Midterm 1: Version D
- Evaluate: [latex]3b - \sqrt{b^2-4ac}[/latex] if [latex]a=4, b=4,[/latex] and [latex]c=1.[/latex]
- Solve for [latex]x[/latex] in the equation [latex]2(x - 4)+8 = -6+3(x+3).[/latex]
- Isolate the variable [latex]r_2[/latex] in the equation [latex]\dfrac{1}{R}=\dfrac{1}{r_1}+\dfrac{1}{r_2}.[/latex]
- Solve for [latex]x[/latex] in the equation [latex]\dfrac{x}{15} - \dfrac{x-3}{3} = \dfrac{1}{3}.[/latex]
- Write the equation of the horizontal line that passes through the point [latex](-2, 5).[/latex]
- Find the equation that has a slope of [latex]\dfrac{2}{3}[/latex] and passes through the point [latex](-2, 4).[/latex]
- Find the equation of the line passing through the points [latex](12, -7)[/latex] and [latex](8, -9).[/latex]
- Graph the relation [latex]y=\dfrac{2}{3}x-2.[/latex]
For questions 9 to 11, find each solution set and graph it.
- [latex]-27 \le 6x -9 \le 3[/latex]
- [latex]\left| \dfrac{2x+2}{6}\right| = 2[/latex]
- [latex]| 2x-1 | > 6[/latex]
- Graph the relation [latex]y = |2x| - 1.[/latex]
- For a given triangle, the first and second angles are equal, but the third angle is 10° less than twice the first angle. What are the measures of the three angles?
- Find two consecutive even integers such that their sum is 20 less than the first integer.
- [latex]y[/latex] varies jointly with [latex]m[/latex] and the square of [latex]n[/latex] and inversely with [latex]d.[/latex] If [latex]y = 16[/latex] when [latex]m = 3, n = 4,[/latex] and [latex]d = 6,[/latex] find the constant [latex]k,[/latex] then use [latex]k[/latex] to find [latex]y[/latex] when [latex]m = -2, n = 4,[/latex] and [latex]d = 8.[/latex]
