Philip and his good buddy Leroy are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Philip has already finished 3 oil changes today, and can complete more at a rate of 1 oil change per hour. Leroy just came on shift, and can finish 2 oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How many oil changes will Philip and Leroy each have done? How long will that take?

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step-by-step explanation:

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).

x^3-4x^2+3x-2/x^2+1

step-by-step explanation:

factor the numerator and denominator and cancel the common factors