🧮 algebra

1. **State the problem:** Simplify the expression $\frac{7}{22} \times \frac{96x^3}{8x^2}$.\n\n2. **Write the expression:** $$\frac{7}{22} \times \frac{96x^3}{8x^2}$$\n\n3. **Multi

1. **Stating the problem:** We are given the equation $$3(x-4)^2=27$$ and need to identify mistakes made by Andre and Clare in solving it (Part A), and then find the correct soluti

1. **State the problem:** We need to solve the equation $$25 = 4z^2$$ for $z$.

1. The problem is to simplify the expression $\sqrt[3]{\frac{40}{27}}$. 2. Recall the property of cube roots: $\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$.

1. **State the problem:** Solve the system of linear equations: $$-8x + 4y = -24$$

1. **Stating the problem:** We need to find the values of $a$ and $b$ given some conditions or equations (not provided in the prompt). 2. **Formula and rules:** To find $a$ and $b$

1. **State the problem:** Solve the system of linear equations: $$-2x = y$$

1. **State the problem:** Solve the system of equations given by: $$x = y$$

1. **State the problem:** Solve the system of equations: $$-y = x$$

1. **State the problem:** We are given two linear equations: $$-10x + 3y = 34$$

1. **State the problem:** Solve the system of linear equations: $$-6x + y = -50$$

1. **State the problem:** Solve the system of equations: $$y = x - 15$$

1. **Stating the problem:** We are given data of daily visitors $V(m)$ in millions over months $m$ since January 2009, and we want to model this data using an exponential decay fun

1. **State the problem:** Solve the inequality $$\frac{1}{3}n - 10 > 22$$. 2. **Formula and rules:** To solve inequalities, we perform operations to isolate the variable on one sid

1. The problem involves solving the equation $$111 + 48 = 1 \frac{46}{1} + 13$$ where the mixed number is $$1 \frac{46}{1}$$ which simplifies to $$1 + 46 = 47$$. 2. First, simplify

1. **Problem statement:** Find the coordinates of point A on the parabola $y = ax^2$ where an equilateral triangle $OAB$ with side length 4 lies, with $O$ at the origin.

1. The problem is to find which area model represents the expression $ (2x + 3)(3x + 3) $. 2. The formula to expand this product is the distributive property: $$ (a + b)(c + d) = a

1. **Stating the problem:** We have an area model with tiles arranged in 3 rows and 5 columns representing algebraic terms. The first two rows have 3 blue squares labeled $x^2$ and

1. **Problem statement:** Find the lengths of line segments $OA$ and $OB$ where points $A$ and $B$ are the intersections of the line $y=x$ with the parabolas $y=x^2$ and $y=-\frac{

1. **State the problem:** Simplify and solve the equation $2i + x + 3y = -7i^{15}y - 5x$ for $x$ and $y$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $\frac{1}{i^{50}}$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Recall the powers of $i$:** The powers of $i