🧮 algebra

1. The problem asks to find the result of the expression $$\frac{7}{9} - \frac{3}{9}$$. 2. Since the denominators are the same, we can subtract the numerators directly: $$\frac{7}{

1. **State the problem:** Simplify the expression $9x^2(5-\sqrt{x})$. 2. **Recall the distributive property:** To simplify expressions like this, multiply $9x^2$ by each term insid

1. **Problem:** Solve the equation $7 - (4x - 5) = 18$. 2. **Formula and rules:** To solve linear equations, first simplify both sides by removing parentheses and combining like te

1. **Énoncé du problème** : Montrer que la fonction carrée $f(x) = x^2$ est croissante sur $[0; +\infty[$ et décroissante sur $]-\infty; 0]$. 2. **Définition d'une fonction croissa

1. The problem is to solve the equation $2x + 3 = 11$ for $x$. 2. The formula used here is to isolate the variable $x$ by performing inverse operations.

1. **State the problem:** We are given the cost function $C(x) = 0.5x^2 + 50x + 100$ and the revenue function $R(x) = 80x - 0.01x^2$. We need to find the profit function $P(x)$, th

1. **State the problem:** Solve the equation $$\sqrt{x} + 2 = 8$$ and check the solution. 2. **Isolate the square root term:** Subtract 2 from both sides:

1. **Problem statement:** A competitor runs a 20 km race. - First 4 km at 6 minutes per km.

1. **Planteamiento del problema:** Resuelve la ecuación $$-5(2 - x) + 3(2x + 4) = 5(4x - 2)$$ 2. **Fórmulas y reglas:** Para resolver ecuaciones lineales, aplicamos la propiedad di

1. **State the problem:** Greg rows at 2 1/2 miles per hour in still water. It takes the same time to row 3 miles upstream and 4 1/2 miles downstream. We need to find the rate of t

1. **State the problem:** Solve the equation $$200 - (x - 30) \times 50 = \square$$ for $x$. 2. **Rewrite the equation:**

1. The problem is to convert the fraction \(\frac{1}{4}\) into decimal form. 2. The formula to convert a fraction to decimal is to divide the numerator by the denominator.

1. **State the problem:** Find the distance between the points $(-3,4)$ and $(5,1)$. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given b

1. **Stating the problem:** Multiply the three fractions $\frac{4}{5}$, $\frac{20}{9}$, and $\frac{18}{8}$.\n\n2. **Formula used:** To multiply fractions, multiply the numerators t

1. The problem is to solve the equation or expression labeled as "oef 9" (exercise 9). Since the exact problem is not provided, please provide the full problem statement for accura

1. **Stel het probleem vast:** We lossen de eerste oefening op, namelijk 8) Het gemiddelde van een rij getallen is 38. We bepalen het nieuwe gemiddelde als elk waarnemingsgetal wor

1. **State the problem:** Write the expression $\frac{8}{\sqrt{3}}$ in the form $\frac{a\sqrt{b}}{c}$ where $a$, $b$, and $c$ are integers. 2. **Formula and rule:** To rationalize

1. **State the problem:** Expand and simplify the expression $$(3 + \sqrt{7})(4 + \sqrt{7})$$. 2. **Formula used:** Use the distributive property (FOIL method) for binomials: $$(a

1. **State the problem:** Expand and simplify the expression $$\sqrt{8} (\sqrt{50} - 10\sqrt{10})$$. 2. **Recall the properties of square roots:**

1. **Problem statement:** Solve the logarithmic equations: 3) $$\log_3^2 x + \log_3 x^2 = 8$$

1. **State the problem:** We are given two functions $f(x) = \frac{x+4}{x}$ and $g(x) = x+3$. We need to find the composition $(f \circ g)(x)$, which means $f(g(x))$, and then dete