🧮 algebra

1. The problem is to identify which points lie on the graph of the function $y=4x$. 2. The function $y=4x$ means for any $x$ value, $y$ should be $4$ times $x$.

1. **State the problem:** Juan's savings account balance quadrupled during the year. After withdrawing 300, the balance was 400. We need to find the balance before it quadrupled. 2

1. Problem 6: Find the slope of the line passing through points (7, -2) and (3, -2). The slope formula is $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1, y_1) = (7, -2)$ and $(x_2,

1. **State the problem:** We need to find the equation of a line with slope $m=1$ that passes through the point $(-2,5)$. The equation should be in slope-intercept form $y=mx+b$. 2

1. **State the problem:** We are given a function $f(x)$ with points $(1,5)$, $(0,1)$, and $(-1, \frac{1}{5})$. We need to analyze the graph of $g(x)$, describe the transformation

1. **State the problem:** Solve for $x$ in the equation $$2(3x + 8) = 70$$ and simplify the answer. 2. **Apply the distributive property:** Multiply 2 by each term inside the paren

1. **Problem:** Calculate the product $i(3 + 4i)$. 2. **Recall:** Multiplying complex numbers involves distributing and using $i^2 = -1$.

1. The problem asks to simplify and compare the expressions $\frac{1}{8}x + 2$ and $\frac{1}{2}(4 + \frac{1}{4}x)$.\n\n2. Start with the first expression: $\frac{1}{8}x + 2$. This

1. **Stating the problem:** Find the value of the ordered pair $(3,4)$ in the context of algebraic expressions or coordinate points. 2. **Understanding ordered pairs:** An ordered

1. We are asked to simplify the fractions: a) $\frac{15}{35}$, b) $\frac{20}{36}$, c) $\frac{4}{48}$, d) $\frac{75}{90}$, e) $\frac{64}{256}$, f) $\frac{112}{144}$. Simplifying fra

1. **State the problem:** Calculate 55% of 80. 2. **Formula:** To find a percentage of a number, use the formula:

1. **State the problem:** Solve for the unknown in the proportion equations given. 2. **Recall the rule for proportions:** If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \tim

1. **Problemstellung:** Wir sollen die Koordinaten der Schnittpunkte zweier Parabeln berechnen. 2. **Formel und Vorgehen:** Schnittpunkte zweier Funktionen $y=f(x)$ und $y=g(x)$ fi

1. **State the problem:** We are given the function $f(x) = -4\sqrt{-x}$ and want to understand its properties and graph. 2. **Recall the square root function:** The basic square r

1. The problem asks to identify the type of function based on the graph description. 2. The graph starts near (0, -2), increases gradually, passes through (4, 0), and curves slight

1. **State the problem:** We need to find the value of $x$. 2. **Identify the equation:** Since the user did not provide an explicit equation, we assume the problem is to solve for

1. **State the problem:** Solve the inequality $$-2(-3x + 2) \neq 20$$. 2. **Apply the distributive property:** Multiply $$-2$$ by each term inside the parentheses.

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate $x$ by performing inverse operations. We subtract 3 from both sides to undo th

1. **State the problem:** Simplify the expression $$\left(\frac{a^{-1}}{-ab \cdot 2a^3}\right)^2$$. 2. **Rewrite the denominator:** The denominator is $$-ab \cdot 2a^3 = -2ab a^3$$

1. **State the problem:** We are given two functions $g(x) = 4x - 4$ and $f(x) = x + 4$. We need to find the function $\left(\frac{g}{f}\right)(x)$, which means dividing $g(x)$ by

1. **State the problem:** We are given two functions $f(x) = 4x + 3$ and $g(x) = x + 5$. We need to find the product function $(f \cdot g)(x)$, which means multiplying $f(x)$ and $