Lines a b c and d are shown below. Which lines are parallel? Which line are perpendicular? Explain and jutsify your answer using slopes
Answers
Answer:
Lines A and C are parallel
Lines B and D are perpendicular
Step-by-step explanation:
Given
See attachment for lines A to D
Required
Determine the parallel and perpendicular lines
To start with, we calculate the slope of each line.
Line A
The points on line A are:
[tex](x_1,y_1) = (3,-4)[/tex]
[tex](x_2,y_2) = (-1,2)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 - (-4)}{-1 - 3}[/tex]
[tex]m = \frac{2 +4}{-4}[/tex]
[tex]m = \frac{6}{-4}[/tex]
[tex]m_1 = -\frac{3}{2}[/tex]
Line B
[tex](x_1,y_1) = (-1,8)[/tex]
[tex](x_2,y_2) = (2,6)[/tex]
Calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6 - 8}{2 -(-1)}[/tex]
[tex]m = \frac{-2}{2 +1}[/tex]
[tex]m_2 = -\frac{2}{3}[/tex]
Line C
[tex]y - 9 = -\frac{3}{2}(x + 8)[/tex]
Open bracket
[tex]y - 9 = -\frac{3}{2}x -\frac{3}{2}* 8[/tex]
[tex]y - 9 = -\frac{3}{2}x -3* 4[/tex]
[tex]y - 9 = -\frac{3}{2}x -12[/tex]
Make y the subject
[tex]y = -\frac{3}{2}x -12+9[/tex]
[tex]y = -\frac{3}{2}x -3[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_3 = -\frac{3}{2}[/tex]
Line D
[tex]12x - 8y = 40[/tex]
Subtract 12x from both sides
[tex]12x-12x - 8y = -12x+40[/tex]
[tex]- 8y = -12x+40[/tex]
Divide through by -8
[tex]\frac{- 8y}{-8} = \frac{-12x}{-8}+\frac{40}{-8}[/tex]
[tex]y= \frac{12x}{8}-\frac{40}{8}[/tex]
[tex]y= \frac{3}{2}x-5[/tex]
The slope intercept of an equation is: [tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
By comparison:
[tex]m_4 = \frac{3}{2}[/tex]
So, the slopes of the lines are:
[tex]m_1 = -\frac{3}{2}[/tex] [tex]m_2 = -\frac{2}{3}[/tex] [tex]m_3 = -\frac{3}{2}[/tex] [tex]m_4 = \frac{3}{2}[/tex]
Lines with the same slope are parallel.
So:
Lines A and C with slope of [tex]-\frac{3}{2}[/tex] are parallel
Lines with the following relationship are perpendicular:
[tex]m * M = -1[/tex]
Lines B and D are perpendicular because:
[tex]-\frac{2}{3} * \frac{3}{2} = -1[/tex]
[tex]-\frac{6}{6} = -1[/tex]
[tex]-1 = -1[/tex]
Related Questions
is this right re answer what's wrong please !?
Answers
Answer:
explination...
Step-by-step explanation:
so from how i’m understanding it, it would be 12(90) + 20(121).
so 12 x 90 is 1080. so that’s already a good amt, but then 20 x 121 is 2420. now if we add those together,
2420
+1080
-————
3500
so instead of there being more money than she spent, she actually gets the same amount back. so just rearange what’s you out to make sense in a way that matches the problem and you should be good (that was saying it nicely sorry if that seemed rude haha)
Can someone please help me. I’ll mark you brainiest.
Answers
Answer:
$47,682.78
Step-by-step explanation:
future value: F = $64,700
present value: P = x
annual interest rate: r = 2.18%
compounding periods per year: n = 365
[tex] F = P(1 + \dfrac{r}{n})^{nt} [/tex]
[tex] 64,700 = P(1 + \dfrac{0.0218}{365})^{365 \times 14} [/tex]
[tex] 64,700 = P(1 + 0.0000597260274)^{5110} [/tex]
[tex] 64,700 = P(1.0000597260274)^{5110} [/tex]
[tex] 64,700 = P(1.356883989) [/tex]
[tex] P = 47,682.78 [/tex]
Answer: $47,682.78
What point must a proportional equation pass through?
Answers
Answer:
A graph of a proportional relationship must pass through (0, 0).
Step-by-step explanation:
Each point (or pair) in a proportional relationship must share the same difference. 2
Find the area of parallelogram ABCD given me A = 300 and the following measures.
AB = 10 in., AD= 6 in
A-
30 in
3013 in 60 in
Answers
Answer:
30 in²
or
60 inches
Hope this helps ^-^
Can someone explain why 12/9 is correct. Will mark brainliest.
Answers
Answer:
Cause u got confused with the numbers you had to switch them up, i dont know what you did wrong but it was the other way around.
Step-by-step explanation:
1
2
х
-2
0
N
4
6
g(x)
4
1
-2
-5
-8
Answers
3
4 -
8
5
1 -
8 797968686
Answers
What is the anwser to: h + 5.7 = −5.7
Answers
-11.4
explanation:
h + 5.7 = -5.7
subtract 5.7 from both sides
h = -11.4
Answer:
h=-11.4
Step-by-step explanation:
because, 5.7+-5.7=-11.4
What is 9 to the power of 9?
Answers
Answer: the answer is 387,420,489
Step-by-step explanation:
Evaluate: 8×6+(12-4)÷2
Answers
Answer:
52
Step-by-step explanation:
I want to explain why so, first subtract 4 from 12 then youll get 8 the divide it by 2 and get 4 so then evaluate 8 x 6 which is 48 then add it to 4 to get the answer of 52
Answer:
The correct answer is 52
Step-by-step explanation:
HAVE A GOOD DAY!
