer is:

In the above example cancer is an independent variable. (b)

Step-by-step explanation:

In order to explain the choice made, let m first explain what independent and  dependent variables are:

Independent variable: An independent variable is a variable that is under the direct control of the experimenter, and can be changed at will. In this example, the number of cigarettes or amount of tobacco smoked is the independent variable because it can be manipulated at will, to determine the outcome of the dependent variable.

Dependent variable: A dependent variable is a variable that the experimenter sets out to study. The independent variable is not under the direct manipulation of the experimenter but has values that come about as a result of the change of the independent variable. In this example, cancer is the dependent variable, because it is the result of the manipulation of the amount of tobacco.

Therefore, it is not true to say that cancer is the independent variable as seen in option b

6 0
2 years ago
I make $348 a week at my new job. what is my yearly salary?
rosijanka [135]

Answer:

$18,096 a year

Step-by-step explanation:

There are around 52 weeks in a year. You make $348 a week.

52 x 348 = $18,096

3 0
2 years ago
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