Exam 12: Prerequisites

Solve the problem. -A flare fired from the bottom of a gorge is visible only when the flare is above the rim. If it is fired with an initial velocity of $128 \mathrm { ft } / \mathrm { sec }$ , and the gorge is $192 \mathrm { ft }$ deep, during what interval can the flare be seen? $\left( h = - 16 t ^ { 2 } + v _ { 0 } t + h _ { 0 } \right)$

Solve the inequality algebraically. Write the solution in interval notation. - $| 4 - 4 x | - 3 < 4$

Solve the problem. -The area of a square is numerically 4 less than the perimeter. Find the length of the side, if the side is greater than 1.

Find the center and radius of the circle. - $( x + 7 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$

Write the expression in the form bi, where b is a real number. - $\sqrt { - 272 }$

Use words to describe the interval of real numbers. -

Find the value of x or y so that the line through the pair of points has the given slope. - $( - 1,2 )$ and $( 4 , y ) ; m = - 2$

Determine whether the equation is linear in x. - $x ^ { 2 } + 8 x = x ^ { 3 } + 2$

Describe and graph the interval of real numbers. - $- 3 < x \leq 4$

Solve the equation. - $\frac { x + 7 } { 8 } = \frac { x + 8 } { 9 }$

Solve the inequality and draw a number line graph of the solution. - $4 x - 3 \leq 8 x + 9$

Determine the equation of the line described. Put answer in the slope-intercept form, if possible. -Through $( 3 , - 6 )$ , perpendicular to $- 3 x + 2 y = - 21$

Write the statement using absolute value notation. -The distance between $y$ and $- 7$ is greater than 3 .

Find the standard form equation for the circle. -Center $( 0,2 )$ , radius 4

Solve the equation graphically by finding x-intercepts. - $x ^ { 2 } + 36 = 12 x$

Perform the indicated operation. Write the result in standard form. - $( 4 - 9 i ) ^ { 2 }$

Find the value of x and the value of y for which (x, 2) and (8, y) are points on the graph. - $2 x - 3 y = 9$

Solve the equation. - $13 ( x - 52 ) = 26$

Write the sum or difference in the standard form a + bi. -(-5 + 4i) - 7

Solve the equation by extracting the square roots. - $3 y ^ { 2 } - 12 = 3 - 3 y ^ { 2 }$