🧮 algebra

1. **State the problem:** We need to find all points on the number line that are exactly 7 units away from point P, which is located at $-2$. 2. **Formula used:** The distance betw

1. **State the problem:** We are asked to factor the polynomial $49n^2 + 14n + 1$.

1. The problem asks for the value of $A + B$ where $A$ and $B$ are points on the number line. 2. From the graph description, point $A$ is at $-2$ and point $B$ is at $2$.

1. **State the problem:** We are given two functions: Function 1 represented by points on a graph and Function 2 represented by a table of values. We need to determine which statem

1. **State the problem:** Solve the system of equations: $$x = 8y + 32$$

1. **State the problem:** Find the greatest common factor (GCF) of the terms $4x^2y$ and $6xy$. 2. **Recall the formula and rules:** The GCF of two terms is the product of the lowe

1. **State the problem:** Find the inverse of the function $f(x) = 2x^2 - 10x + 14$. 2. **Rewrite the function:** Let $y = 2x^2 - 10x + 14$.

1. **Problem statement:** Solve the equation $x^2 = \frac{25}{4}$ for $x$. 2. **Formula and rules:** To solve $x^2 = a$, take the square root of both sides: $x = \pm \sqrt{a}$.

1. **State the problem:** Solve the equation $4x^2 = 28$ and write the solutions using ± notation. 2. **Write the formula and rules:** To solve for $x$ when you have an equation of

1. Énoncé du problème : Trouver et expliquer la solution pour le système donné par $ (y - 5)^2 = 4(x + 12) $

1. **State the problem:** Solve the system of linear equations: $$4x + 2y = -16$$

1. **State the problem:** Find the largest two consecutive odd integers such that four times the larger reduced by the smaller is less than 100. 2. **Define variables:** Let the sm

1. **Problem:** For each quadratic function, find the axis of symmetry and the turning point. 2. **Formula:** The axis of symmetry for a quadratic function $y = ax^2 + bx + c$ is g

1. **State the problem:** Simplify the expression $$\sqrt{108a^6}$$ by removing all perfect squares from inside the square root, assuming $$a$$ is positive. 2. **Recall the rule:**

1. Problem: Find the scale factor for a model car 12 inches long representing a 192-inch-long car. 2. Formula: Scale factor = \frac{Model\ length}{Actual\ length}

1. **State the problem:** Rewrite the expression $\left(27 \sqrt[3]{z^2}\right)^{\frac{1}{3}}$ in the form $k \cdot z^n$ where $n$ is an integer, fraction, or exact decimal. 2. **R

1. **State the problem:** Simplify the expression $\frac{1}{5} \ln 32 - \ln 2$. 2. **Recall logarithm rules:**

1. **State the problem:** Solve the system of linear equations: Top-left pair:

1. **Problem:** For the quadratic function $y = x^2 - 8x + 8$, find (a) the axis of symmetry and (b) the turning point. 2. **Formula:** The axis of symmetry for a quadratic $y = ax

1. **State the problem:** Find the domain of the function $$K(x) = \frac{9 - 8x}{x^2 - 8x - 9}$$. 2. **Recall the domain rule:** The domain of a rational function is all real numbe

1. **State the problem:** We need to find the maximum cost of each drawer pull if the total bill for a lawnmower and 15 drawer pulls is within a $400 budget.