🧮 algebra

1. Problem 7 states: If $(x-4)$ varies inversely as $(y+3)$, and given $x=8$ when $y=2$, find $x$ when $y=1$. 2. Write the inverse variation equation:

1. Problem 7: If $(x - 4)$ varies inversely as $(y + 3)$ and $x = 8$ when $y = 2$, find the value of $x$ when $y$ equals one of the options. Step 1: Write inverse variation formula

1. State the problem: Solve for $x$ the quadratic equation $$2x^2 - 4x - 6 = 0.$$\n\n2. Use the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a=2$, $b=-4$, and

1. Problem: Complete the blanks in the expressions involving powers and roots linked to the number 5 and 625. 2. Given:

1. The problem asks to express the product $2^{1/5} \times 2^{2/5}$ in radical form. 2. Recall that when multiplying powers with the same base, add the exponents:

1. The problem asks us to multiply the expressions $2^{1/5}$ and $2^{2/5}$ and express the result in radical form. 2. Recall the exponent rule: when multiplying powers with the sam

1. The problem is to simplify the expression $X^2-2\sqrt{30}-11$. 2. Notice that this expression contains a variable $X^2$, a constant term $-11$, and a term involving the square r

1. State the problem: Evaluate the expression $15 + [2^2 \{0.5 (3 - 7) + 8\} - 3^3]$. 2. Simplify inside the parentheses first: $3 - 7 = -4$.

1. We are given the function $y = \frac{12}{x}$ where $x \neq 0$, and an incomplete table of values. We need to fill in the missing $y$ values for given $x$ values. 2. Recall that

1. Stating the problem: Simplify the expression $$\frac{y_3}{y_5}$$. 2. Understanding the expression: Here, $y_3$ and $y_5$ represent variables with subscripts. When dividing varia

1. The problem is to understand the expression "To the power of three minus y to the power of 5." However, this phrase is ambiguous without a clear base for the powers. 2. If the i

1. The problem is to simplify the expression \( x^2 - 8xy \). 2. This expression consists of two terms: \( x^2 \) and \( -8xy \).

1. State the problem: Simplify the expression $\frac{6x - 4}{2} + \frac{20x + 25}{5}$.\n\n2. Simplify each term separately:\n- Divide $6x - 4$ by 2: $$\frac{6x - 4}{2} = \frac{6x}{

1. **State the problem:** Simplify the expression $$\frac{6x - 4}{2} + \frac{20x + 25}{5}$$

1. State the problem: We want to solve the equation $y = y^2$ for $y$. 2. Rearrange the equation to bring all terms to one side:

1. **Problem statement:** Solve the quadratic equation $x^2 + 6x + 5 = 0$ by completing the square. 2. **Step 1: Move constant to the other side.**

1. We are given the equation $\frac{3}{x+2} - \frac{1}{x} = \frac{1}{5x}$.\n2. To solve this equation, first find a common denominator for the terms on the left. The denominators a

1. Let's start by stating the problem: solve the quadratic equation by completing the square. 2. Consider a quadratic equation in the form $$ax^2 + bx + c = 0$$ where $$a \neq 0$$.

1. **State the problem:** We need to evaluate the expression $$4(x^2 - 1) + \frac{x^3}{4} + 12$$ when $$x = -2$$.

1. We are asked to solve the quadratic equation $4x^2 + ? = 0$ (assuming the general form $ax^2 + bx + c = 0$). 2. To proceed, I'll demonstrate solving a quadratic equation by two

1. Given the equation $a - \frac{1}{a} = 3$, find the value of $\frac{5a}{a^{2} + 2a - 1}$. Step 1: Multiply both sides of the equation by $a$ to clear the fraction: