Midterm 3: Version D
For problems 1–4, perform the indicated operations and simplify.
- [latex]\dfrac{15m^3}{4n^2}\div \dfrac{45m^6}{13n^3}\cdot \dfrac{3m^4}{39n^2}[/latex]
- [latex]\dfrac{3x^2-9x}{3x+9}\div \dfrac{x^2+2x-15}{12x}[/latex]
- [latex]\dfrac{2}{x+4}-\dfrac{6}{x-3}=3[/latex]
- [latex]\dfrac{\dfrac{x^2}{y^2}-9}{\dfrac{x+3y}{y^3}}[/latex]
Reduce the expressions in questions 5–7.
- [latex]\sqrt{25y^4}+2\sqrt{49y^2}+\sqrt{25y^3}[/latex]
- [latex]\dfrac{15}{3-\sqrt{5}}[/latex]
- [latex]\left(\dfrac{a^0b^4}{c^8d^{-12}}\right)^{\frac{1}{4}}[/latex]
Find the solution set.
- [latex]\sqrt{2x+9}-3=x[/latex]
For problems 9–12, find the solution set by any convenient method.
- [latex]\phantom{1}[/latex]
- [latex]8x^2=32x[/latex]
- [latex]3x^2=48[/latex]
- [latex]\phantom{1}[/latex]
- [latex]x^2=5x-4[/latex]
- [latex]x^2-4x+3=0[/latex]
- [latex]\dfrac{2}{x}=\dfrac{x}{x+4}[/latex]
- [latex]x^4-48x^2-49=0[/latex]
- 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.
- Find three consecutive odd integers such that the product of the first and the third is 41 more than four times the second integer.
- 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?