Midterm 1: Version E
- Simplify the following:
- [latex]-(3)^2[/latex]
- [latex](- 3)^2[/latex]
- [latex]- 3^2[/latex]
- [latex]3 ( 2 + 4 ) - ( 2 \cdot 4 )[/latex]
- [latex]- | -5 + 8|[/latex]
- Solve for [latex]x[/latex] in the equation [latex]2(x - 4) + 18 = -12 + 4(x + 3).[/latex]
- Isolate the variable [latex]r_1[/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}{12} - \dfrac{x-4}{3}=\dfrac{2}{3}.[/latex]
- Find the equation of the horizontal line that passes through the point [latex](-4, -6).[/latex]
- Find the equation that has a slope of [latex]\dfrac{2}{5}[/latex] and passes through the point [latex](-1, 1).[/latex]
- Find the equation of the line passing through the points [latex](0, -1)[/latex] and [latex](2, 5).[/latex]
- Graph the relation [latex]y=\dfrac{2}{3}x + 1.[/latex]
For questions 9 to 11, find each solution set and graph it.
- [latex]-20 \le 8x - 4 \le 28[/latex]
- [latex]\left| \dfrac{2x+2}{6} \right| \le 2[/latex]
- [latex]\left| \dfrac{3x-4}{5}\right| >1[/latex]
- Graph [latex]3x - 2y < 12.[/latex]
- Find three consecutive odd integers such that the sum of the first integer, two times the second integer, and three times the third integer is 94.
- Karl is going to cut a 800 cm cable into 2 pieces. If the first piece is to be 3 times as long as the second piece, find the length of each piece.
- [latex]y[/latex] varies jointly with [latex]m[/latex] and inversely with the square of [latex]n.[/latex] If [latex]y = 12[/latex] when [latex]m = 3[/latex] and [latex]n = 4,[/latex] find the constant [latex]k,[/latex] then use [latex]k[/latex] to find [latex]y[/latex] when [latex]m = 3[/latex] and [latex]n = -3.[/latex]