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Fofino [41]
1 year ago
9

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

Mathematics
1 answer:
slega [8]1 year ago
6 0

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

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

-------------

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}\\\\

-------------

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}\\\\

-------------

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\\\\

------------------------------

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.

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Answer:

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Changing the grouping of the factors, but does not change the value of the product.

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8 0
3 years ago
Fido weighs 26 pounds more then fifi fifi weighs12 pounds less than rover if the sum of their weights is 71 how much does fifi w
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Answer:

11 pounds

Step-by-step explanation:

Let the weight of Rover is x pounds.

As Fifi weighs 12 pounds less than Rover, so,

The weight of Fifi = x-12...(i)

As Fido weighs 26 pounds more then Fifi, so,

The weight of Fido = (x-12)+26=x+14.

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x+(x-12)+(x+14)=71

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3x=71-2=69

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Step-by-step explanation:

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You are choosing between two different cell phone plans. The first plan charges a rate of 24 cents per minute. The second plan c
kupik [55]

Answer:

C_{1}(t) = 0.24*t

C_{2}(t) = 34.95 + 0.12*t

291.25 talk minutes would produce the same cost for both plans.

Step-by-step explanation:

Both plans can be modeled by a first order equation in the following format:

C(t) = C_{0} + f*t

In which C_{0} is the initial cost, f is the fee that is paid for each minute, and t is the number of minutes.

Cost of the first plan:

The problem states that the first plan charges a rate of 24 cents per minute, which means that f = 0.24.There is no initial cost, so C_{0} = 0.

The equation for this plan is:

C_{1}(t) = 0.24*t

Cost of the second plan:

The problem states that the second plan charges a monthly fee of $34.95 plus 12 cents per minute. So C_{0} = 34.95 and f = 0.12

The equation for this plan is:

C_{2}(t) = 34.95 + 0.12*t

Find the number of talk minutes that would produce the same cost for both plan:

This is the instant t in which:

C_{1}(t) = C_{2}(t)

0.24t = 34.95 + 0.12t

0.12t = 34.95

t = \frac{34.95}{0.12}

t = 291.25

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