🧮 algebra

1. The problem asks to solve number 2, but no specific problem statement was provided. 2. Please provide the exact problem or equation for number 2 so I can solve it accurately.

1. **Stating the problem:** We are given two linear equations:

1. **Problem statement:** Factor the expression $$ab + 2ac + 3b^2 + 6bc - 5a - 13b + 4c - 10$$ We will arrange and factor it first with respect to variable $a$, then with respect t

1. **State the problem:** Solve the equation $x(x + 1) - 56 = 4x(x - 7)$ and find the sum of its solutions. 2. **Write the equation:**

1. **Problem (a):** A businessman sold a refrigerator for 2745 making a profit of 15% on the cost price. Find the cost price. 2. **Formula:** Profit% = \frac{Selling Price - Cost P

1. **Stating the problem:** Simplify the expression $$4 - 8 \div \frac{2}{3}$$ and evaluate the division $$\frac{1}{2} \div \frac{1}{2}$$. Also, interpret the handwritten note $$6

1. **State the problem:** We are given the cost function $NC = 3.02(x^2 + 200)^{0.02}$ and the revenue function $NR = (2\sqrt{x} + 1) + 1.75$. We want to find the profit function $

1. **State the problem:** Solve each system of equations using substitution. Identify which three systems have the solution $(4,16)$ and unscramble their letters to find a secret c

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