Practice Test 61 - Algebra 2

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

Find the modulus of the complex number $z = 6 - 8i$ . (Recall: $|a+bi|=\sqrt{a^2+b^2}$ , the distance from the origin to $(a,b)$ on the complex plane.)
A radioactive substance has a half-life of 5 years. If there are initially 800 grams of the substance, which function models the amount remaining after $t$ years?
Determine the inverse function for $f(x)=3x-7$ .
A student is choosing how many hours to spend tutoring in math and science this week. Let $x$ be hours of math tutoring and $y$ be hours of science tutoring. Constraints: - Total tutoring time is at most 12 hours: $x+y\le 12$ . - The student wants at least twice as much math as science: $x\ge 2y$ . - At least 3 hours of science: $y\ge 3$ . - Non-negativity: $x\ge 0$ , $y\ge 0$ . Determine which solutions are viable: $(6,3)$ , $(5,3)$ , $(8,4)$ .
The function $p(x)$ satisfies $p(-x) = -p(x)$ for all $x$ . If $h(x) = p(x-3) + 2$ , which property does $h(x)$ possess?
Write the system as $AX=B$ (use variable order $x, y, z$ ): $\begin{cases} -x + 2y + z = 3 \\ 4x - y = 0 \\ 2x + 5y - 3z = -7 \end{cases}$
A number and its reciprocal have a sum of $\frac{10}{3}$ . Write and solve an equation to find the number. Let $x$ = the number, with $x\ne 0$ .
A tank is being filled by two hoses. Hose A can fill the tank in 6 hours, and Hose B can fill the tank in 8 hours. Write and solve an equation to find how long it takes to fill the tank if both hoses run together. Let $t$ = the number of hours to fill the tank together.
A profit function is $P(x)=x^2-8x+15$ , where zeros represent break-even points. Factor $P(x)$ and find the break-even x-values.
Describe the end behavior of the exponential function $h(x)=5(0.7)^x$ . (Relate to the parent function $y=(0.7)^x$ .)
In the expression $2x^3 - 5x^2 + x - 8$ , how many terms are there, and what are they? (Remember: terms are separated by $+$ or $-$ , and the sign belongs to the term.)
The function $g(x)=-2x^3+5x$ models the net water flow rate (in liters/minute) into a tank as a function of valve setting $x$ . Describe the end behavior of $g$ .
A quantity $Q$ follows the pattern $Q_{n+1}=0.92\,Q_n$ each week. What percent does the quantity change each week, and is it growth or decay?
Use Pascal's Triangle (row 5: $1,5,10,10,5,1$ ) to expand $(x+y)^5.$
From the graph, determine if the rate of change is constant. The curve passes through $(0,0)$ , $(1,1)$ , $(2,4)$ , and $(3,9)$ and is smooth and curved upward (not a straight line).
A water tank is being filled at a constant rate. The volume of water (in gallons) after $t$ minutes is $V(t)=25t+10.$ The tank is monitored from $t=0$ minutes until $t=18$ minutes. What domain makes sense for this situation, and should the graph be discrete points or continuous?
Complete the square: Rewrite $x^2+y^2-4x+8y=5$ in standard form and identify $r^2$ .
A point $(a,b)$ on the complex plane represents the complex number $a+bi$ . Which complex number corresponds to the point $(-2,-7)$ ?
All points $(x,y)$ that are 6 units from the origin form a circle. 1) Write an equation in two variables for this circle. 2) Choose the best graph setup (labels and scale) to draw it accurately. Which choice is correct?
Graph $f(x)=\frac{(x-4)(x+1)}{(x-2)(x+3)}$ by identifying its zeros, vertical asymptotes, and horizontal asymptote.

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