🧮 algebra

1. Problem: Simplify the expressions using exponent laws and compute numerical values where possible. 2. Recall the exponent multiplication rule: $$a^m \times a^n = a^{m+n}$$ and t

1. The problem asks us to find the equation of a function $g(x)$ that shifts the graph of $f(x) = \frac{1}{x}$ left by 2 units and up by 4 units. 2. The general rule for shifting a

1. **State the problem:** Factorise fully the expression $wy - y - 1 + w$. 2. **Group terms:** Group the terms to find common factors:

1. The problem asks us to find the equation of a function $g(x)$ that shifts the graph of $f(x) = 2^x$ right by 5 units and down by 3 units. 2. The general rule for shifting a func

1. Problema: Determinați numerele xy pentru care x și y verifică relația: $$2025 - \left\{35 - \left[25 - \frac{16 \cdot (x + y)}{8}\right] : 3 \cdot 2 - 5\right\} : 8 \cdot 3 = 20

1. **State the problem:** We need to find the average rate of change of the function $f(x)$ on the interval $[-6, -1]$ by using the points on the graph at $x = -6$ and $x = -1$. 2.

1. The problem is to solve the equation $$(x + 4)^2 = -4$$ for all values of $x$. 2. Recall that the square of any real number is always non-negative, so $$(x + 4)^2 \geq 0$$ for a

1. **State the problem:** Solve the quadratic equation $$2v^2 + 11v + 13 = 0$$ for all real solutions in simplest form. 2. **Recall the quadratic formula:** For an equation $$ax^2

1. The problem is to understand the inequality symbol \textgreater{} and how it affects expressions. 2. The symbol \textgreater{} means "greater than". For example, $a > b$ means $

1. **State the problem:** Solve the inequality $$2(\sqrt{x} + 7) < -18$$. 2. **Understand the problem:** The expression involves a square root, which means the domain of $x$ must s

1. Let's analyze the given linear equations and find the intercepts. 2. The equation given is $y = \frac{8}{3}x - 4$.

1. **State the problem:** We are given the linear equation $$y = \frac{2}{3}x - 4$$ and the y-intercept is $$-4$$. We need to find the x-intercept. 2. **Recall the definition of in

1. **State the problem:** We have a cubic function $p(x) = 3m(x+1)^2$ with a y-intercept of $-12$. We need to find the missing factor $m$. 2. **Recall the y-intercept:** The y-inte

1. The problem is to find the x-intercept of a line when the y-intercept is given as -4. 2. The y-intercept is the point where the line crosses the y-axis, so the coordinates are $

1. **State the problem:** We need to graph the function $$y = 3\sqrt[3]{x} - 5$$ by transforming the parent function $$y = \sqrt[3]{x}$$. 2. **Parent function and transformations:*

1. The problem is to verify if the equation manipulation from $2x + 3y = 12$ to $y = \frac{2}{3}x - 4$ is correct. 2. Start with the original equation:

1. **State the problem:** We need to graph the function $$y = -\left| \frac{1}{4}x \right| + 2$$ by transforming the parent absolute value function $$y = |x|$$.

1. The problem asks to complete the chart by finding the x-intercept, y-intercept, and slope-intercept form $y=mx+b$ for each equation. 2. Recall the intercepts:

1. **State the problem:** Simplify the expression $-2^4/4-4(12/6)+10$. 2. **Recall order of operations:** Exponents first, then multiplication and division from left to right, then

1. The problem is to convert the equation from standard form $3x - 2y = 6$ to slope-intercept form $y = mx + b$ and verify why the conversion is correct. 2. The standard form of a

1. **State the problem:** Simplify the expression $-2^4/4-4(48/6)+10$. 2. **Recall order of operations:** Exponents first, then multiplication and division from left to right, and