The weights and heights of six mathematics students are given in the following table:
weight (in pounds)
height (in centimeters)
165
172
123
157
212
183
175
178
165
163
147
167
in the statement, "height is a function of weight," which variable is the input and which is the output?
a.
weight is output, height is input
b.
both weight and height are the input
c.
weight is input, height is output
d.
both weight and height are the output

c.  Weight is input, height is output

Step-by-step explanation:

It is given here that "Height is a function of Weight".

which means

Thus, value of Height is depend on the value of Weight.

Thus, Weight is input variable and Height is output variable.

Hence option (c) is correct.

Further,

The variable that we can change is called the Input variable.

 The Output variable depends upon the input variable, as we change the value of the input variable the value of the output variable is also get changed.

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240