🧮 algebra

1. **State the problem:** We need to find the value of $x$ such that $f(x) = 4$ given the function $f(x) = 2x + 2$. 2. **Write the equation:** Set $f(x)$ equal to 4:

1. **State the problem:** We are given the linear equation $y = -4x + 5$ and need to understand its graph and key features. 2. **Formula and rules:** This is a linear function in s

1. **Problem:** A bag of popcorn contains 483 calories and serves 3.5 people. How many calories are in each serving? 2. **Formula:** To find calories per serving, divide total calo

1. **Problem:** A bag of popcorn contains 483 calories and serves 3.5 people. How many calories are in each serving? 2. **Formula:** To find calories per serving, divide total calo

1. The problem asks for the vertex of the graph of the function $f(x+3)$. 2. The vertex of a function $f(x)$ is the point where the graph changes direction, often given as $(h, k)$

1. **State the problem:** We need to find the value of the function $f(x) = -x^2 + 3x - 1$ at $x = -4$. 2. **Write the formula:** The function is given by

1. **State the problem:** Create a polynomial function in factored form with three real zeros based on the birthday 05/27/07. 2. **Identify the zeros:** The zeros are 5 (month), 27

1. **State the problem:** We know that 42 students own their instrument, which is 37.5% of the total number of students in the band. We need to find the total number of students. 2

1. **Determine if each number is rational or irrational:** a) $\sqrt{\frac{49}{16}}$

1. **State the problem:** Calculate the gross pay for the week given hourly wage, hours worked, and tips. 2. **Formula:** Gross pay = (Hourly wage × Hours worked) + (Percentage of

1. **State the problem:** Calculate the gross pay for the week given the hourly wage and work hours. 2. **Given:** Hourly wage = 13 per hour.

1. **State the problem:** We have a polynomial $g(x)$ and know the remainders when divided by two linear polynomials: - When divided by $x+2$, remainder is $-1$.

1. **State the problem:** Simplify the expression $2^{4x-1}$ and identify which of the given options it equals. 2. **Recall the properties of exponents:**

1. Das Problem lautet: Löse die Aufgaben. Da keine spezifische Aufgabe gegeben ist, kann ich nur allgemeine Hinweise geben. 2. Um eine algebraische Gleichung zu lösen, verwendet ma

1. **Problem statement:** A freezer starts at $-14^\circ C$ and warms up by $3^\circ C$ per hour after being unplugged. When the temperature rises above $0^\circ C$, it is plugged

1. **State the problem:** We need to graph the union of the inequalities $x + y \leq -5$ or $x - y \geq 7$.

1. **State the problem:** Factor the polynomial $$125j^2 - 5$$ completely. 2. **Identify common factors:** Both terms have a common factor of 5.

1. **State the problem:** Factor the quadratic expression $$4m^2 + 36m + 80$$ completely. 2. **Identify the common factor:** Notice that each term has a common factor of 4.

1. **State the problem:** Factor the quadratic expression $2m^2 - 3m - 2$ completely. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. **State the problem:** Factor the quadratic expression $w^2 + 10w + 16$ completely. 2. **Recall the factoring formula:** For a quadratic $w^2 + bw + c$, we look for two numbers

1. **State the problem:** We need to find which expressions are equivalent to $$-5n^2(3n^2 - 6n)$$. 2. **Use the distributive property:** Multiply $$-5n^2$$ by each term inside the