🧮 algebra

1. **State the problem:** We are given the polynomial $$f(x) = 4x^3 + 15x^2 - 63x - 54$$ and told that one zero is $$x = -6$$. We need to find another zero of $$f(x)$$. 2. **Use th

1. **State the problem:** Calculate the total cost of a meal and beverage costing 14 with a 20% tip and 6% sales tax. 2. **Formulas:**

1. Let's start by understanding that you want an easy explanation for a math problem suitable for Grade 7. 2. Since you didn't specify a particular problem, I'll explain a common G

1. **State the problem:** Solve the quadratic equation $3x^2 - 6x = 0$ for $x$. 2. **Formula and rules:** To solve quadratic equations, we can factorize the expression and use the

1. Stating the problem: Divide the mixed fraction $-\frac{2}{5}_3$ by the mixed number $3\frac{6}{7}$. 2. First, convert the mixed numbers to improper fractions. For $-\frac{2}{5}_

1. The problem asks to write the equation for the sequence 500, 2000, 3500, ... in "first term" form. 2. The "first term" form of an arithmetic sequence is given by the formula:

1. **State the problem:** Ryan has 18 feet of wood and uses three-fourths of a foot for each ladder step. After making some steps, he has 15 feet of wood left. We need to find how

1. **State the problem:** There were five times as many children as adults at the picnic. If at least 120 people attended, find how many adults and children were at the picnic. 2.

1. Stating the problem: Solve the equation $\frac{c + 20}{2} = 14$ for $c$. 2. Formula and rules: To solve for $c$, multiply both sides of the equation by 2 to eliminate the denomi

1. The problem involves simplifying and understanding the expression $x^2 - 100$ and the related expressions given. 2. First, recognize that $x^2 - 100$ is a difference of squares,

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: $$4x + 2y = -16$$