🧮 algebra

1. Stating the problem: Solve for $k$ in the equation $$\frac{-13.3 + k}{11.796} = -0.296.$$ 2. Multiply both sides by 11.796 to isolate the numerator:

1. The problem states that $\sqrt[3]{\sqrt{x}} = 2$. We need to find the value of $x$ that satisfies this equation. 2. Rewrite the equation using exponents: $\sqrt{x} = x^{\frac{1}

1. **State the problem:** Solve for $x$ in the equation $$\frac{2}{2x^2 + 3x - 1} = \frac{1}{x^2 - 1}.$$\n\n2. **Rewrite the equation:** Cross-multiply to eliminate the denominator

1. **State the problem:** Solve the equation $$(x - 3)^{\frac{3}{5}} = 8$$ for $x$. 2. **Isolate the expression:** The equation is already isolated with the power expression on one

1. The problem is to check the value of an expression or function at $x = -8.5$. 2. Since the user did not specify the exact expression or function, let's assume a general example:

1. The problem is to solve the equation and then check the solution for the number 2. 2. Since the user did not specify the exact equation, let's assume the equation is $x = 2$.

1. The problem is to find the slopes of the linear equations numbered 12 to 22. 2. Recall that the slope of a line in the form $Ax + By = C$ is given by $m = -\frac{A}{B}$.

1) Rendre le dénominateur entier naturel : A = \frac{\sqrt{7} - \sqrt{3}}{\sqrt{7} + \sqrt{3}}

1. The problem is to find the slopes from given linear equations. 2. Recall that the slope of a line in the form $y = mx + b$ is the coefficient $m$ of $x$.

1. The problem is to find the slope of a line given its equation. 2. The slope of a line in the form $y = mx + b$ is the coefficient $m$ of $x$.

1. The problem is to rewrite and analyze the given linear equations from 11 to 18. 2. For equation 11: Given \(3x + 2y = 6\) and \(2y = -3x + 6\), both represent the same line. Sol

1. **Problem 1:** Simplify and verify the expression $$\frac{2}{x+2} + \frac{4}{x-2} = \frac{x-1}{x^2-4}$$. 2. First, note that $$x^2 - 4 = (x+2)(x-2)$$.

1. **State the problem:** A company wants to reduce its number of stores by 40% over two years. 2. After the first year, the company has already reduced the stores by 20%. We need

1. The problem is to understand or verify the expression $6 + 8\sqrt{2}$. 2. This expression is a sum of a rational number 6 and an irrational number $8\sqrt{2}$.

1. The problem is to understand what it means when the denominator of a fraction is 1. 2. A fraction is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominat

1. **State the problem:** We want to show that $\frac{4 + \sqrt{8}}{\sqrt{2} - 1}$ can be written in the form $a + b\sqrt{2}$ where $a$ and $b$ are integers. 2. **Rationalize the d

1. **State the problem:** Expand and simplify the expression $$(4x^2 - y^2)^2$$ as a polynomial in standard form. 2. **Recall the formula:** The square of a binomial difference is

1. The problem is to expand and simplify the expression $$(5x^4 + y^2)^2$$ into a polynomial in standard form. 2. Use the formula for the square of a binomial: $$(a + b)^2 = a^2 +

1. The problem asks us to expand and simplify the expression $$\left( 2x^5 - y^2 \right)^2$$ as a polynomial in standard form. 2. Recall the formula for the square of a binomial: $

1. The problem is to expand the expression $$(2x^5 - y^2)^2$$. 2. Use the formula for the square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$.

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.