🧮 algebra

1. The problem is to find which value of $x$ satisfies the equation $$-18 + 3x = 24$$. 2. The formula used here is to isolate $x$ by performing algebraic operations. We add 18 to b

1. The problem states: You have 37 units of money and need to save 3 units for bus fare. We want to find the inequality representing the amount of money $m$ you can spend. 2. Since

1. **State the problem:** We need to find the equation of a transformed exponential function of the form $$y = A \cdot 2^x + k$$ based on the given graph. 2. **Recall the base func

1. **State the problem:** Solve the equation $$\frac{8}{15} m = 3 \frac{1}{5}$$ for $m$. 2. **Convert mixed number to improper fraction:**

1. The problem is to solve for $m$ in the equation $\frac{5}{8} m = 3 \frac{1}{5}$. 2. First, convert the mixed number $3 \frac{1}{5}$ to an improper fraction:

1. **State the problem:** We want to describe the long run behavior of the function $$f(x) = 2(2)^x + 3$$ as $$x \to -\infty$$ and $$x \to \infty$$. 2. **Recall the properties of e

1. **Problem statement:** We start with the function $f(x) = 3^x$ and apply transformations: (a) Shift the graph 7 units upward.

1. The problem is to solve the equation $$z - \frac{4}{5} = \frac{7}{10}$$ for $z$. 2. To isolate $z$, add $\frac{4}{5}$ to both sides of the equation:

1. **Problema:** Calcolare il limite della funzione $$y = \frac{x}{(2x + 1)^2 - (x - 1)^2}$$ e semplificare l'espressione. 2. **Formula e regole importanti:** Per semplificare il d

1. The problem asks us to evaluate the expression $$3a + 2.8$$ for different values of $$a$$. 2. The expression is a linear function of $$a$$, where you multiply $$a$$ by 3 and the

1. **State the problem:** Solve the quadratic equation $$x^2 + 39 = 12x$$ for $x$. 2. **Rewrite the equation in standard form:** Move all terms to one side:

1. **State the problem:** We need to evaluate the expression $$3a + 2.8$$ for different values of $$a$$, starting with $$a = 1.3$$. 2. **Formula:** The expression is a linear funct

1. **State the problem:** Solve the quadratic equation $$2x^2 - x = 4$$ for $x$ and write the exact simplified solutions. 2. **Rewrite the equation:** Move all terms to one side to

1. **Problem Statement:** Ronan is painting 5 doors, and he has painted \(\frac{1}{3}\) of each door. We need to find a model that represents the total amount of painting completed

1. **Problem Statement:** Match each exponential function formula to its corresponding graph based on the description of the curve and key points. 2. **Recall the general form:**

1. **State the problem:** Solve the equation $h - 7\left(\frac{5}{6}\right) = 5\left(\frac{1}{2}\right)$ for $h$. 2. **Write down the equation:**

1. The problem asks to find the values of $x, y, z$ such that the numbers $x^2 - yz$, $y^2 - xz$, and $z^2 - xy$ form an arithmetic progression (AP) of 4 terms. 2. Recall that for

1. **State the problem:** Solve the system of inequalities by graphing: $$y \leq 3x + 3$$

1. Let's factor the quadratic expression $x^2 + 5x + 6$. 2. The problem is to express $x^2 + 5x + 6$ as a product of two binomials.

1. **State the problem:** We need to find the equation of the trend line passing through the points (2, 1) and (6, 8) in slope-intercept form $y=mx+b$. 2. **Formula for slope:** Th

1. **Problem Statement:** Simplify the algebraic expression $7a^2 - 11a + 24 - a - 7a + 2(a^2 - 2a + 3) - 3(-a^2 - 3a - 4) + 2(2a^2 - 7a + 6) + 5a^2 - a + 18 - 3(a^2 + 4 - a)$. 2.