🧮 algebra

1. **State the problem:** Determine the values of $x$ for which the rational expression $$\frac{x^2 + 64}{8}$$ (a) equals zero and (b) is undefined.

1. **State the problem:** We have a dot plot showing shower times (in minutes) for 20 students, with a total shower time of 180 minutes. 2. **Given data:**

1. **Problem:** Evaluate $4 \frac{1}{2} \div \frac{3}{8}$. 2. **Convert mixed number to improper fraction:**

1. The problem is to graph the quadratic function $f(x) = -\frac{1}{2}x^2 + 3$. 2. This is a quadratic function, which generally has the form $f(x) = ax^2 + bx + c$.

1. The problem is to understand and solve a typical Grade 8 AEP (Advanced Education Program) math question, but since no specific question was provided, I will explain a common alg

1. **State the problem:** Find the sum of the arithmetic sequence from the 30th term to the 75th term.

1. Stating the problem: We need to add the fractions $\frac{10}{7}$ and $\frac{9}{7}$.\n\n2. Formula: When adding fractions with the same denominator, add the numerators and keep t

1. The problem asks: What fraction of Mel's dinners in April were fish dinners? 2. To find the fraction of fish dinners, we use the formula:

1. **State the problem:** Solve the quadratic equation $$x^2 - 4 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can use factor

1. The problem is to find the equation of the line created by two given points or lines. 2. The general formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is

1. **State the problem:** Solve the system of equations by graphing: $$y - 5x = -26$$

1. **State the problem:** Simplify the expression $$\frac{(-3u^{-3}h^{3})^{5}}{12u^{-9}h^{10}}$$ and express it with only positive exponents. 2. **Apply the power to each factor in

1. **State the problem:** Simplify the expression $$\frac{-4(r^4t^{-2})^{-1}}{4r^2t^4}$$ so that it contains only positive exponents. 2. **Recall the rules:**

1. **State the problem:** Kayleigh ran 20 miles. Charlie ran 3 times as many miles as Kayleigh, and Zion ran 2 times as many miles as Charlie. We need to find how many miles Zion r

1. The problem asks to identify the graph of the function $$h(x) = -\tan\left(\frac{1}{2}x\right)$$ from two options. 2. The parent tangent function is $$\tan(x)$$, which has verti

1. **Problem statement:** Kelly needs to rent tables for exactly 240 people using 6-person rectangular tables and 10-person round tables. The constraints are:

1. **Problem statement:** Kelly needs to rent tables for exactly 240 people using 6-person rectangular tables and 10-person round tables. The constraints are:

1. **State the problem:** Given the equation $$\frac{1}{4}x + 5 = 7$$, prove that $$x = 8$$. 2. **Review the given proof steps:**

1. **State the problem:** Karen spends money on food, hall, and DJ, then sells tickets. We need to find the percentage profit she makes. 2. **Calculate total cost:**

1. **Problem 1(a): Expand and simplify** $3(2y - 5) + 7(y + 2)$ 2. Use the distributive property: multiply each term inside the parentheses by the factor outside.

1. **State the problem:** Solve the equation $8(x-3)-2(3-x)=2(x+2)-5(5-x)$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor outside.