🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{4a^4 + 8a^4}{6a^2}$$. 2. **Combine like terms in the numerator:** Since both terms have $a^4$, add the coefficients:

1. **State the problem:** Simplify the expression $4a^2 + 8a^2$. 2. **Identify like terms:** Both terms have the variable $a$ raised to the power of 2, so they are like terms and c

1. **State the problem:** Simplify the expression $$(5-y)(2y-5)-(4-y)2$$. 2. **Use the distributive property (FOIL) to expand each product:**

1. **State the problem:** Solve for $X$ in the equation $X = X$. 2. **Understand the equation:** The equation $X = X$ is an identity, meaning it is true for all values of $X$.

1. The problem asks us to interpret and find the value of $C(6)$ given a table of vehicle age in years and corresponding values in thousands. 2. From the table, $C(t)$ represents t

1. Stating the problem: Simplify the expression $4m^2 - 20am$. 2. Identify common factors: Both terms have a factor of $4m$.

1. The problem is to evaluate the expression $10 \times -15^2$. 2. According to the order of operations (PEMDAS/BODMAS), exponents are evaluated before multiplication.

1. **State the problem:** Simplify the expression $8a^3 - 6a^2$. 2. **Identify common factors:** Both terms have a common factor involving $a^2$ and a numerical factor.

1. **State the problem:** Find the equation of the line passing through points approximately (-1,12) and (1,-12) in slope-intercept form $y=mx+b$. 2. **Formula:** The slope $m$ of

1. **State the problem:** Simplify the expression $24a - 12ab$. 2. **Identify common factors:** Both terms have a common factor of $12a$.

1. The problem is to organize the given domain and range statements and inequalities into a coherent order, matching domains with their corresponding ranges and conditions. 2. We s

1. **State the problem:** Evaluate the expression $$|5 - 10| - |-6| - 4$$. 2. **Recall the definition of absolute value:** The absolute value of a number $x$, denoted $|x|$, is the

1. Problem: Simplify the expression $$a \cdot \left(\frac{a}{a-2}+1\right) : \left(a + \frac{a^{2}}{2-a}\right)$$. 2. First, rewrite the division as multiplication by the reciproca

1. **Problem Statement:** Determine which exponential formulas correspond to the curves labeled IV, V, and VI on the graph. 2. **Given formulas:**

1. The problem asks for the growth factor when water usage increases by 3% per year. 2. The growth factor in exponential growth is calculated as $1 + r$, where $r$ is the growth ra

1. The problem gives the exponential growth function $$Q = 79(1.002)^t$$ and asks to identify the starting value $a$, the growth factor $b$, and the growth rate $r$ as a percent. 2

1. **State the problem:** Tom bought a stamp for 900 and it increases in value by 6.3% each year. We want to find the value after 18 years assuming geometric growth. 2. **Formula u

1. **State the problem:** Simplify the expression $\left(\frac{a}{2} - 2\right) \left(\frac{a^2}{4} + a + 4\right)$.\n\n2. **Recall the distributive property:** To multiply two bin

1. The problem asks for the town's highest temperature given two temperatures: -28 °F and 138 °F. 2. To find the highest temperature, we compare the two values.

1. **State the problem:** Solve the simultaneous equations using the elimination method: $$2x + 3y = 13$$

1. **State the problem:** Simplify the expression $$(a+b+c)(a+b-c)$$. 2. **Recall the formula:** This is a product of two binomials with a similar structure. We can use the distrib