Exam 7: Rational Expressions and Applications

Solve the problem. -A lot is in the shape of a right triangle. The shorter leg measures 60 meters. The hypotenuse is 20 meters longer than the length of the longer leg. How long is the longer leg?

Solve the problem. -The height of a box is 4 inches. Its length is 4 inches more than its width. Find the length if the volume is 180 cubic inches.

Factor completely. If the polynomial is prime, say so. -3 - 24

Answer the question. -The monomial 16x²y⁸ is a perfect square.True or False?

Solve the problem. -A rectangle has a length of x + 3 and a width of x - 3, and has an area of 40 square units. Find the length and width of the rectangle. (A = LW)

Solve the problem. -The product of two consecutive integers is 8 less than 8 times their sum. Find the integers.

Factor completely. If the polynomial is prime, say so. -25 - 80xy + 64

Factor the polynomial completely. -1000 - 1

Factor by grouping. - - 4r + rt - 4t

Solve the problem. -What pair of integers would be used to rewrite the middle term when factoring 22 - 152x + 120 by grouping?

Solve the problem. -The diagram below shows the side view of a plan for a slanted roof. Find the unknown length in this roof plan. Round approximations to the nearest tenth. 20 ft

Choose the one alternative that best completes the statement or answers the question.Solve the equation. -r(r - 18) = -81

Choose the one alternative that best completes the statement or answers the question.Determine the correct factored form of the given equation. -4x² + 4x - 24

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Maria's teacher asked her to solve the following problem: "One leg of a right triangle is 5 m longer than the other. The length of the hypotenuse is 25 m. Find the lengths of the legs." Maria called the legs x and y and translated the problem into the following equation: After that she was unsure of how to proceed. Why is Maria's equation not very useful? Write the correct equation and find the solution to the problem showing all the steps of your work.

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Tom's teacher asks him to solve the following problem: "The product of two consecutive even numbers is 168. Find the numbers." Tom rewords the problem and translates to the following equation: Why is this equation not correct and what would the correct equation be?

Factor completely. If the polynomial is prime, say so. -25 - 40m + 7

Factor out the greatest common factor. - + 21

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Explain the error in the following: + 2x - 15 = (x - 5)(x + 3)

Factor out the greatest common factor. -25y - 100

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -What steps would you take to factor ?