🧮 algebra

1. Stating the problem: Solve the equation $$\sqrt[3]{(2+x)^2} + \sqrt[3]{(2-x)^2} = \sqrt[3]{8 + 2x^2}$$. 2. Let us define $$a = \sqrt[3]{(2+x)^2}$$ and $$b = \sqrt[3]{(2-x)^2}$$.

1. **State the problem:** Rearrange the equation $$cq - u = h$$ to make $$q$$ the subject. 2. **Add $$u$$ to both sides:**

1. **Problem a:** Write the equation of a parabola in the form $y = ax^2 + bx + c$ passing through points $(0,0)$, $(5,5)$, and $(6,0)$, opening downward. 2. Since the parabola pas

1. Stwierdzamy, że funkcja ma postać $f(x) = x^2 + bx + c$ i przechodzi przez punkty $A=(-4,29)$ oraz $B=(1,-6)$. 2. Podstawiamy punkt $A$ do równania: $$29 = (-4)^2 + b(-4) + c =

1. **State the problem:** Find the equation of the line passing through the points $(4,-3)$ and $(5,-5)$. 2. **Calculate the slope $m$:**

1. The problem asks for the equation of the line passing through the points $(-4,5)$ and $(-4,-2)$. 2. First, calculate the slope $m$ using the formula $$m=\frac{y_2 - y_1}{x_2 - x

1. **State the problem:** Find the equation of the line passing through the points $(5,-6)$ and $(-5,-4)$. 2. **Calculate the slope $m$:**

1. **State the problem:** Find the equation of the line passing through the points $(8,3)$ and $(8,-2)$. 2. **Calculate the slope:** The slope $m$ is given by $$m = \frac{y_2 - y_1

1. **State the problem:** Find the equation of the line passing through the points $(2,-3)$ and $(2,6)$. 2. **Calculate the slope:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{

1. **State the problem:** Find the equation of the line passing through the points (-8, -3), (-1, 0), (5, 1), and (10, 2) in slope-intercept form $y=mx+b$. 2. **Calculate the slope

1. **State the problem:** Find the equation of the line passing through the points $(4,-7)$ and $(8,-6)$. 2. **Calculate the slope $m$:**

1. **State the problem:** Find the equation of the line passing through the points $(-3,-4)$ and $(-4,-6)$.\n\n2. **Calculate the slope $m$:** The slope formula is $$m=\frac{y_2 -

1. **State the problem:** Find the equation of the line passing through the points $(6,0)$ and $(3,4)$. 2. **Calculate the slope $m$:**

1. **State the problem:** Find the equation of the line passing through the points $(3,6)$ and $(1,-2)$. 2. **Calculate the slope $m$:**

1. **State the problem:** Find the equation of the line passing through the points $(6,1)$ and $(3,3)$. 2. **Calculate the slope $m$:**

1. **State the problem:** Express $\frac{3}{4} + \frac{5 - x}{6x}$ as a single fraction in simplest terms. 2. **Find a common denominator:** The denominators are 4 and $6x$. The le

1. Énonçons le problème : factoriser l'expression $ (x-5) + (5-x)^2 $.\n\n2. Observons que $5-x = -(x-5)$, donc $ (5-x)^2 = (-(x-5))^2 = (x-5)^2 $.\n\n3. L'expression devient donc

1. **State the problem:** Solve the system of equations for Exercises 5 to 18. ---

1. **State the problem:** We have a parabola $g(x) = ax^{2} + q$ opening downwards with $x$-intercepts $R$ and $S(2,0)$, and $y$-intercept $T(0,8)$. A line $f(x) = mx + c$ passes t

1. **State the problem:** We have a parabola $g(x) = ax^2 + q$ with x-intercepts $R(x_R,0)$ and $S(2,0)$, and y-intercept $T(0,8)$. A line $f(x) = mx + c$ passes through points $R$

1. **State the problem:** We analyze the functions $f$, $g$, and $h$ based on the graph and given points. 2. **Range of $g$:** The range is the set of all $y$-values that $g$ attai