🧮 algebra

1. **State the problem:** We need to find the three inequalities that define the unshaded region on the graph.

1. **Problem:** Liu deposited 3500 into a savings account 2 years ago with a simple interest rate of 4%. We need to find how much interest Liu earned. 2. **Formula for simple inter

1. **State the problem:** Solve the equation $$19^{4 - 2x} - 8 = 38$$ and round the solution to the nearest ten-thousand. 2. **Isolate the exponential term:** Add 8 to both sides t

1. Planteamos el sistema de ecuaciones a resolver por el método de reducción: $$\begin{cases} 3X + 4Y = -6 \\ 2X + 3Y = 13 \end{cases}$$

1. The problem is to express a given improper fraction as a mixed number in simplest form. 2. The formula to convert an improper fraction $\frac{a}{b}$ to a mixed number is:

1. The problem is to divide the fractions $\frac{4}{7}$ by $\frac{1}{3}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}

1. Planteamos el sistema de ecuaciones a resolver por el método de reducción: $$\begin{cases} 3X + 4Y = -6 \\ 2X + 3Y = 13 \end{cases}$$

1. El problema es factorizar el denominador de la función \(G(s) = \frac{1}{(s+2)(s^2 + 10s + 7)}\). 2. El denominador ya está parcialmente factorizado como \((s+2)(s^2 + 10s + 7)\

1. The problem asks for the cube of 5. 2. The cube of a number $n$ is calculated using the formula:

1. **State the problem:** A band has 24 male members. There are $x$ more male members than female members. We need to write an expression for the total number of members in the ban

1. **State the problem:** Simplify the expression $$\left(\frac{x^4}{y^6}\right)^8$$. 2. **Recall the power of a quotient rule:** When raising a quotient to a power, apply the expo

1. **State the problem:** Factor each algebraic expression. 2. **Problem a:** Factor $36x - 9$.

1. **State the problem:** Simplify each algebraic expression by combining like terms. 2. **Recall the rule:** To simplify, add or subtract coefficients of the same variable and com

1. **State the problem:** Simplify the expression $$(3x^6)^3 (2x^2)^4$$. 2. **Recall the exponent rules:**

1. **Problem a:** Evaluate the expression $3(2x - 5) + \frac{x}{4}$ when $x = 8$. 2. **Step 1:** Substitute $x = 8$ into the expression:

1. **State the problem:** We need to find algebraic expressions for each sentence.

1. **State the problem:** Brent is $x$ years old. George is 8 years older than Brent, so George's age is $x + 8$. Joan is 4 times as old as George. We need to find an expression fo

1. **State the problem:** We are given two points $(15,10)$ and $(30,15)$ and need to find the value of $y$ when $x=17.9$ using linear interpolation. 2. **Formula for linear interp

1. **Problem statement:** We are given the function $g(x) = 2x^2 + \frac{1}{x}$ and asked to analyze and plot it. 2. **Function form:** The function is a combination of a quadratic

1. **Problem statement:** Use linear interpolation to find the value of $y$ when $x=26.5$ given points $(30, 51)$ and $(20, 36)$. 2. **Formula for linear interpolation:**

1. **Stating the problem:** We are given the function $$y = 3\sqrt{x^4 + 4x^3 + 5}$$ and we want to understand or analyze it. 2. **Understanding the function:** The function involv