Midterm 3: Version D

For problems 1–4, perform the indicated operations and simplify.

1. [latex]\dfrac{15m^3}{4n^2}\div \dfrac{45m^6}{13n^3}\cdot \dfrac{3m^4}{39n^2}[/latex]
2. [latex]\dfrac{3x^2-9x}{3x+9}\div \dfrac{x^2+2x-15}{12x}[/latex]
3. [latex]\dfrac{2}{x+4}-\dfrac{6}{x-3}=3[/latex]
4. [latex]\dfrac{\dfrac{x^2}{y^2}-9}{\dfrac{x+3y}{y^3}}[/latex]

Reduce the expressions in questions 5–7.

5. [latex]\sqrt{25y^4}+2\sqrt{49y^2}+\sqrt{25y^3}[/latex]
6. [latex]\dfrac{15}{3-\sqrt{5}}[/latex]
7. [latex]\left(\dfrac{a^0b^4}{c^8d^{-12}}\right)^{\frac{1}{4}}[/latex]

Find the solution set.

8. [latex]\sqrt{2x+9}-3=x[/latex]

For problems 9–12, find the solution set by any convenient method.

9. [latex]\phantom{1}[/latex]
   1. [latex]8x^2=32x[/latex]
   2. [latex]3x^2=48[/latex]
10. [latex]\phantom{1}[/latex]
    1. [latex]x^2=5x-4[/latex]
    2. [latex]x^2-4x+3=0[/latex]
11. [latex]\dfrac{2}{x}=\dfrac{x}{x+4}[/latex]
12. [latex]x^4-48x^2-49=0[/latex]
13. The base of a triangle is 2 cm less than its height. If the area of this triangle is 40 cm², find the lengths of its height and base.
14. Find three consecutive odd integers such that the product of the first and the third is 41 more than four times the second integer.
15. Karl paddles downstream in a canoe for 2 hours to reach a store for camp supplies. After getting what he needs, he paddles back upriver for 3 hours before he needs to take a break. If he still has 4 km to go and he can paddle at 6 km/h on still water, what speed is the river flowing at?

Midterm 3: Version D Answer Key