9514 1404 393
Answer:
f(x) = -1/3x +23/3
Step-by-step explanation:
You can use the linear regression function of a graphing calculator or spreadsheet to show you the equation of the line through these points:
f(x) = -1/3x +23/3
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Approaching this in the usual way, we recognize we have points ...
(-1, 8) and (5, 6)
The slope of the line through those points is ...
m = (y2 -y1)/(x2 -x1)
m = (6 -8)/(5 -(-1)) = -2/6 = -1/3
Then the point-slope equation of the line is ...
y - 8 = -1/3(x +1)
Adding 8 gives us a form we can use for a function definition:
f(x) = -1/3(x +1) +8
f(x) = -1/3x +7 2/3
Answer:
I am not sure if this is right but the answer is
The area of a circle with circumference 18π is 254.5
Answer:
y = -28 ÷ x
Step-by-step explanation:
The standard format of a inversely proportional equation goes by the format of y = k ÷ x. The question asks us to write an equation if y = 7 when x = -4 and y varies inversely with x.
So we substitute the values y = 7 and x = -4 in the equation y = k ÷ x
K = constant, we have to work this out
7 = k ÷ -4
7 × - 4 = k
k = - 4 × 7
k = -28
k = -28 So then we put this back into the original y = k ÷ x to find our final equation which is y = -28 ÷ x
Solve each problem. Volume of a Box A piece of sheet metal is 2.5 times as long as it is wide. It is to be made into a box with an open top by cutting 3 -inch squares from each corner and folding up the sides, as shown at the top of the next page. Let x
represent the width of the original piece of sheet metal. (a) Represent the length of the original piece of sheet metal in terms of x.
(b) What are the restrictions on x?
(c) Determine a function V
that represents the volume of the box in terms of x
(d) For what values of x
(that is, original widths) will the volume of the box be between 600 and 800 cubic inches? Determine the answer graphically, and give values to the nearest tenth of an inch