Midterm 1: Version D

Midterm 1 Preparation

Evaluate: $3b - \sqrt{b^2-4ac}$ if $a=4, b=4,$ and $c=1.$
Solve for $x$ in the equation $2(x - 4)+8 = -6+3(x+3).$
Isolate the variable $r_2$ in the equation $\dfrac{1}{R}=\dfrac{1}{r_1}+\dfrac{1}{r_2}.$
Solve for $x$ in the equation $\dfrac{x}{15} - \dfrac{x-3}{3} = \dfrac{1}{3}.$
Write the equation of the horizontal line that passes through the point $(-2, 5).$
Find the equation that has a slope of $\dfrac{2}{3}$ and passes through the point $(-2, 4).$
Find the equation of the line passing through the points $(12, -7)$ and $(8, -9).$
Graph the relation $y=\dfrac{2}{3}x-2.$

For questions 9 to 11, find each solution set and graph it.

$-27 \le 6x -9 \le 3$
$\left| \dfrac{2x+2}{6}\right| = 2$
$| 2x-1 | > 6$
Graph the relation $y = |2x| - 1.$
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.
$y$ varies jointly with $m$ and the square of $n$ and inversely with $d.$ If $y = 16$ when $m = 3, n = 4,$ and $d = 6,$ find the constant $k,$ then use $k$ to find $y$ when $m = -2, n = 4,$ and $d = 8.$

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