🧮 algebra

1. **Problem:** Factor $x^2+6x+9$. 2. Use the perfect-square trinomial formula $a^2+2ab+b^2=(a+b)^2$.

1. **State the problem:** Factor the quadratic expression $$x^2 + 6x + 9$$. 2. **Recall the formula:** A quadratic expression of the form $$ax^2 + bx + c$$ can be factored by findi

1. **State the problem:** Factor the quadratic expression $$x^2 + 6x + 9$$. 2. **Recall the formula:** A quadratic expression of the form $$ax^2 + bx + c$$ can be factored by findi

1. Let's start by understanding what a quadratic equation is. A quadratic equation is any equation that can be written in the form $$ax^2 + bx + c = 0$$ where $a$, $b$, and $c$ are

1. **State the problem:** Calculate the value of $$\left(-\dfrac{2}{5}\right)^2$$. 2. **Recall the rule:** When squaring a fraction, square both the numerator and the denominator s

1. **State the problem:** Simplify the expression $$(8^{-8})(8^{3})$$. 2. **Recall the exponent multiplication rule:** When multiplying powers with the same base, add the exponents

1. **State the problem:** Simplify the expression $$\frac{\sqrt{49} + \sqrt{\sqrt{81}}}{\sqrt{4}}$$. 2. **Recall important formulas and rules:**

1. **State the problem:** Solve the equation $$2X \times 2 + 5 = 95$$ for $X$. 2. **Write the equation clearly:** $$2X \times 2 + 5 = 95$$.

1. The problem is to understand the expression $a^2 + b^2$. 2. This expression represents the sum of the squares of two variables $a$ and $b$.

1. **Problem:** Find the number removed when the mean of five numbers is 24, and after removing one number, the mean of the remaining four numbers is 20. 2. **Formula:** Mean of $n

1. **State the problem:** We need to factor the quadratic expression $$x^2 + 6x + 9$$. 2. **Recall the factoring formula:** A quadratic expression of the form $$ax^2 + bx + c$$ can

1. **State the problem:** We need to graph the parabola given by the equation $$y=\frac{1}{4}x^2$$ and plot five points: the vertex, two points to the left, and two points to the r

1. **State the problem:** Convert the decimal $0.45$ into a percent. 2. **Recall the formula:** To convert a decimal to a percent, multiply the decimal by 100 and add the percent s

1. **State the problem:** We need to graph the parabola given by the equation $$y = (x + 4)^2 + 1$$ and plot five points: the vertex, two points to the left, and two points to the

1. **State the problem:** Simplify the expression $$(-3y^{-3}z^{4})^{2}$$ and write the answer using only positive exponents. 2. **Recall the power of a product rule:** $$(ab)^{n}

1. The problem is to understand the expression $\frac{ }{ }$, which represents a fraction with an empty numerator and denominator. 2. A fraction is generally written as $\frac{a}{b

1. **Stating the problem:** We are asked about a polynomial, but no specific polynomial or question is given. 2. **General information about polynomials:** A polynomial is an expre

1. **State the problem:** The ratio of flour to sugar is $4:1$. We have $16$ cups of flour and want to find the amount of sugar needed. 2. **Formula and rule:** If the ratio of flo

1. Problem 11: Simplify the ratio $15:25$. The ratio $15:25$ means $\frac{15}{25}$.

1. **Problem:** Use substitution to solve the linear system. $$x = 2y - 56$$

1. Let's start by understanding what a square root is. 2. The square root of a number $x$ is a value $y$ such that $$y^2 = x$$.