Answer:
x = -4
Step-by-step explanation:
Solve for x:
(5 x)/4 = x/2 - 3
Put each term in x/2 - 3 over the common denominator 2: x/2 - 3 = x/2 - 6/2:
(5 x)/4 = x/2 - 6/2
x/2 - 6/2 = (x - 6)/2:
(5 x)/4 = (x - 6)/2
Multiply both sides by 4:
(4×5 x)/4 = (4 (x - 6))/2
(4×5 x)/4 = 4/4×5 x = 5 x:
5 x = (4 (x - 6))/2
4/2 = (2×2)/2 = 2:
5 x = 2 (x - 6)
Expand out terms of the right hand side:
5 x = 2 x - 12
Subtract 2 x from both sides:
5 x - 2 x = (2 x - 2 x) - 12
5 x - 2 x = 3 x:
3 x = (2 x - 2 x) - 12
2 x - 2 x = 0:
3 x = -12
Divide both sides of 3 x = -12 by 3:
(3 x)/3 = (-12)/3
3/3 = 1:
x = (-12)/3
The gcd of -12 and 3 is 3, so (-12)/3 = (3 (-4))/(3×1) = 3/3×-4 = -4:
Answer: x = -4
Answer:
(-1,-1)
Step-by-step explanation:
To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2
(1+-3)/2 = -2/2 = -1
To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2
(-6+4)/2 = -2/2 = -1
(-1,-1)
3/6 = x/7
Multiply x and 6, 3 and 7:
6x = 7*3
x = 21/6
x = 7/2
Answer:
y = -(8/5)x + 3
Step-by-step explanation:
Step 1: Rewrite the given equation into slope-intercept form by solving for y
8y−16=5x
8y = 5x + 16
y = (5/8)x + 2
Perpendicular lines have slopes that are opposite reciprocals of each other. That means you take the slope, flip the fraction, and change the sign.
Here our given line is y = (5/8)x + 2 so the slope 5/8
The opposite reciprocal of 5/8 is -8/5
We set up the equation
y = -(8/5)x + b
we are given a point (x, y) of (5, -5), so plug that in and solve for b
-5 = -(8/5)(5) + b
-5 = -8 + b
3 = b
So our equations is y = -(8/5)x + 3
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