Practice Test 40 - Algebra 2

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

The temperature $F$ (degrees Fahrenheit) depends on the Celsius temperature $C$ by the relationship "multiply by $\tfrac{9}{5}$ and then add 32." Write an equation relating $F$ and $C$ , and choose appropriate axes labels and a reasonable scale to graph the relationship for $-20\le C\le 40$ .
What is $x$ in $2\cdot 2^{5x}=70$ ? Express the solution as a logarithm (exact form) and then approximate using a calculator.
After restricting the domain of $f(x)=x^2$ to $x \geq 0$ so it passes the horizontal line test, what is the inverse function $f^{-1}(x)$ ?
Determine whether the system has one solution, no solution, or infinitely many solutions. $\begin{cases} 2x - 4y = 8 \\ x - 2y = 4 \end{cases}$
A savings balance is modeled by $A(t)=A_0(1.05)^t$ , where $t$ is in years. Which statement best describes what the transformation $(1.05)^t = \left((1.05)^{1/12}\right)^{12t}$ reveals about the growth?
When solving $x^2 + 6x - 1 = 0$ by completing the square, a student writes $x^2 + 6x + 9 = 1 + 9$ , then $(x + 3)^2 = 10$ . What should be the student's next step to find the exact solutions?
For the logarithmic function $f(x)=\log_5(x+1)$ , what is the domain and the vertical asymptote?
A bacteria culture has 12,000 cells at hour 0. Each hour, the number of cells increases by 8%. Which statement correctly classifies this change and gives an exponential model for the number of cells after $t$ hours?
If $a^{\log_a(7)} + \log_a(a^9) = k$ , what is the value of $k$ ?
Function $f$ is given algebraically by $f(x)=(x-2)(x+1)$ . Function $g$ is shown on the coordinate plane as a curve that crosses the x-axis at $x=-4$ and $x=3$ . Which function has the greater number of x-intercepts?
A school club is assembling care packages using granola bars and juice boxes. Let $x$ = number of granola bars and $y$ = number of juice boxes. Each granola bar costs $1.20 and each juice box costs $0.80. The club has at most $60 to spend, needs at least 50 total items, and cannot include more than 40 juice boxes. Quantities must be whole numbers and nonnegative. Which system of inequalities (with context constraints) represents this situation?
A company models the average time (in hours) needed to assemble $n$ devices by $A(n)=1.2n+5$ . Here $n$ is the number of devices assembled. Compare the mathematical domain and the realistic domain for $n$ . Which statement is correct?
Does the function $f(x)=3x^2-6x+1$ have a constant rate of change? Explain using the idea of linear vs. nonlinear functions.
A taxi company charges a flat pickup fee plus a per-mile charge. The total fare (in dollars) for a trip of $m$ miles is $F = 2.75m + 4.50$ . In this function, interpret the parameter $2.75$ in context.
The matrix equation $\begin{bmatrix}2&-1\\3&4\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}5\\7\end{bmatrix}$ represents which system of linear equations?
A quantity is multiplied by $(1.05)^t$ after $t$ years. Which expression is equivalent and reveals the daily growth factor (assume 365 days per year)?
Use logarithm properties to evaluate without a calculator: $\log_2(8\cdot 32)$
Write the exponential function $k(x)=a\cdot b^x$ that passes through $(1,9)$ and $(3,81)$ . Which formula is correct?
A student applies the Rational Zero Theorem to $f(x) = 6x^3 - 13x^2 + 6x - 1$ and creates the list: $\pm 1, \pm \frac{1}{2}, \pm \frac{1}{3}, \pm \frac{1}{6}$ . After testing $x = 1$ , the student finds $f(1) = -2 \neq 0$ . What should the student conclude?
Use technology to solve the system by the inverse-matrix method. Write it as $AX=B$ and compute $X=A^{-1}B$ . $\begin{cases} 2x+y-z=3\\ x-y+2z=5\\ 3x+2y+z=7 \end{cases}$ What is $X=\begin{bmatrix}x\\y\\z\end{bmatrix}$ ?

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