🧮 algebra

1. **State the problem:** There are 270 students in year 7 studying French, German, or Spanish. We know: - $\frac{2}{9}$ of the students study French.

1. **State the problem:** Expand the logarithmic expression $$\log \left( \frac{2(x+7)^5}{\sqrt[3]{x^4}} \right)$$ using properties of logarithms. 2. **Recall the properties of log

1. **State the problem:** Solve for $v$ in the equation $$1 = \sqrt{4v - 23} - 2$$ where $v$ is a real number. 2. **Isolate the square root term:** Add 2 to both sides to isolate t

1. **State the problem:** A homeowner wants to resod a front lawn that measures 10 \frac{1}{2} yards long and 6 \frac{2}{3} yards wide. The landscaper charges 8 per square yard for

1. **State the problem:** Solve the system of linear equations: $$-3x + 3y = 4$$

1. **State the problem:** Solve the quadratic equation by completing the square for $$x^2 - 10x + 19 = 0$$. 2. **Recall the method:** To complete the square, rewrite the quadratic

1. **State the problem:** Find the equation of the hyperbola with foci at $(-1, -1 - \sqrt{20})$ and $(-1, -1 + \sqrt{20})$ and asymptotes $y = \frac{1}{2}x - \frac{1}{2}$ and $y =

1. The problem gives two equations: $$KES + EES + SEE + MEES = 6543$$

1. **State the problem:** We want to find the maximum value of the function $$z = 4x + 3y$$ subject to the constraints:

1. **State the problem:** Solve the literal equation $$3n - 5p + 2n = 10p$$ for $$n$$. 2. **Combine like terms:** On the left side, combine $$3n$$ and $$2n$$ to get $$5n$$.

1. **State the problem:** Evaluate the expression $$\frac{5i}{3 - i}$$ where $i$ is the imaginary unit with the property $i^2 = -1$. 2. **Formula and rules:** To simplify a complex

1. **State the problem:** Simplify the expression $\frac{5i}{3 - i}$. 2. **Formula and rules:** To simplify a complex fraction with a complex denominator, multiply numerator and de

1. **State the problem:** Bill Pierson buys a 125-foot roll of latex tubing for 35 and sells all of it for 57.50. We need to find Bill's profit per foot, rounded to the nearest cen

1. The problem is to evaluate an expression or value, but the specific expression is not provided. 2. To evaluate an expression, you substitute values into the expression and simpl

1. **Stating the problem:** We need to find digits represented by letters in the cryptarithm equation $KAKS + KUUS = 8888$ where each letter represents a single digit. 2. **Underst

1. **State the problem:** Simplify the expression $\frac{5i}{3 - i}$. 2. **Formula and rules:** To simplify a complex fraction with a complex denominator, multiply numerator and de

1. Let's start by stating the problem: Understanding logarithms (log) and how they work. 2. A logarithm answers the question: To what power must we raise a base number to get anoth

1. **State the problem:** Solve the logarithmic equation or expression given (user did not specify the exact problem, so we will explain general solving steps for logarithmic equat

1. The problem is to graph the solution to the inequality $|w| > 2$ on the number line. 2. Recall the definition of absolute value: $|w|$ represents the distance of $w$ from 0 on t

1. The problem is to understand the concept of logarithms (log) and how to work with them. 2. A logarithm answers the question: to what power must we raise a base number to get ano

1. Let's start by understanding the problem: you want help with a math question at grade 9 level. 2. Since you didn't specify a particular problem, I'll explain a common grade 9 to