🧮 algebra

1. **State the problem:** Simplify the radical expression $$\sqrt{72}$$. 2. **Recall the formula and rules:** To simplify a square root, find the prime factorization of the number

1. **State the problem:** Simplify the radical expression $$\sqrt{160}$$. 2. **Recall the formula and rules:** To simplify a square root, factor the number inside the radical into

1. **Problem Statement:** Find the inverse of each function given. 2. **Formula and Rules:** To find the inverse function $f^{-1}(x)$, swap $x$ and $y$ in the equation $y=f(x)$ and

1. **State the problem:** We need to identify and compare the graph of the function $$n(x) = \frac{1}{3}x^2 - 5$$ with the graph of $$f(x) = x^2$$. 2. **Recall the base function:**

1. **State the problem:** Find the inverse function of $f(x) = \frac{3}{4}x + 2$. 2. **Recall the formula:** To find the inverse, swap $x$ and $y$ and solve for $y$. If $y = f(x)$,

1. **State the problem:** Find the inverse function of $f(x) = 3x + 1$. 2. **Formula and rules:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in the equation and

1. **State the problem:** We have the list of numbers: 5.25, | -6/5 |, -4 4/5, -1.2. We want to arrange them in descending order (from largest to smallest). 2. **Convert all terms

1. **State the problem:** We are given the list of numbers: $5.25$, $| - \frac{6}{5} |$, $-4 \frac{4}{5}$, and $-1.2$. We need to determine which two terms are arranged correctly i

1. **State the problem:** We are given the line equation $x + 4y = 8$ and need to find the slopes of lines perpendicular and parallel to it. 2. **Rewrite the line in slope-intercep

1. **State the problem:** We need to solve for $a$ in a factored form given $y=5$, $s=-2$, and $t=4$. 2. **Assume the factored form:** Typically, a factored form involving $a$, $s$

1. **State the problem:** Given values $s = -2$, $t = 4$, and $y = 5$, we need to understand what to do with these variables. Since no specific operation or equation is provided, l

1. **State the problem:** Solve for $a$ in the equation $$y = a(x - s)(x - t)$$ given $s = -5$, $t = -2$, and $y = -4$. 2. **Write the formula with given values:** Substitute $s$ a

1. The problem asks which points lie on the graph of $$y = f(x) + 4$$, where $$f(x)$$ is a parabola with vertex at $$(-4,1)$$. 2. The graph $$y = f(x) + 4$$ is the original parabol

1. **State the problem:** We need to determine which points lie on the graph of the transformed function $$y = f(x + 7) - 3$$ given points and the original function $$f(x)$$. 2. **

1. **Problem:** Write an equation in slope-intercept form given slope and y-intercept. Given: slope $m=\frac{3}{5}$, y-intercept $b=6$.

1. **State the problem:** Solve the equation $$\frac{x - 2}{8} = 10$$ for $$x$$. 2. **Formula and rules:** To solve for $$x$$, multiply both sides of the equation by 8 to eliminate

1. **State the problem:** Solve the equation $3 - 5x = -42$ for $x$. 2. **Isolate the term with $x$:** Subtract 3 from both sides to get the term with $x$ alone.

1. **State the problem:** Solve the equation $10x - 2 = -62$ for $x$. 2. **Add 2 to both sides** to isolate the term with $x$:

1. **State the problem:** Solve the equation $3x - 9 = 27$ for $x$. 2. **Write the formula and rules:** To solve for $x$, isolate $x$ on one side of the equation by performing inve

1. **Énoncé du problème :** Mélissa a 20 paires de souliers de plus que Noémie.

1. **State the problem:** Solve the inequality $4x + 7 \neq 11$ for $x$. 2. **Write the inequality:**