🧮 algebra

1. **Problem T:** Solve the system \(7x + y = 12\) and \(y = 4x - 21\). 2. Substitute \(y = 4x - 21\) into the first equation:

1. **State the problem:** We have two equations representing ticket purchases: $$2x + 5y = 64$$

1. **State the problem:** Kyle is adding the two equations: $$4x - 2y = 18$$

1. **State the problem:** Solve for $w$ in the equations: $$18 \cdot w \cdot 3 = 270$$

1. **State the problem:** We are given two expressions involving $h$: $$h = 12 \cdot 11 \cdot 2,244$$

1. Problem 5: Solve the equation $$2^{x-1} + 2^x + 2^{x+1} = 7$$ 2. Use the property of exponents: $$2^{x-1} = \frac{2^x}{2}$$ and $$2^{x+1} = 2 \cdot 2^x$$.

1. **State the problem:** We are given the expression $$4(2 + 6)(3y + 7)$$ and asked to evaluate the truth of several statements about its terms and factors. 2. **Analyze each stat

1. The problem asks us to identify true statements about the algebraic expression $4a + 7b + 2$. 2. Let's analyze each option:

1. **State the problem:** Simplify the expression $$w - 4(-x + 5w) + 6x$$ using distribution and combining like terms. 2. **Recall the distributive property:** $$a(b + c) = ab + ac

1. **State the problem:** Simplify the expression $$4w - 2(5x - 4w) - 7x$$. 2. **Use the distributive property:** Multiply $$-2$$ by each term inside the parentheses:

1. **State the problem:** Simplify the expression $5(-3w - z) - 3(-5z - 7w)$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside.

1. **Problem 10:** The daily sales function is given by $$s = -p^2 + 120p + 1400$$ where $p$ is the price per unit. 2. **Part (a): Find the vertex by completing the square.**

1. **State the problem:** We have two days with jogging and walking times and total distances. We want to find the relationship between jogging and walking speeds. 2. **Define vari

1. **State the problem:** We have two equations representing the total cost of bags of popcorn and plates of nachos purchased by Jeremy and Kendrick: $$4p + 2n = 18.50$$

1. **State the problem:** Simplify the expression $2\sqrt{18} \times 18 - 3 \sqrt{50} \div \sqrt{32} \div 2$. 2. **Recall important rules:**

1. **State the problem:** Simplify the expression $$2\sqrt{18} \times \sqrt{6} - 3 \sqrt{50} + \sqrt{32} \times 2$$. 2. **Recall the properties of square roots:**

1. **State the problem:** We have a polynomial function $$f(x) = x^4 + x^3 + 2x^2 + ax + b$$ where $$a$$ and $$b$$ are constants. 2. **Given:** When $$f(x)$$ is divided by $$(x - 1

1. **State the problem:** Solve the system of equations using the substitution method: $$\begin{cases} 5x + 4y = 37 \\ x = 2y - 1 \end{cases}$$

1. **State the problem:** Simplify the expression $$\left[\frac{1 + a^{2} \sqrt{(a^{2} + a) a + a^{-1}}}{\sqrt[a]{1 + a^{2} \sqrt{a}} \cdot \left(1 + a^{2} \sqrt[a]{a^{a}}\right)}\

1. **State the problem:** Solve the system of equations by substitution: $$\begin{cases} 6x - 5y = -14 \\ y = 4x \end{cases}$$

1. **State the problem:** Solve the system of equations by substitution: $$y = 3x - 13$$