Part A

Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

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Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

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Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

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Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

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Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

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Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0

1 year ago

¿Cuál de los siguientes valores de n hace CIERTA

olga_2 [115]

Answer:

B

Step-by-step explanation:

n³-125=0

n³=125

n= ³√125

n=5

8 0

3 years ago

A snowstorm began on Monday evening. It snowed steadily until 6:00 am on Tuesday morning when the snow was 12 inches deep. Kevin

poizon [28]

Answer:

what is expected at 7am is 15 inches deep snow but what we have is 12 inches deep snow. The equation has failed in its prediction.

Step-by-step explanation:

In this question, we are asked to calculate if the prediction made by an equation modeled is correct.

Firstly let’s look at the equation in question;

y = 3t - 6

where y is the snow depth and t is the number of hours after midnight.

now we are looking at 7am, that’s 7 hours past 12am, meaning 7 hours after midnight.

let’s plug the value of t as 7 into the equation

y = 3(7) - 6

y = 21-6

y = 15 inches

according to the equation by Kevin, what is expected is 15 inches deep snow but what we have is 12 inches deep snow. The equation has failed in its prediction.

3 0

3 years ago

Factorise<br>3x^2+22x+35

Butoxors [25]

Answer:(3x + 7) (x +5)

Step-by-step explanation:

4 0

3 years ago

My dividend is 8 times larger than my divisor.I am an even number less than 15. What quotient am I?

Gwar [14]

You are dividing to find the answer

7 0

3 years ago