If y varies inversely as x. Using the coordinates (5, 3) and (x, 2.5), find the missing value x.

(6, 2.5 )

Step-by-step explanation:

Given y varies inversely as x then the equation relating them is

y = ← k is the constant of variation

To find k substitute the coordinate point (5, 3 ) into the equation, that is

3 = ( multiply both sides by 5 )

15 = k

y = ← equation of variation

Using (x, 2.5 ) with y = 2.5 , then

2.5 = ( multiply both sides by x )

2.5x = 15 ( divide both sides by 2.5 )

x = 6

Thus point is (6, 2.5 )

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.

(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