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]
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
first, substitute 3 for y in 14y. 14y means you are multiplying 14 and y, so when you plug in 3 for y, you're multiplying 14 and 3! :)
14y ⇒ 14(3)simplify by multiplying 14 · 3.
14(3) = 42so, when y = 3, 14y = 42.
you can check the answer by solving for y in 14y = 42.
divide both sides of the equation by 14.
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Answers
36% of 110 is 39.6
I hope I helped!!!
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A rectangular garden has dimensions of 100 feet by 10 feet. Next season, the garden is decreased to 25 of its size. What is the scale of the drawing for the new garden shown below?
A rectangle that is 8 inches long and four-fifths of an inch wide.
Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answers
Explanation: We need to find the area of the field using the side angle side method, which uses the equation (ab*sin C)/2.
Thus, we have (120*325*sin 70)/2=18324 square feet.
Farmer need 750.5 feet fencing for his triangular field.
What is triangle?"Triangle is two dimensional geometrical shape with three sides and three vertices. Sum of all the angles of a triangle is equals to 180°.
Formula used
Cosine rule
As per the diagram,
cosθ = (b² +c² -a²) / 2bc
cos 70° = 0.3420
According to the question,
Let AB = c , AC = b are given sides of measure 120 feet and 325 feet respectively.
and BC = a
Angle between given sides be θ = 70°
Substitute the value in the formula we get,
cos70° = [ (325)² +(120)² - a²] / 2(120)(325)
⇒ 0.3420 = [ 120025 - a²] / 78000
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Answers
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Answers
Answer:
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2 is incorrect
3 is incorrect
4 is incorrect
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Step-by-step explanation:
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2. 1/2(0.5+3) = 1/4+3/2 = 7/4
3. 6(0.5+4) = 27
4. 1/6(0.5+4) = 0.75
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A.62.8
B.20.9
C.41.9
D.120
Answers
Answer: a
Step-by-step explanation:
