🧮 algebra

1. **State the problem:** Simplify the expression $a + a \times a$. 2. **Recall the order of operations:** Multiplication is performed before addition.

1. **State the problem:** We need to graph the rational function $$R(x) = \frac{x + 6}{x(x + 12)}$$. 2. **Identify intercepts:**

1. **State the problem:** We need to analyze the rational function $$R(x) = \frac{x+6}{x(x+12)}$$ to determine where its graph is above or below the x-axis and identify the correct

1. **Problem statement:** A student answered 120 True/False questions. Each correct answer gives 1 mark, each wrong answer deducts 1/4 mark. The student scored 90 marks. If all gue

1. The problem is to calculate the final grade based on weighted components. 2. The weights and achieved percentages are:

1. **State the problem:** Solve for $w$ in the equation $1.74 = w - 3.68$. 2. **Formula and rule:** To isolate $w$, add $3.68$ to both sides of the equation to cancel out the $-3.6

1. **State the problem:** Evaluate the expression $\frac{x}{6} + 3$ when $x = -24$. 2. **Substitute the value:** Replace $x$ with $-24$ in the expression:

1. **State the problem:** Calculate the product of the mixed fractions $1 \frac{7}{8}$ and $2 \frac{7}{15}$ and express the result as a reduced mixed fraction. 2. **Convert mixed f

1. The problem is to find the number of terms in the finite arithmetic sequence: 16, 11, 6, 1, ..., -239. 2. The formula for the $n$-th term of an arithmetic sequence is:

1. **State the problem:** Calculate the product of the fractions $\frac{6}{7} \times \frac{14}{21} \times \frac{14}{3}$.\n\n2. **Recall the multiplication rule for fractions:** Whe

1. **Problem:** The function $y=5\sin(x)-7$ is translated to $y=5\sin(x)$. We need to find the translation. 2. **Understanding the problem:** The original function is shifted verti

1. The problem asks to add the fractions $\frac{1}{3}$ and $\frac{1}{2}$. To add fractions, we need a common denominator. 2. The least common denominator (LCD) of 3 and 2 is 6.

1. **Problem 1: Multiply the fractions** $\frac{2}{3} \times \frac{6}{5}$. 2. Use the multiplication rule for fractions: multiply numerators and denominators:

1. **State the problem:** We need to factor the quadratic expression $x^2 + 5x + 6$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers t

1. The problem is to find the number that replaces the box in the equation $\frac{3}{4} = \frac{\Box}{20}$. 2. We use the property of equivalent fractions: if $\frac{a}{b} = \frac{

1. **State the problem:** Solve the equation $3^{1-2x} = 4^x$ for $x$. 2. **Recall the formula and rules:** When bases are different, take the logarithm of both sides to solve for

1. The problem is to verify the equation $1=1$. 2. This is a simple equality statement asserting that the number one is equal to itself.

1. The problem asks: In 2015, how many more dollars was Apple's stock price compared to its price in 2010? 2. From the graph description, the stock price in 2010 was about $30.

1. **State the problem:** We are given the function $f(x) = -5^x$ and asked to find its vertical and horizontal asymptotes. 2. **Recall the definitions:**

1. **State the problem:** We have 11 ducks, each having either 8 or 9 ducklings. The total number of ducklings is 92. We need to find how many ducks had 8 ducklings. 2. **Define va

1. **State the problem:** Simplify the expression $$\frac{\left(\frac{2}{3} a^{9} b^{-10} c^{4}\right)^{-1} \left(\frac{5}{4} a^{-2} b^{3} c^{-5}\right)^{-2}}{\left(-\frac{1}{3} a^