31 Midterm 1: Version A
- Evaluate: \(-b - \sqrt{b^2 - 4ac}\) if \(a=4,\) \(b=-3,\) and \(c=-1.\)
- Solve for \(x\) in the equation \(2(x - 5) - 85 = 3 - 9(x + 6).\)
- Isolate the variable \(b\) in the equation \(A = \dfrac{h}{B-b}\).
- Solve for \(x\) in the equation \(\dfrac{x+1}{4} - \dfrac{5}{8} = \dfrac{x-1}{8}\).
- Write an equation of the vertical line that passes through the point \((-2, 5).\)
- Find the equation that has a slope of \(\dfrac{2}{5}\) and passes through the point \((-1, -2).\)
- Find the equation of the line passing through the points \((-2, 0)\) and \((6, 4)\).
- Graph the relation \(y = \dfrac{2}{3}x - 1\).
For questions 9 to 11, find each solution set and graph it.
- \(6x - 5(1 + 6x) > 67\)
- \(-10 \le 4x - 2 \le 14\)
- \(\left| \dfrac{3x+2}{5} \right| = 2\)
- Graph the relation \(5x + 2y < 15.\)
- Find two numbers such that 5 times the larger number plus 3 times the smaller is 47, and 4 times the larger minus twice the smaller is 20.
- Karl is going to cut a 36 cm cable into 2 pieces. If the first piece is to be 5 times as long as the second piece, find the length of each piece.
- \(y\) varies jointly with \(m\) and \(n\) and inversely with the square of \(d.\) If \(y = 3\) when \(m = 2,\) \(n = 8,\) and \(d = 4,\) find the constant \(k,\) then use \(k\) to find \(y\) when \(m = 15,\) \(n = 10,\) and \(d = 5.\)
