4x - 3y =5
3y = 4x - 5
y = 4/3 x - 5/3
Equation of the line passing through the point (-6,3) and parallel to L
a) Parallel lines have same slope so slope = 4/3
y - 3 = 4/3(x + 6)
y - 3 = 4/3 x + 8
y = 4/3 x + 11
Answer:
Equation y = 4/3 x + 11
b) Perpendicular lines, slope is opposite and reciprocal so slope = -3/4
y - 3 = -3/4 (x + 6)
y - 3 = -3/4 x - 4.5
y = -3/4 x - 1.5
Answer:
Equation y = -3/4 x - 1.5
<h3>
Answer: Choice B) x = 65, y = 10</h3>
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Work Shown:
The upper pair of angles 60 degrees and (2x-y) degrees are supplementary angles. This is because of the parallel lines. Note how they are same side interior angles. Therefore, (2x-y) and 60 combine to 180 degrees like so
(2x-y)+60 = 180
2x-y = 180-60 ... subtract 60 from both sides
2x-y = 120 ... call this equation 1
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Similarly, (2x+y) and 40 also combine to 180
(2x+y) + 40 = 180
2x+y = 180-40 ... subtract 40 from both sides
2x+y = 140 ... call this equation 2
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Line up equation 1 and equation 2. Then add straight down
That becomes 4x = 260 which solves to x = 65 when you divide both sides by 4.
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If x = 65, then,
2x-y = 120
2(65)-y = 120
130 - y = 120
-y = 120-130
-y = -10
y = 10
or
2x+y = 140
2(65)+y = 140
130+y = 140
y = 140-130
y = 10
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Either way end up with x = 65 and y = 10
Answer:
1 or 2
Step-by-step explanation:
Answer:
Length = 12 cm
Step-by-step explanation:
using the Pythagorean theorem:
Length² = 13² - 5² = 169 - 25 = 144
Length = √144 m= 12 cm
Answer:
x = number of bicycles = 35
y = number of cars = 55
Step-by-step explanation:
Let
x = number of bicycles
y = number of cars
x + y = 80 (1)
2x + 4y = 270 (2)
From (1)
x = 80 - y
Substitute x = 80 - y into (2)
2x + 4y = 270 (2)
2(80 - y) + 4y = 270
160 - 2y + 4y = 270
- 2y + 4y = 270 - 160
2y = 110
y = 110/2
y = 55
Substitute y = 55 into (1)
x + y = 80 (1)
x + 55 = 80
x = 80 - 55
x = 35
x = number of bicycles = 35
y = number of cars = 55