🧮 algebra

1. **State the problem:** Solve the equation $-2r=16$ for $r$. 2. **Formula and rules:** To solve for $r$, divide both sides of the equation by the coefficient of $r$, which is $-2

1. **State the problem:** Solve the equation $$3r = 9$$ for $$r$$. 2. **Formula and rules:** To solve for $$r$$, divide both sides of the equation by the coefficient of $$r$$, whic

1. **State the problem:** We have two exponential functions $f$ and $g$ defined on the interval $[0,4]$. Function $f$ is given by a table of values, and function $g$ passes through

1. **State the problem:** We are given the quadratic equation $x^2 + 10x + 27 = 0$ and need to complete the square to rewrite it in the form $(x + a)^2 = b$. 2. **Recall the formul

1. **State the problem:** Simplify the expression $$\frac{a^3b^5}{a^4b}$$ to find an equivalent expression. 2. **Recall the laws of exponents:**

1. **State the problem:** We need to determine the end behavior of the function $$f(x) = 3|x - 7| - 7$$ as $x$ approaches positive and negative infinity. 2. **Recall the properties

1. **State the problem:** We are given the expression $$3^{8/5}$$ and asked to rewrite it in the form $$\sqrt[5]{a^b}$$, where $$a$$ and $$b$$ are numbers to find. 2. **Recall the

1. **State the problem:** We have a function $f$ and want to find the function $g$ that results from translating $f$ down by 4 units. 2. **Recall the translation rule:** Translatin

1. **State the problem:** Factor the quadratic expression $$9x^2 + 3x - 2$$. 2. **Recall the factoring method:** For a quadratic $$ax^2 + bx + c$$, we look for two binomials $$(mx

1. **State the problem:** We need to find the equation of a line that goes through the point $(6, -4)$ and is perpendicular to the line given by the equation $$6 = 4y + 3x$$. 2. **

1. **State the problem:** We need to find the equation of the line that passes through the points $(3, -5)$ and $(-2, 7)$. 2. **Formula used:** The equation of a line can be found

1. **State the problem:** Solve the inequality $$|x + 9| - 3 \geq -2$$. 2. **Isolate the absolute value:** Add 3 to both sides:

1. **State the problem:** Solve the equation $$-9|a - 1| + 3 = -42$$ for $a$. 2. **Isolate the absolute value term:** Subtract 3 from both sides:

1. Let's understand the fraction $\frac{8}{5}$. A fraction represents a part of a whole or a division of two numbers. 2. The fraction $\frac{8}{5}$ means 8 divided by 5.

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$12x + 30y = 180$$. 2. **Recall the intercept definitions:**

1. **State the problem:** Find the x-intercept and y-intercept of the linear equation $$-x + y = 3$$. 2. **Recall the intercept definitions:**

1. The problem asks to identify which point on a number line corresponds to the value $-0.135$. 2. We know the points are labeled A, B, C, and D, and the value $-0.135$ lies betwee

1. **Stating the problem:** Simplify or analyze the given fractions and expressions involving large numerators and denominators. 2. **Understanding the fractions:** Each term is a

1. **State the problem:** We want to find the product of $y$ to the second power and $y$ to the sixth power, i.e., calculate $y^2 \times y^6$. 2. **Recall the exponent multiplicati

1. **Problemos aprašymas:** Turime taškus A($-2$, $-4$), B($6$, $4$), C($-5$, $1$) ir D($4$, $-2$) koordinačių plokštumoje OXY.

1. **State the problem:** We are given the vertex of a quadratic relation as $ (6, -4) $ and the value of $ a = 3 $. We need to find the equation in vertex form. 2. **Recall the ve