45 divided by .5 equals 86
86 times .5 equals 43
answer is 86
Answer: 7 multiple choice questions and 8 free response questions
Step-by-step explanation: m is the number of multiple choice questions and f is the number of free response questions.
m+f=15
m+2f=23
You can subtract the first equation from the second, and get f=8
m+8=15
m=7
Answer:
L' = (-36, 0)
Step-by-step explanation:
If the point (x, y) is dilated by a scale factor of k about the center (0, 0), then its image is the point (kx, ky)
∵ A dilation has a center (0, 0)
∵ The point L is (-4, 0)
∴ x = -4 and y = 0
∵ The scale factor of dilation is 9
∴ k = 9
→ By using the rule above
∵ kx = 9(-4) = -36
∵ ky = 9(0) = 0
∵ The image of the point L is (kx, ky)
∴ L' = (kx, ky)
∴ L' = (-36, 0)
Answer:
2
Step-by-step explanation:
For a quadratic function the average rate of change on an interval is the rate of change at the midpoint of the interval. The rate of change of a function is given by its derivative.
The derivative of f(x) = x^2 is f'(x) = 2x. The midpoint of the interval is (4+(-2))/2 = 1. Then the average rate of change is ...
f'(1) = 2(1) = 2
The average rate of change of f(x) on [-2, 4] is 2.
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<em>Alternate solution</em>
The average rate of change is the slope of the line between the end points of the interval:
m = (y2 -y1)/(x2 -x1)
m = (f(4) -f(-2))/(4 -(-2)) = (20 -8)/(6) = 2
The average rate of change on [-2, 4] is 2.
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The attached graph shows the points on the curve and a line with slope 2 between them. It also shows the various slope calculations.
Answer:
see attached
Step-by-step explanation:
The line at the lower left of the shaded region is x+y=12. The shaded area is above that line because is represents a minimum amount of exercise.