🧮 algebra

1. **State the problem:** Solve for $y$ in the equation $$12 = - \frac{4}{5} y$$. 2. **Isolate $y$:** To solve for $y$, divide both sides of the equation by $-\frac{4}{5}$.

1. **State the problem:** We need to find the slope and y-intercept of the line given by the equation $$y = 4 - 7x$$. 2. **Rewrite the equation in slope-intercept form:** The slope

1. **State the problem:** We are given the quadratic function $$y = x^2 - 9x + 14$$ and need to find the x-coordinate of the turning point using symmetry. 2. **Recall the symmetry

1. **State the problem:** Given the function $f(x) = -x^2 + 2x + 3$, find points $A$, $B$, and $C$ where the graph cuts the axes, then find the area of triangle $\Delta ABC$, and f

1. **State the problem:** We need to graph the solution set of the system of inequalities:

1. **State the problem:** Solve the equation for $t$ given by

1. The problem states that the sequence starts at 14 and increases by 8 each time. This is an arithmetic sequence with first term $a_1=14$ and common difference $d=8$. 2. The $n$th

1. The problem is to find the next number in the sequence: 13, 10, 6, 8, 9, 5, 2, ... 2. Let's analyze the differences between consecutive terms:

1. The problem is to find the next number in the sequence: 31, 18, 47, 65, 113, 178, 291, ... 2. First, calculate the differences between consecutive terms:

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: $$\frac{2}{4} = \frac{1}{2}$$.