🧮 algebra

1. **State the problem:** Given the equation $$(x^5)^{\frac{1}{3}} \sqrt[3]{x^2} = x^a$$ with $x > 0$, find the value of $a$.

1. The problem is to reduce the fraction $\frac{2}{11}$ to its lowest terms. 2. To reduce a fraction, we find the greatest common divisor (GCD) of the numerator and denominator.

1. **State the problem:** Reduce the improper fraction $\frac{14}{12}$ to its lowest terms. 2. **Formula and rules:** To reduce a fraction, divide the numerator and denominator by

1. The problem is to compare the two fractions $\frac{5}{6}$ and $\frac{5}{7}$.\n\n2. To compare fractions, we can find a common denominator or cross-multiply.\n\n3. Using cross-mu

1. **State the problem:** We need to evaluate each algebraic expression for the given variable values in Option A and Option B. 2. **Expressions:**

1. Stating the problem: Simplify the expression $$\frac{28}{70} \cdot \frac{30}{12}$$. 2. Use the rule for multiplying fractions: multiply the numerators together and the denominat

1. The problem is to simplify the fraction $\frac{30}{24}$. 2. To simplify a fraction, we divide the numerator and denominator by their greatest common divisor (GCD).

1. **State the problem:** Simplify the product of the fractions $$\frac{38}{22} \cdot \frac{66}{9} \cdot \frac{21}{57}$$. 2. **Write the expression:**

1. **State the problem:** Solve the equation $$4(x + 2) = 8$$ for $$x$$. 2. **Use the distributive property and isolate the term with $$x$$:**

1. **State the problem:** Solve the linear system: $$3x + 4y = 72.1/2x + 2y = -2$$

1. The problem asks us to find where the function $f(x)$ is less than zero, i.e., where $f(x)<0$. 2. From the graph description, $f(x)$ has a peak around $x=-4$, a trough near $x=2

1. **Problem statement:** Solve the inequality $f(x) < 0$ using the graph of $y = f(x)$. Write the solution set in interval notation. 2. **Understanding the problem:** We need to f

1. The problem is to perform a manual solution, but since no specific problem was given, I will demonstrate solving a simple linear equation: $2x + 3 = 7$. 2. The formula or approa

1. **State the problem:** We need to find the equation of a parabola given its focus at $(0, -5)$ and its directrix $y = 11$.

1. **State the problem:** We are given a parabola with a focus at $ (3, 6) $ and a directrix $ y = -4 $. We need to find the equation of the parabola and describe its properties. 2

1. **State the problem:** Kareem mixes lemonade with a ratio of 3 cups lemon juice to 4 cups water. He uses 32 cups of water and we need to find how many cups of lemon juice are in

1. **State the problem:** Solve for $x$ in the equation $$\frac{7}{3}x - 5 = -\frac{7}{4}x - \frac{1}{2}.$$\n\n2. **Write down the equation:** $$\frac{7}{3}x - 5 = -\frac{7}{4}x -

1. **State the problem:** Solve for $y$ in the equation $$7(y - 9) - 2 = -7(-4y + 7) - 9y.$$\n\n2. **Apply the distributive property:** Multiply out the parentheses on both sides.\

1. **State the problem:** We are given the distance functions for a minivan and a pickup truck as functions of time in hours, $x$. The minivan's distance is given by $y=45x$. We ne

1. **Problem Statement:** Find the average rate of change of the sheep's mass between $t=103$ and $t=111$ days, where $M(t) = 27.6 + 0.3t - 0.001t^2$.

1. Stating the problem: Simplify the expression $$\frac{\sqrt{-6}}{\sqrt{-3} \times \sqrt{-5}}$$ and write the result in the form $a + bi$ where $a$ and $b$ are real numbers. 2. Re