🧮 algebra

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

1. **State the problem:** Multiply the expressions $$\sqrt{10c^5} \cdot \sqrt{8c}$$ assuming all variables represent positive real numbers. 2. **Recall the property of radicals:**

1. **State the problem:** Multiply the expressions $$\sqrt{4n^3} \cdot \sqrt{50n}$$ assuming all variables represent positive real numbers. 2. **Use the property of radicals:** $$\

1. **State the problem:** Solve the system of equations using the elimination method. 2. **First system:**

1. **State the problem:** Graph the function $f(x) = -2 \left(\frac{1}{5}\right)^x$ and identify the asymptote.

1. The problem is to add the fractions $\frac{12}{7}$ and $-\frac{5}{7}$.\n\n2. Since the denominators are the same, we can add the numerators directly: $$\frac{12}{7} + \left(-\fr

1. **State the problem:** Simplify the expression $$\frac{m}{3} + \frac{2m}{3}$$. 2. **Formula and rules:** When adding or subtracting rational expressions with the same denominato

1. **State the problem:** Rachel loaned Adam 8510 at an interest rate of 13% for 2 years. We need to find how much Adam will pay at the end of 2 years. 2. **Formula for simple inte

1. Problemet är att beräkna arean av det markerade området som begränsas av x-axeln, grafen till funktionen $f(x) = 9x^2$, och linjen $x=2$.\n\n2. Formeln för arean under en kurva