🧮 algebra

1. **Problem statement:** Determine which of the terms on the cards have the value 1. 2. **Recall the rules:**

1. The problem is to simplify or work with the expression $x^3$. 2. The expression $x^3$ means $x$ multiplied by itself three times: $x \times x \times x$.

1. **State the problem:** We have a function defined as $g(x) = a\cos(2x) + d$, where $a$ and $d$ are constants. We are given some values of $g(x)$ at specific $x$ values and need

1. The problem is to arrange the numbers three fourths, five sixths, four fifths, and 0.95 in order from smallest to largest. 2. First, convert all fractions to decimal form to com

1. **State the problem:** We want to express the rational function $$\frac{10 - 17x + 14x^2}{(2 + x)(1 - 2x)^2}$$ in partial fractions of the form $$\frac{A}{2 + x} + \frac{B}{1 -

1. **State the problem:** Express the rational function $$\frac{x^2 + 2x - 8}{x^3 (x^4 - 2)}$$ in partial fractions. 2. **Identify the denominator factors:** The denominator is $$x

1. **State the problem:** Andrew is thinking of a number that is greater than 40 and less than 52, and this number has 3 ones in it. 2. **Analyze the problem:** The number must be

1. **Problem 1:** Simplify the expression $$\frac{2x^4 y^{-4} z^{-3}}{3x^2 y^{-3} z^4}$$. 2. Use the quotient rule for exponents: $$\frac{a^m}{a^n} = a^{m-n}$$.

1. **State the problem:** Six friends attend a concert where each ticket costs 75 and the total parking cost is 24. They split the parking cost equally. We need to find how much ea

1. **State the problem:** Find the value of $a$ in the vertex form of a quadratic function $f(x) = a(x - h)^2 + k$ given the vertex and a point on the parabola.

1. **State the problem:** We are given a quadratic function $f(j) = j^2$ and need to complete the function table for $j = -1, 0, 1, 2$ by calculating $f(j)$ for each value. 2. **Fo

1. **State the problem:** We are given the function $f(g) = g^2 + 4$ and a table with values of $g$ as $-2$, $0$, $2$, and $4$. We need to find the corresponding values of $f(g)$ f

1. **State the problem:** Solve the compound inequality $$5k + 9 \geq 14$$ or $$-7k - 5 \geq 2$$ and graph the solution on a number line. 2. **Solve the first inequality:**

1. **State the problem:** Solve the compound inequality $$6 < k - 1 \leq 11$$ and graph the solution on a number line. 2. **Write the inequality:** $$6 < k - 1 \leq 11$$

1. **State the problem:** Solve the compound inequality $$-6 \leq \frac{5g - 8}{3} < 4$$ for $g$ and graph the solution on a number line. 2. **Recall the rule:** When solving inequ

1. **State the problem:** Solve the compound inequality $$t + 17 \leq 18 \text{ or } \frac{t + 16}{3} > 6$$ and graph the solution on a number line from 0 to 9. 2. **Solve the firs

1. **State the problem:** Solve the compound inequality $$9f - 2 > 16 \text{ or } \frac{f + 20}{2} \leq 10$$. 2. **Solve the first inequality:**

1. **State the problem:** Solve the compound inequality $$9f - 2 > 16$$ or $$\frac{f + 20}{2} \leq 10$$. 2. **Solve the first inequality:**

1. **State the problem:** Solve the compound inequality $$5 \geq \frac{3n - 2}{2} \geq -10$$ and graph the solution. 2. **Understand the inequality:** This means $$\frac{3n - 2}{2}

1. The problem is to solve the compound inequality: $$j - 16 > -10 \text{ or } 2j + 5 \leq -7$$ and then graph the solution. 2. Solve each inequality separately.

1. **State the problem:** Solve the compound inequality $$j - 16 > -10 \text{ or } 2j + 5 \leq -7$$ and graph the solution. 2. **Solve the first inequality:**