🧮 algebra

1. **State the problem:** Simplify the expression $20\sqrt{20} \div 4\sqrt{4}$. 2. **Recall the properties:** The square root of a product can be separated as $\sqrt{a} \times \sqr

1. Stating the problem: Simplify the expression $\sqrt{5} \times \sqrt{11}$. 2. Formula used: The product of square roots rule states that $\sqrt{a} \times \sqrt{b} = \sqrt{a \time

1. The problem asks to convert 12°F to Celsius using the formula: $$C = \frac{5}{9} (F - 32)$$

1. The problem is to evaluate the expression $7x + 2y + \frac{x}{2}$ when $x=2$ and $y=4$. 2. The expression is a linear combination of $x$ and $y$ with an additional fractional te

1. **State the problem:** We need to find the distance between a bird flying 3500 m above sea level and a diver 40 m below sea level. 2. **Understand the positions:** The bird is a

1. **State the problem:** Evaluate the expression $3 \times (-3)^2 \times 10^0$. 2. **Recall the rules:**

1. **State the problem:** Solve for $x$ in the equation $$\frac{x}{-6} = 6.$$\n\n2. **Formula and rule:** To isolate $x$, multiply both sides of the equation by $-6$ (the denominat

1. The problem is to find the Greatest Common Factor (GCF) of 18 and 24. 2. The factors of 18 are correctly listed as $1, 2, 3, 6, 9, 18$.

1. **State the problem:** We are given the formula relating surface area $A$ and volume $V$ of a cube: $$A = 6V^{\frac{2}{3}}$$ and the surface area $A = 486$ square inches. We nee

1. The problem asks to express the fifth root of $n^4$ using rational exponents. 2. Recall the rule for radicals and exponents: $$\sqrt[b]{a^c} = a^{\frac{c}{b}}$$ where $b$ is the

1. **State the problem:** We are given two functions: $$h(x) = x^2 - 7$$

1. **State the problem:** We are given two functions: $$q(x) = x^2 + 9$$

1. **State the problem:** Solve the inequality $$\frac{1}{7}(42x + 28) < 28$$ to find the values of $x$ that satisfy it. 2. **Use the distributive property:** Multiply both sides b

1. **State the problem:** Solve the equation $$16(5 - 2x)^2 + 33 = 42$$ for $x$. 2. **Isolate the squared term:** Subtract 33 from both sides:

1. **State the problem:** Solve the equation $5(3x + 6)^2 + 9 = 44$ for $x$. 2. **Isolate the squared term:** Subtract 9 from both sides:

1. **State the problem:** Solve the equation $5(x - 4)^2 = 30$ for $x$. 2. **Isolate the squared term:** Divide both sides by 5 to simplify.

1. **State the problem:** Solve the quadratic equation $$5(x^2 - 7) - 1 = 9$$ for all values of $x$ in simplest form. 2. **Expand and simplify:** Distribute the 5 inside the parent

1. **State the problem:** Solve the quadratic equation $$4(x + 6)^2 - 50 = 26$$ for all values of $x$ in simplest form. 2. **Isolate the squared term:** Add 50 to both sides to mov

1. **State the problem:** Solve the quadratic equation $$4(x + 1)^2 - 7 = 45$$ for all values of $x$ in simplest form. 2. **Add 7 to both sides to isolate the squared term:**

1. **State the problem:** Solve the quadratic equation $$5(x - 7)^2 = 10$$ for all values of $x$ in simplest form. 2. **Isolate the squared term:** Divide both sides of the equatio

1. **State the problem:** We are given the function $f(x) = 3x^2 + x^3$ and asked to analyze its intercepts, symmetry, and graph behavior. 2. **Find x-intercepts where the graph to