🧮 algebra

1. **State the problem:** We are given two numbers, $x$ and $y$. The sum of twice the first number and the second number is 22, and subtracting the second number from thrice the fi

1. **Problem b)** Given the inequality $|c - 10| + 12 > 18$, find the interval of $c$. 2. Start by isolating the absolute value term:

1. The problem asks to analyze the algebraic expression $3x + 4$ and answer four questions about it. 2. First, count the number of terms in $3x + 4$. A term is a part of the expres

1. The problem is to factor the given algebraic expressions and identify equivalent expressions. 2. Factor each expression:

1. **State the problem:** We have two functions:

1. **State the problem:** We need to find the current ages of Muneer and Mujeeb given two conditions about their ages in the past and future. 2. **Define variables:** Let $M$ be Mu

1. **Factoring algebraic expressions:** Given: $2x + 10$

1. Let's define variables for the prices: - Let $C$ be the cost of one coat.

1. **Problem:** Find the value of $x$ such that \[ [x \quad 1] \begin{bmatrix} 1 & 0 \\ -2 & 0 \end{bmatrix} = [0 \quad 0] \] 2. **Step 1:** Perform the matrix multiplication:

1. **Stating the problem:** Find the graphs of the functions:

1. Problem (35): Solve the quadratic equation $$-x^2 - 8x + 3 = 0$$. 2. Rewrite the equation as $$-x^2 - 8x + 3 = 0$$ or equivalently $$x^2 + 8x - 3 = 0$$ by multiplying both sides

1. Problem (25): Simplify $\frac{\sqrt{6} \sqrt{24}}{2\sqrt{6}}$ and verify if it equals 12. Step 1: Simplify numerator $\sqrt{6} \sqrt{24} = \sqrt{6 \times 24} = \sqrt{144} = 12$.

1. **Solve the equation** $x^2 - 18 = 0$. 2. Add 18 to both sides: $$x^2 = 18$$

1. **Solve the quadratic equation** $x^2 - 10x + 16 = 0$. Step 1: Factor the quadratic.

1. **State the problem:** We have a box with 40 marbles. The ratio of red marbles to total marbles is $2:5$, and the ratio of green stones to total stones is $3:10$. We want to fin

1. **State the problem:** Calculate the total cost for Yaa who buys 2 skirts, 1 dress, and 4 pairs of pantyhose during a 20% off sale on skirts.

1. The problem states that a mountain path is 12.1 miles long and a hiker walks at a rate of 1.96 miles per hour. 2. We need to find the time it takes for the hiker to walk the ent

1. Stating the problem: Solve the logarithmic equation $$\log_5 (x+3) - \log_5 (x-1) = 2$$. 2. Use the logarithmic property: $$\log_b A - \log_b B = \log_b \left(\frac{A}{B}\right)

1. The problem states that Kofi earned 50 Cedis yesterday mowing lawns. 2. Today, Kofi earned 60% of what he earned yesterday.

1. We are given multiple logarithmic expressions and an equation to simplify or solve. 2. Simplify each logarithmic expression:

1. The function given is $f(x) = -x^2 - x + 6$. 2. To find the equation of $h$, we first reflect $f$ about the x-axis. Reflection about the x-axis changes $f(x)$ to $-f(x)$.