🧮 algebra

1. **State the problem:** Evaluate the expression $$-7^3 - 3(-4)^3$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\left(\frac{(-4)^3}{(-2)^4}\right)^2$$. 2. **Recall the rules:**

1. **State the problem:** Solve the equation $$(2^4)^{t-2} \times 2^{2t} = (2^2)^{t+2}$$ for $t$. 2. **Recall exponent rules:**

1. **State the problem:** We have two functions $f$ and $g$ given by their graphs. We need to find the domain and range of $f$, evaluate expressions involving $f$ and $g$, find inv

1. **State the problem:** Sam paid a taxi fee of 25 and gave an 18% tip. We want to create a proportion to find the tip amount $x$. 2. **Set up the proportion:** The tip percentage

1. The problem is to find the vertex of the quadratic function $$x^2 + 4x + 4$$. 2. The vertex form of a quadratic function is $$y = a(x-h)^2 + k$$, where $$(h,k)$$ is the vertex.

1. **State the problem:** Find the axis of symmetry for the quadratic function $$x^2 - 7x + 14$$. 2. **Recall the formula:** The axis of symmetry for a quadratic function $$ax^2 +

1. The problem is to find the axis of symmetry of the quadratic function $$4x^2 - 2x + 10$$. 2. The formula for the axis of symmetry of a quadratic function $$ax^2 + bx + c$$ is gi

1. **State the problem:** We are given two functions $h(x) = -5x + 1$ and $g(x) = 2x^2$. We need to find $g(h(-1))$, which means we first find $h(-1)$ and then substitute that resu

1. **State the problem:** We are given two functions $h(x) = -5x + 1$ and $g(x) = 2x^2$. We need to find the value of $h(-2) \times g(2)$. 2. **Recall the formulas:**

1. **State the problem:** We are given two functions $h(x) = -5x + 1$ and $g(x) = 2x^2$. We need to find the value of $h(7) - g(3)$. 2. **Recall the formulas:**

1. **State the problem:** We need to find $f(g(4))$ given the functions $f(x) = 2x + 7$ and $g(x) = x^2 - 1$. 2. **Understand the composition:** $f(g(4))$ means we first find $g(4)

1. **State the problem:** We are given the rational function $$f(x) = \frac{x + 4}{x^2 + 13x + 36}$$ and want to analyze its properties and graph shape. 2. **Factor the denominator

1. **State the problem:** We need to solve the inequality $b \leq 4$ and understand its graph. 2. **Formula and rules:** The inequality $b \leq 4$ means $b$ is less than or equal t

1. Problem: What is 280% of 67? 2. Formula: To find a percentage of a number, use the formula $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number}$$

1. The number 1.4142 is an approximation of the square root of 2, written as $\sqrt{2}$. 2. The exact value of $\sqrt{2}$ is an irrational number, meaning it cannot be expressed ex

1. **State the problem:** We need to find how many students out of 680 said the 4th of July was their favorite holiday, given that 35% of students chose it. 2. **Formula used:** To

1. **State the problem:** Simplify the expression \(\frac{2x + by + a}{15y} \div \frac{3y^2}{2y + b}\). 2. **Rewrite the division as multiplication:**

1. **State the problem:** Kareem pays a monthly fee of 19 plus 0.07 per minute. The total charge is at least 94.39. We want to find the possible number of minutes $m$ he used.

1. **State the problem:** Diane wants to rent a truck and compare costs between two companies. Company A charges a flat fee of 121.

1. **State the problem:** Simplify the expression $$\frac{12x^{61}}{7y^{15}} \cdot \frac{y}{8x^{27}}$$. 2. **Write the formula and rules:** When multiplying fractions, multiply num