🧮 algebra

1. The problem is to simplify or understand the expression $23\sqrt{2}$. 2. The expression consists of a coefficient 23 multiplied by the square root of 2.

1. **State the problem:** We need to find what percent of 5,000 people had a mild allergic reaction if 30 people reacted. 2. **Write the proportion:** The problem gives the proport

1. **State the problem:** Solve the expression $\frac{39 - 3}{6} + 3^2$. 2. **Apply the order of operations (PEMDAS/BODMAS):**

1. **State the problem:** We want to find the limit as $n$ approaches infinity of the expression $$\frac{n^8 + n^2 + 1}{n^6 + 2} \cdot \frac{2n + 3}{n^3 + 1}.$$\n\n2. **Recall the

1. **State the problem:** Make $x$ the subject of the equation $$y = \frac{\sqrt{x + 1}}{x - 4}.$$\n\n2. **Understand the formula and rules:** We want to isolate $x$ on one side. T

1. **State the problem:** Make $x$ the subject of the equation $$y = \sqrt{\frac{x + 1}{x - 4}}.$$\n\n2. **Rewrite the equation:** To isolate $x$, first square both sides to remove

1. **State the problem:** Make $x$ the subject of the formula $$y = \sqrt{\frac{3x - 2}{x + 1}}$$. 2. **Square both sides** to eliminate the square root:

1. The problem asks us to identify which line has a slope of 1 and which has a slope of 2 on the given grid graph. 2. Recall that the slope of a line is calculated as the "rise ove

1. **State the problem:** We have six lines labeled A to F and a list of slopes: $\frac{1}{2}$, 2, 1, 0.25, $-\frac{3}{4}$, and $-2$. We need to match each line A to E with a slope

1. **Solve the quadratic equation** $x^2 - 5x + 6 = 0$. Use the factorization method: find two numbers that multiply to 6 and add to -5. These are -2 and -3.

1. Problem 10a: Calculate the total donations from Mr. Smith and Ms. Brown. 2. Use the formula for adding fractions: $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$.

1. **Problem 1:** Determine which equation is NOT equivalent to $9 |x - 1| = 27$. 2. Start by simplifying the given equation:

1. **State the problem:** We need to find the value of $2x + 5$ given the equation $$3(2x + 5) = 6(2x + 5) - 12.$$ 2. **Write down the equation:** $$3(2x + 5) = 6(2x + 5) - 12.$$

1) Résoudre dans $\mathbb{R}$ l'équation $|x - 2| - |x| = 6$. **Étapes :**

1. **State the problem:** Simplify the expression $$(2x^3 - x^2)(x^2 - x + 6)$$. 2. **Recall the distributive property:** To simplify a product of two polynomials, multiply each te

1. **State the problem:** We need to find how many times greater the number of viruses is compared to the number of phytoplankton in a 1-liter sea water sample. 2. **Given data:**

1. **State the problem:** Simplify the expression $$\frac{(ps^4)^{-4}}{(-p^5 s^{-4} p^{-3})^3}$$ and write the answer with only positive exponents. 2. **Recall exponent rules:**

1. **State the problem:** Simplify the expression $$\frac{y^{4} g^{-2}}{\left(-h^{0} g^{3} y^{-1}\right)^{5}}$$ and write the answer with only positive exponents. 2. **Recall impor

1. The problem is to solve the equation or expression shown in the picture. Since the picture is not provided, I will explain a general approach to solving algebraic problems. 2. F

1. Problem 37: Given digits A and B, two-digit numbers AB and 5A satisfy the equation $$AB \times 3 = 5A$$. Find $$A^2 + B^2$$. 2. Let the two-digit number AB be $$10A + B$$ and 5A

1. **State the problem:** We need to multiply the two polynomials $$(-5x^2 - 2x + 2)$$ and $$(5x^3 + 3)$$. 2. **Formula and rules:** To multiply polynomials, use the distributive p