Practice Test 31 - Algebra 2

20 questions. Answer them in any order, then submit to see your score and every explanation.

What is $\frac{4 + 3i}{2 - i}$ expressed in standard form $a + bi$ ?
When simplifying $\frac{x^3 - 8}{x^2 + 2x + 4}$ , which structural recognition of the numerator is most helpful?
A theater charges $15 for admission and plans to increase the price by $2 each month. If $a_n$ represents the admission price in the nth month, which recursive formula correctly models this situation, and what will be the price in the 8th month?
Let the parent function be $f(x)=|x|$ . Which function represents shifting the graph of $f$ left 1 unit and down 2 units?
A teacher models the number of pages a student has left to read after $d$ days by $P(d)=120-18d.$ The student plans to finish the book in 7 days. Compare the mathematical domain and the realistic domain for this situation.
Compute the product of a complex number and its conjugate, and note it equals the modulus squared. Find $(5-4i)(5+4i)$ .
A rectangle has length $(x+3)$ inches and width $(x-1)$ inches. Write an equation for the area $A$ (square inches) in terms of $x$ , and choose appropriate axes labels and a reasonable scale to graph $A$ for $0\le x\le 10$ .
For the system (variable order $x, y, z$ ) $\begin{cases} 3x+2y-z=7 \\ -x+4y+5z=-2 \end{cases}$ what are the matrices $A$ , $X$ , and $B$ in $AX=B$ ?
The decibel level of a sound is given by $\text{dB}=10\log_{10}\left(\frac{I}{I_0}\right)$ , where $I$ is the sound intensity and $I_0$ is a reference intensity. A sound has intensity $I=2000I_0$ . Find its decibel level, rounded to the nearest tenth, and interpret the result in context.
A ball's height is modeled by $y=-x^2+6x$ and a laser beam is modeled by $y=2x$ . Where do they intersect? (Solve the system; intersection points are the solutions.) $\begin{cases} y = -x^2 + 6x \\ y = 2x \end{cases}$
A rectangle is being designed for a poster. Let $L$ = length (in inches) and $W$ = width (in inches). Constraints: - Perimeter must be at most 40 inches. - Area must be at least 75 square inches. - Both dimensions must be positive: $L>0,\ W>0$ . Which system represents these constraints?
A water tank is being drained at a constant rate modeled by $V = 500 - 25t$ , where $V$ is the volume of water in liters and $t$ is time in minutes. What does it mean that the slope $m = -25$ in this context?
In geometry, the area of a triangle can be written as $A = \dfrac{1}{2}bh$ , where $b$ is base and $h$ is height. Solve $A = \dfrac{1}{2}bh$ for $h$ .
The population of a bacteria culture doubles every 4 hours. If there are initially 250 bacteria, which equation represents the population $P$ after $t$ hours, and what would be the appropriate scale for the y-axis when graphing this relationship for the first 16 hours?
What is the conjugate of the complex number $-3+8i$ ?
Consider $f(x)=(x-3)^2+1$ with domain all real numbers. This parabola fails the horizontal line test on its full domain. Which domain restriction makes $f$ invertible?
Use the quadratic formula to solve: $2x^2 - 3x - 2 = 0$ .
A small ball is thrown upward from a platform. Its height (in meters) after $t$ seconds is modeled by $h = -4.9t^2 + 12t + 1$ . Graphing is needed for $0 \le t \le 3$ . Which option gives the correct equation and appropriate axes labels and a reasonable scale?
A medication amount remaining in the bloodstream is recorded every hour: Hour $t$ : 0, 1, 2, 3 Amount (mg): 60, 51, 43.35, 36.8475 From the table, what is the percent rate of change per hour, and is it growth or decay?
What is the 4th term (counting from the first term as term 1) in the expansion of $(x+y)^6?$ (Pascal's Triangle row 6: $1,6,15,20,15,6,1$ .)

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