🧮 algebra

1. **State the problem:** Find the domain, range, asymptote, and y-intercept of the functions:

1. **State the problem:** The PTA needs to raise 15000 from its membership. Each membership brings in 25. They already have 2500. We want to find how many memberships, $m$, are nee

1. The problem asks to write $x^3 \cdot x^3$ without exponents and then fill in the blank for $x^3 \cdot x^3 = x^\square$. 2. Recall the exponent multiplication rule: when multiply

1. **State the problem:** Carlos has 4 tennis balls and 5 baseballs, making a total of 9 balls. We need to find fractions and comparisons of these quantities. 2. **Total number of

1. **State the problem:** We are comparing the graphs of three functions: $$f(x) = 5^x$$

1. **State the problem:** Solve the equation $3x + 1 = -44$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Subtract 1

1. **State the problem:** We are given two equations:

1. **Problem Statement:** Perform synthetic division of a polynomial by a linear divisor of the form $x - c$. 2. **Formula and Rules:** Synthetic division is a shortcut method for

1. **State the problem:** We need to divide the polynomial $5x^3 + 8x^2 - x + 6$ by the binomial $x + 2$. 2. **Formula and method:** Polynomial division can be done using long divi

1. **State the problem:** Find the roots of the quadratic function $$h(x) = 2x^2 - 8x$$.

1. **Write the equation $f(x) = x^2 + 2x - 4$ in vertex form.** The vertex form of a quadratic is $$f(x) = a(x-h)^2 + k$$ where $(h,k)$ is the vertex.

1. **State the problem:** Write the quadratic function $f(x) = x^2 + 2x - 4$ in vertex form. 2. **Recall the vertex form formula:** The vertex form of a quadratic function is $$f(x

1. The problem asks to explain why the expression $\frac{4}{3} \pi r^3$ is a monomial and to identify its degree. 2. A monomial is an algebraic expression consisting of only one te

1. The problem asks to explain why the expression $$\frac{4}{3} \pi r^3$$ is a monomial and to identify its degree. 2. A monomial is an algebraic expression consisting of only one

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^2 b^{\frac{1}{2}}}\right)^{\frac{1}{2}}$$. 2. **Write the formula and rules:** When simplifying expression

1. The problem is to solve for $h$ in an equation (not specified by the user). 2. Since the exact equation is not given, let's assume a general linear equation involving $h$, for e

1. **Problem statement:** Simplify the expression $(\sqrt{x} - 2\sqrt{y})(\sqrt{x} + 2\sqrt{y}) + (3\sqrt{x} + \sqrt{y})^2$ using distribution. 2. **Recall formulas:**

1. **Problem Statement:** Identify intervals of increase/decrease, symmetry, domain, and range for the function $f(x) = 3x^2$. 2. **Function Type:** This is a quadratic function of

1. **Problem Statement:** Identify the intervals of increase/decrease, symmetry, domain, and range for the function $f(x) = 3x - 5$. 2. **Formula and Rules:** For a linear function

1. **State the problem:** Simplify the expression $$\left(\frac{100a}{25a^{2}b^{\frac{1}{2}}}\right)^{-\frac{1}{2}}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{100a^{-2}b^{2/3}}{25a^{2}b^{-1/3}}$$. 2. **Recall the rules:**