🧮 algebra

1. The problem is to find the constant term that completes the polynomial $m^2 - 4m + \_$ to make it a perfect-square quadratic. 2. A perfect-square quadratic has the form $\left(m

1. The user requests answers with 3 relevant numbers, which means answers should be rounded or expressed with three significant figures. 2. To demonstrate, let's solve a sample pro

1. The problem is to find the product of $6x$ and the polynomial $(x^2 - 4x - 3)$. 2. The formula used here is the distributive property: $a(b + c + d) = ab + ac + ad$.

1. **State the problem:** A laptop originally costs 209. The price is increased by 12%. We need to find the new price after the markup. 2. **Formula used:** To find the new price a

1. The problem asks to find the sale price of diapers originally costing 28.75 with a 10% markdown. 2. The formula for the sale price after a discount is: $$\text{Sale Price} = \te

1. **State the problem:** Solve the equation $$\frac{2tq}{5} = 0$$ for the variable $tq$. 2. **Recall the rule:** A fraction equals zero if and only if its numerator is zero (and t

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