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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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Help pleaseeeeeeee.
Dmitry_Shevchenko [17]
Answer: 11x

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

Explanation:

Let L be the length of rectangle B
There are two copies of L (along the top and bottom of the rectangle). The vertical pairs of sides are both 7x each.

For the triangle, we have three sides of 12x since this is an equilateral triangle. All three sides are congruent for any equilateral triangle.

The perimeter of the triangle is
P = s1+s2+s3
P = 12x+12x+12x
P = 36x

The perimeter of the rectangle is 
P = 2*L+2*W
P = 2L+2*7x
P = 2L+14x

Since both perimeters are the same, this means 
perimeter of triangle = perimeter of rectangle
36x = 2L+14x
36x-14x = 2L+14x-14x
22x = 2L
2L = 22x
2L/2 = 22x/2
L = 11x

So the length of the rectangle, in terms of x, is 11x. This is the final answer.

Note: if we knew the value of x, then we could find the numeric value of the length for the rectangle. But since we don't know x, we leave it as 11x.

7 0
3 years ago
What is the slope-intercept equation<br> for the following line?<br> y = [?]x + []
Alexus [3.1K]

Answer:

y=-4x-3

I Hope It Helps!

7 0
3 years ago
Use the graph that shows the solution to f(x)=g(x)
Radda [10]
Add 2 to both sides and x will equal 2
5 0
3 years ago
Is the answer a b c or d???
Hoochie [10]
A) $7. 69 change she will get back when she use 50.00 for her pants and sweater
7 0
3 years ago
A manufacturer of cell phone screens is concerned because 12 percent of the screens manufactured using a previous process were r
fomenos

Answer: A.

H_0:p=0.12\\\\H_a:p

Step-by-step explanation:

Null hypothesis(H_0) : A statement describing population parameters as per the objective of the study. It usually takes "≤,≥,=" signs.  

Alternative hypothesis (H_a): A statement describing population parameters as per the objective of the study. It usually takes ">, <, ≠" signs.

Let p be the proportion of screens that will be rejected.

12 percent of the screens manufactured using a previous process were rejected at the final inspection.

(i.e. p= 0.12)

Objective of the study = whether the new process<em> reduces </em>the population proportion of screens that will be rejected

i.e. p< 0.12

So, the appropriate hypotheses to investigate whether the new process reduces the population proportion of screens that will be rejected:

H_0:p=0.12\\\\H_a:p

8 0
3 years ago
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