The equation y=21.2x represents Austin's earnings in dollars and cents, y, for working x hours. Find the rate of change.

Given:

The equation is

Where, y is earnings for working in dollars and cents and x is the number of working hours.

To find:

The rate of change.

Solution:

The slope intercept form of a linear function is

         ...(i)

Where, m is the slope and b is the y-intercept.

We have,

           ...(ii)

On comparing (i) and (ii), we get

Therefore, the rate of change is 21.2 dollar and cents per hour.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

there will be 35 boys in each team. : )