🧮 algebra

1. The problem states that we will not put brackets around variables in expressions. 2. This means when writing algebraic expressions, variables like x, y, or z will be written pla

1. **Problem statement:** We have a cubic polynomial $f(x)$ such that:

1. The problem is to simplify the nested square root expression $$\sqrt{13 + 4\sqrt{3}}$$. 2. We try to express it in the form $$\sqrt{a} + \sqrt{b}$$ where $$a$$ and $$b$$ are pos

1. The problem is to factor the expression $4a5 + 3c$. 2. First, interpret the expression correctly: $4a5$ means $4 \times a \times 5$, which simplifies to $20a$.

1. **Problem statement:** We have a cubic polynomial $f(x)$ such that:

1. **Problem 5:** Identify which graph represents the polynomial function $f(x) = 2x^3 - 5x^2 + 4x + 1$. - The function is a cubic polynomial with leading coefficient positive ($2$

1. The problem is to find the equation of the line passing through the points $(4, -3)$ and $(10, -12)$. 2. First, calculate the slope $m$ using the formula:

1. **State the problem:** Find the slope of the line segment connecting the points $(a,b)$ and $(-a,b)$. Interpret the meaning of the slope. 2. **Recall the slope formula:** The sl

1. **Problem 10:** Solve for $x$ in the equation $$\frac{2x + 4}{3} - \frac{x}{2} = \frac{3}{2}.$$ Step 1: Find a common denominator to combine terms. The denominators are 3 and 2,

1. **State the problem:** Define what a polynomial function is. 2. **Explanation:** A polynomial function involves variables raised to non-negative integer powers combined using ad

1. Simplify: $a^3 \times a^2$ Using the law of exponents for multiplication with the same base, add the powers:

1. Stating the problem: Solve the equation $$\frac{x-1}{x-4} = \frac{2}{4}$$. 2. Simplify the right side: $$\frac{2}{4} = \frac{1}{2}$$.

1. **Problem b:** Elena has 75 pounds. How many foam fingers can she buy if each costs 10 pounds? 2. To find the number of foam fingers Elena can buy, divide her total money by the

1. Stating the problem: Solve the equation $$\frac{x}{2} - 6 = 8 - \frac{2x}{3}$$ for $x$. 2. Eliminate the fractions by multiplying every term by the least common denominator (LCD

Problem: Solve the equation $x/2 - 6 = 8 - 2x/3$. 1. Move terms to combine like terms.

1. Problem: Determine the domain, range, and whether the relation \{(3,1),(5,2),(7,3),(9,4),(12,4)\} is a function. - Domain: The set of all first elements (x-values): $\{3,5,7,9,1

1. **State the problem:** Solve the system of equations using the elimination method to eliminate $y$: $$\begin{cases} 2x + 3y + z = 13 \\ 3x + 2y + 4z = 17 \\ 4x + 5y + 2z = 24 \e

1. The problem asks to convert the mixed number $2 \frac{4}{9}$ into a decimal. 2. First, convert the fraction $\frac{4}{9}$ to a decimal. Since $9$ is a denominator that produces

1. **Identify whether the functions are injective, surjective, or bijective:** a) $f : \mathbb{R} \to \mathbb{R}, f(x) = x^2 + 4$

1. **State the problem:** Expand and simplify the expression $2(x + 4) + 1$. 2. **Expand the expression:** Use the distributive property to multiply 2 by each term inside the paren

1. Problem: Find the determinant of matrix $$A = \begin{pmatrix} 2 & -1 & 4 \\ -4 & 3 & 0 \\ 5 & -2 & 1 \end{pmatrix}$$. Step 1: Use the formula for the determinant of a 3x3 matrix