🧮 algebra

1. The problem is to continue simplifying or operating with the given expressions. 2. Let's start with the first fraction: $$\frac{x^2 - 1}{x^2 - 3x}$$.

1. **Stating the problem:** We are given that the cost $C$ of registering for an examination is partly constant and partly varies with the number of subjects $N$. We know:

1. **State the problem:** Simplify the expression $3x^3 + 2 - x(5xy^2)(-\frac{1}{5}x)$.\n\n2. **Recall the rules:** When multiplying terms with the same base, add exponents: $x^a \

1. **State the problem:** Express the repeating decimal $0.21\overline{21}$ as a fraction using the sum of an infinite geometric series. 2. **Recall the formula for the sum of an i

1. **Problem statement:** Find possible function equations for the given graphs based on their properties.

1. **State the problem:** Simplify the expression $x \cdot x^{-3}$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, ad

1. **State the problem:** Solve the equation $$0 = 2x - 32x^{-3}$$ for $x$. 2. **Rewrite the equation:** The equation is $$0 = 2x - 32x^{-3}$$.

1. **State the problem:** Simplify the expression $\frac{-3x+4}{2x+3}$. 2. **Identify the expression:** This is a rational expression, a fraction where both numerator and denominat

1. The problem is to simplify the expression $6x^0$. 2. Recall the rule that any nonzero number raised to the power of zero equals 1, i.e., $x^0 = 1$ for $x \neq 0$.

1. **State the problem:** Solve the equation $x^2 - x2 = 36$. 2. **Rewrite the equation:** The term $x2$ is ambiguous, but it likely means $2x$. So the equation becomes:

1. **State the problem:** Simplify the expression $10x^2 - 8x^2$. 2. **Recall the rule:** When subtracting like terms, subtract their coefficients and keep the variable part unchan

1. **State the problem:** Simplify the expression $a^4 \cdot a^3$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same base, add

1. **Problem Statement:** We are given population data for an animal over years 0 to 5 and need to find an exponential model that fits this data and then predict the population at

1. **State the problem:** Solve the equation $$0 = (x - 1)(x - 3)$$ for $x$. 2. **Recall the zero product property:** If a product of two factors equals zero, then at least one of

1. **State the problem:** Calculate the value of the expression $$D = 2.75 \times \log 7.7 - \left(\frac{1}{7.7}\right)^{0.5}$$ where \(\log\) denotes the logarithm base 10.

1. **State the problem:** Calculate the value of $$D$$ given the formula $$D = 2.75 \times \log A - \sqrt{\frac{1}{A}}$$ where $$A = 7.7$$ million. 2. **Write the formula and expla

1. **State the problem:** We are given a linear relationship between the total cost $y$ and the number of months $x$ for operating a café. The cost function is $y = 20000 + 6000x$.

1. **State the problem:** We are given data points for $x$ and $y$ and asked to draw the graph of $y$ against $x$ for $0 \leq x \leq 15$ (part c), and to find a possible value of $

1. **State the problem:** Solve for $M$ in the equation $$-\frac{5}{6} + M = \frac{4}{3}.$$\n\n2. **Isolate $M$:** Add $\frac{5}{6}$ to both sides to get $$M = \frac{4}{3} + \frac{

1. **State the problem:** There are 35 kids in a class with boys to girls ratio of 3:4. We need to find how many boys and girls are there. 2. **Use the ratio formula:** If the rati

1. The problem is to find the ratio of 35 to the ratio 3:4. 2. A ratio compares two quantities. The ratio 3:4 means for every 3 parts of one quantity, there are 4 parts of another.