Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. each month, he wants to complete at least 36 miles but not more than 90 miles. the system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal. 3w + 6r ≥ 36 3w + 6r ≤ 90 which combination of hours can keitaro walk and run in a month to reach his goal?

Step-by-step explanation:

The choice to this question are

The given inequalities are

Where is walk and is run.

First, we need to graph this system. The image attached shows both inequalities and the area of solution, where and .

In other words, any  point in side the intesection of shaded areas is part of the solution to this problem.

So, 2 hours walking and 12 hours running is inside the area of solution, because represents point (2,12).

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).