Midterm 3: Version E
For problems 1–4, perform the indicated operations and simplify.
- [latex]\dfrac{12m^3}{5n^2}\div \dfrac{36m^6}{15n^3}\cdot \dfrac{8m^4}{6n^2}[/latex]
- [latex]\dfrac{x^2+2x}{x^2+9x+14}\div \dfrac{2x^3}{2x+14}[/latex]
- [latex]\dfrac{x-3}{7}-\dfrac{x-15}{28}=\dfrac{3}{4}[/latex]
- [latex]\dfrac{\dfrac{x^2}{y^2}-36}{\dfrac{x+6y}{y^3}}[/latex]
Reduce the expressions in questions 5–7.
- [latex]\sqrt{x^7y^5}+2xy\sqrt{36xy^5}-\sqrt{xy^3}[/latex]
- [latex]\dfrac{\sqrt{7}}{3-\sqrt{7}}[/latex]
- [latex]\left(\dfrac{x^0y^4}{z^{-12}}\right)^{\frac{1}{4}}[/latex]
Find the solution set.
- [latex]\sqrt{4x-5}=\sqrt{2x+3}[/latex]
For problems 9–12, find the solution set by any convenient method.
- [latex]\phantom{1}[/latex]
- [latex]\dfrac{x^2}{3}=27[/latex]
- [latex]27x^2=-3x[/latex]
- [latex]\phantom{1}[/latex]
- [latex]x^2-11x-12=0[/latex]
- [latex]x^2+13x=-12[/latex]
- [latex]\dfrac{2}{x}=\dfrac{2x}{3x+8}[/latex]
- [latex]x^4-63x^2-64=0[/latex]
- The width of a rectangle is 5 m less than its length, and its area is 20 more units than its perimeter. What are the dimensions of this rectangle?
- Find three consecutive odd integers such that the product of the first and the third is 35 more than ten times the second integer.
- Wendy paddles downstream in a canoe for 3 hours to reach a store for camp supplies. After getting what she needs, she paddles back upstream for 4 hours before she needs to take a break. If she still has 9 km to go and she can paddle at 5 km/h on still water, what speed is the river flowing at?