<u>Answer:</u>
24
<u>Step-by-step explanation:</u>
Y is 60% of 40
Equation: Y = P% * X
<u>Solving our equation for Y</u>
Y = P% * X
Y = 60% * 40
<u>Converting percent to decimal:</u>
p = 60%/100 = 0.6
Y = 0.6 * 40
Y = 24
Answer:
A(0,3) B(3,4) C(2,1)
Step-by-step explanation:
when reflecting you just the change the sign if either the X or the Y. in this case it's the Y
If the line is perpendicular, then its slope is the reciprocal of the given line's slope. This new line's slope is 1/2. We plug it into slope-intercept form
y = 1/2x + b
Now plug in the given point of (2, 10) and solve for b.
10 = 1/2(2) + b
10 = 1 + b
9 = b
So your equation is y = 1/2x + 9
1.) Solve for x:
5 x + 7 = 3 x + 21
Subtract 3 x from both sides:
(5 x - 3 x) + 7 = (3 x - 3 x) + 21
5 x - 3 x = 2 x:
2 x + 7 = (3 x - 3 x) + 21
3 x - 3 x = 0:
2 x + 7 = 21
Subtract 7 from both sides:
2 x + (7 - 7) = 21 - 7
7 - 7 = 0:
2 x = 21 - 7
21 - 7 = 14:
2 x = 14
Divide both sides of 2 x = 14 by 2:
(2 x)/2 = 14/2
2/2 = 1:
x = 14/2
The gcd of 14 and 2 is 2, so 14/2 = (2×7)/(2×1) = 2/2×7 = 7:
Answer: x = 7
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2.) Solve for x:
3 x - 2 (5 - x) = 3 x - 3 (x - 10)
-2 (5 - x) = 2 x - 10:
2 x - 10 + 3 x = 3 x - 3 (x - 10)
Grouping like terms, 3 x + 2 x - 10 = (3 x + 2 x) - 10:
(3 x + 2 x) - 10 = 3 x - 3 (x - 10)
3 x + 2 x = 5 x:
5 x - 10 = 3 x - 3 (x - 10)
-3 (x - 10) = 30 - 3 x:
5 x - 10 = 30 - 3 x + 3 x
3 x - 3 x = 0:
5 x - 10 = 30
Add 10 to both sides:
5 x + (10 - 10) = 10 + 30
10 - 10 = 0:
5 x = 30 + 10
30 + 10 = 40:
5 x = 40
Divide both sides of 5 x = 40 by 5:
(5 x)/5 = 40/5
5/5 = 1:
x = 40/5
The gcd of 40 and 5 is 5, so 40/5 = (5×8)/(5×1) = 5/5×8 = 8:
<span>Answer: x = 8
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3.) Solve for x:</span>
5 (x + 1) = 3 (2 x + 3) + 5
3 (2 x + 3) = 6 x + 9:
5 (x + 1) = 6 x + 9 + 5
Grouping like terms, 6 x + 5 + 9 = 6 x + (9 + 5):
5 (x + 1) = 6 x + (9 + 5)
9 + 5 = 14:
5 (x + 1) = 6 x + 14
Expand out terms of the left hand side:
5 x + 5 = 6 x + 14
Subtract 6 x from both sides:
(5 x - 6 x) + 5 = (6 x - 6 x) + 14
5 x - 6 x = -x:
-x + 5 = (6 x - 6 x) + 14
6 x - 6 x = 0:
5 - x = 14
Subtract 5 from both sides:
(5 - 5) - x = 14 - 5
5 - 5 = 0:
-x = 14 - 5
14 - 5 = 9:
-x = 9
Multiply both sides of -x = 9 by -1:
(-x)/(-1) = -9
(-1)/(-1) = 1:
<span>Answer: x = -9</span>
Equation = 2x + 7
Y-intercept = (0,7)
