🧮 algebra

1. **State the problem:** We are given an expression for the perimeter of a rectangle as $8w$, where $w$ is the width in inches. 2. **Recall the formula for the perimeter of a rect

1. **State the problem:** Solve the system of equations: $$y^2 = 3x^2 + 4$$

1. **Énoncé du problème :** Soit $n$ un entier naturel, on pose $A_n = 97 \cdot 6^n$ et $B_n = 9409 \cdot 6^{2n}$.

1. **Problem statement:** Identify the symmetries of each given graph. 2. **Symmetry rules:**

1. **State the problem:** Simplify the expression $$\frac{(2^{-3} \cdot 2^{10})^{-2}}{2^{3} (2^{-5} \cdot 2^{-2})^{3}}$$. 2. **Recall the laws of exponents:**

1. **Énoncé du problème :** Soit $n$ un entier naturel, on pose $A_n = 97 \cdot 6^n$ et $B_n = 9409 \cdot 6^{2n}$.

1. The problem asks to find the expressions that represent the sale price of an item originally priced at $i$ dollars with a 25% discount. 2. The formula for the sale price after a

1. The first problem is to factor the trinomial $x^2 + x - 12$. 2. To factor a trinomial of the form $ax^2 + bx + c$, we look for two numbers that multiply to $ac$ and add to $b$.

1. **Planteamiento del problema:** Simplificar la expresión $$\left(\frac{2x^3}{4}\right)^3$$. 2. **Fórmula y reglas importantes:** Para elevar una fracción a una potencia, se elev

1. The problem is to find the greatest common factor (GCF) of the variable $b$. 2. The GCF is the largest factor that divides two or more terms without leaving a remainder.

1. **State the problem:** Factor the expression $$5x^2 y^2 - 15xy + 20x^3 y^2$$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in all terms.

1. **State the problem:** A mother bought 3 packs of Supligen and 4 packs of Orange juice for 13.40.

1. **Problem:** Solve the quadratic equation $x^2 + 4x + 3 = 0$ by factoring. 2. **Formula and rules:** To solve by factoring, first set the equation equal to zero, then factor the

1. **State the problem:** Solve for $y$ in the equation $$-2y - 14 = 2(y - 1)$$. 2. **Use the distributive property:** Expand the right side:

1. El problema es graficar la función cuadrática $f(x) = -5x^2$. 2. La fórmula general para una función cuadrática es $f(x) = ax^2 + bx + c$. En este caso, $a = -5$, $b = 0$, y $c

1. **State the problem:** We need to determine which of the two options, A or B, best represents the total thickness in scientific notation. 2. **Recall the total thickness from pr

1. **State the problem:** Kristin is gluing a paper layer of thickness $0.025$ mm onto a construction board of thickness $7 \times 10^{-2}$ mm. We need to find the total thickness

1. **State the problem:** We are given a list of numbers: $-6, -5.3, -5, -4, -3$ and asked to find the correct number line that shows the sum of each number plus $1.9$. 2. **Formul

1. **State the problem:** We are given that $3^x 5^y = 675$ where $x$ and $y$ are positive integers. We need to find the value of $x + y$. 2. **Prime factorize 675:** To solve for

1. **Problem statement:** Given the function $f(x) = -x^2 - 2x + 6$, find the vertex, intercepts with coordinate axes, domain, range, and describe the graph including its growth di

1. **State the problem:** We need to find the mistake in the steps solving the inequality $$7x + 5 > 4x + 2$$. 2. **Step 1:** The original inequality is $$7x + 5 > 4x + 2$$ (Given)