🧮 algebra

1. **State the problem:** Simplify the expression $$(125 \cdot 7)^{\frac{1}{3}} \cdot x^{\frac{5}{3}} \cdot y^{\frac{9}{3}}$$. 2. **Rewrite the expression using properties of expon

1. **Problem statement:** Given the graph of the function $y = \frac{1}{f(x)}$ with vertical asymptote at $x = -2$, horizontal asymptote at $y = 0$, and points $(-3, -0.5)$ and $(-

1. **State the problem:** Find the value of the expression $$\frac{3m + 2n}{3k - 2m}$$ when $$m=4$$, $$n=3$$, and $$k=5$$. 2. **Write the expression with given values:** Substitute

1. The problem is to evaluate the expression $(-36)$. 2. Since the expression is just a single number with parentheses, it simply represents the number itself.

1. **State the problem:** Solve the inequality $$4x^4 + 16x^3 + 11x^2 - 28x + 6 > 0$$. 2. **Factor the polynomial if possible:** First, try to factor the quartic polynomial to find

1. **State the problem:** Carlos takes 16 minutes to cycle home from work on Wednesday. On Thursday, he cycles the same distance at half the speed. We need to find how long his jou

1. **State the problem:** Find the value of the expression $$\frac{3m+2n}{3k-2m}$$ when $$m=4$$, $$n$$ is missing (assumed to be 0), and $$k=5$$. 2. **Substitute the known values:*

1. **State the problem:** We need to find the value of $x$ that satisfies the equation $$3x + 4 = 9x - 8.$$ 2. **Write down the formula and rules:** To solve for $x$, we want to is

1. **State the problem:** Solve the linear equation $$3x + 4 = 9x - 8$$ to find the value of $x$ that makes the statement true. 2. **Write down the formula and rules:** To solve fo

1. **State the problem:** Solve the system of equations:

1. **State the problem:** Calculate the summation $$\sum_{i=3}^{4} i$$ which means adding the values of $i$ from 3 to 4. 2. **Formula and explanation:** The summation $$\sum_{i=a}^

1. The problem involves two separate variables $a$ and $b$, not their absolute values. 2. When working with two variables, expressions or equations involving $a$ and $b$ are treate

1. Problem Q4: Evaluate logarithms. 2. Recall the logarithm definition: $\log_b a = c$ means $b^c = a$.

1. **Problem:** Evaluate $\log_4 64$. 2. **Formula:** $\log_b a = c$ means $b^c = a$.

1. **Problem statement:** Evaluate $\log_4 64$. 2. **Recall the definition:** $\log_b a = c$ means $b^c = a$.

1. نبدأ بكتابة المعطيات: العدد المجهول هو $x$. 2. العدد الذي أضيف إلى 1 و 3 و 6 يجعل الأعداد في تناسب متسلسل، أي:

1. **Problem Statement:** Convert the fraction $\frac{7}{10}$ to a decimal and then to a percent. 2. **Formula and Rules:**

1. **Problem statement:** Find the equation of the line parallel to the line $x - 3y = 4$ that passes through the point $P'(7, 10)$.

1. The problem is to solve question 2, but since the exact question is not provided, please provide the full question for accurate solving. 2. Generally, to solve algebraic equatio

1. Let's state the problem: You know the midpoint of a line segment but not the endpoints, and you want to find the coordinates of the two original endpoints. 2. The formula for th

1. **State the problem:** Simplify the expression $\sqrt{16} + \sqrt{192}$ and express it in the form $\sqrt{a} + b$. Then find the value of $a - b$. 2. **Simplify each square root