What is the x value in the follow system?
3x - y = 7
2x + y = 3
Answers
Answer:
x=2
Step-by-step explanation:
5 more than the product of 12 and 8
Answers
Select all possible solutions
help!
Answers
You can type 40 words per minute. How many words can you type in 10 minutes?
Answers
400, cus 40*10=400. Brainiest if possible, and tysm!
Answer:
40 * 10 = 400
Step-by-step explanation:
You have to multiply to get the answer :)
Hope yall have a awesome and wonderful day
Write an expression equivalent to 12+5t−4+15t+1
Answers
Answer:
20t + 9
Step-by-step explanation:
12+5t−4+15t+1
20t + 9
(Simplified version)
Answer:
The answer is 20t+9
Step-by-step explanation:
An angle measures 2° more than the measure of its supplementary angle. What is the measure of each angle?
Answers
Answer:
182
Step-by-step explanation:
is what that is plus 2
what is 4x+3x-12+1x
Answers
Answer:
8x-12
Hope it helped plz mark me brainliest PlzPlz
Answer:
8x-12
Step-by-step explanation:
You need to find a number/numbers that have the same variable if the variable is the same then you can add or subtract them
You can add 4x, 3x and 1x
4x plus 3x plus 1x is 8x
Since -12 is alone you can leave it as it is
8x-12
A bag contains 6 red marbles , 6 purple marbles, and 6 yellow marbles. What is the probability of randomly selecting a yellow marble from the bag?
Answers
Answer:
1/3
Step-by-step explanation:
each color takes up 1/3 of the bag
Answer:1/3
Step-by-step explanation:6x6x6=18 divided by 6=3
Pleasee helpp answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
x = 132º
Step-by-step explanation:
the sum of two angles on the same side is 180º so...
x + 48º = 180º subtract 48º from both sides
x = 132º
Find the amount Enca owes at the end of 3 years if $6500 is loaned to her at a rate of 4% compounded monthly
Answers
Answer:
7311.616
Step-by-step explanation:
6500 x 1.04^3
find x=, if x-12=24 now!?
Answers
Answer:
Answer is 36
Step-by-step explanation:
Trust me
Answer:
36 because 24 + 12 = 36
11g − 5g + –17g − –7g = –12
Answers
Answer:
g=3
Step-by-step explanation:
11g-5g+-17g-(-7g)=-12
Add the like terms (nice that in this case they are all on the same side)
6g+-17g-(-7g)=-12
-11g-(-7g)=-12
-4g=-12 Now we divide (phew that was a lot of negatives XD)
g=3
Which rule describes the composition of transformations that maps figure ABCDE to figure A" B" C" D" E"?
Answers
Answer:
It would be the fourth choice.
Step-by-step explanation:
To get ABCDE to A'B'C'D'E', you need to reflect the shape across line M. Then to go from A'B'C'D'E' to A''B''C''D''E'', you need to rotate about point C 180⁰.
It was first reflected across the x axis which would be line m. And since point c is the same place for the two bottom images , after the reflection it was rotated on point c.
The answer should be the 4th choice
which equation represents the line that has a slope of 4 and passes through the point (2, 7)?
(A) y = 4x - 1
(B) y = 4x + 15
y=x+4
D y =
= 2x-4
Answers
Answer:
A) y = 4x - 1
Step-by-step explanation:
y = mx + b
y = 4x + b
7 = 4(2) + b
7 = 8 + b
-1 = b
y = 4x - 1
The ice cream vendor 's cold box holds 24 ice cream cups. The
freezer has 8 cases of ice cream each with 48 cups. How many
trips to the freezer will the vendor make if he sells all the ice cream?
Answers
Answer:
16
Step-by-step explanation:
24/8=3
48/3=16
PLEASE PLEASE HELP ME IM BEGGING
Answers
Step-by-step explanation:
D=M/V
M=D*V
V= M/D
M is mass
D is Density
V is Volume
Substitute and solve
What is 11.69517 rounded to the nearest thousandth?
Answers
The given number 11.69517 rounded to the nearest thousandth is 11.695.
What is the rounding off the number?
Rounding off a number means approximating it to a certain degree of accuracy by replacing it with another number that is nearly equal to it but has a shorter, simpler, or more explicit representation.
To round 11.69517 to the nearest thousandth, we look at the digit in the fourth decimal place, which is 5. Since 5 is greater than or equal to 5, we round up the digit in the third decimal place (9) by adding 1 to it. Therefore, 11.69517 rounded to the nearest thousandth is 11.695.
Hence, the given number 11.69517 rounded to the nearest thousandth is 11.695.
To learn more about rounding off the number, visit:
https://brainly.com/question/28128444
#SPJ1
Answer:
11.695
Step-by-step explanation:
The sum of two number is 65 and their difference is 5.Set up and solve a system of equations to find the two number.Show work
Answers
Answer:
it 60
Step-by-step explanation:
60
Someone help with this please
Answers
Answer:
The answer is the last one!
Step-by-step explanation:
x is the domain and y is the relation
-Sumin <3
Solve for t. If the answer is a decimal, round to the nearest tenth.
Asking again please no answered it :(
More points this time tho
Answers
Step-by-step explanation:
By Pythagoras' Theorem,
t² = 13² - 12²
=> t² = 169 - 144 = 25
=> t = 5 (as t is non-negative).