🧮 algebra

1. **State the problem:** Simplify the expression $\frac{4}{1.2}$. 2. **Formula and rules:** Division of decimals can be simplified by converting the divisor to a whole number. Mul

1. **State the problem:** Solve the exponential equation $$5^{2x+4} + 1 = 26 \cdot 5^{x+1}$$. 2. **Recall the properties of exponents:**

1. The problem is to divide two polynomials using the long division method. 2. The general formula for polynomial long division is: Divide the leading term of the dividend by the l

1. **State the problem:** We need to divide the binary number $111110000001_2$ by $111111_2$ using long division in base 2. 2. **Recall the division process:** Binary long division

1. **State the problem:** Simplify the expression $$\frac{20m^2 n^2 p}{4 m n p}$$. 2. **Recall the rules:** When dividing terms with the same base, subtract the exponents: $$\frac{

1. **State the problem:** Solve the equation $$(2^x)^2 + 2^x - 6 = 0$$ for $x$. 2. **Rewrite the equation:** Note that $$(2^x)^2 = 2^{2x}$$, so the equation becomes:

1. Énonçons le problème : Résoudre l'inéquation $$x^2 + 2x + 1 \geq 0$$. 2. Rappelons la formule et les règles importantes :

1. Énonçons le problème : Résoudre l'inéquation $$3x^2 + 2x + 7 \geq 0$$. 2. Rappelons que pour une fonction quadratique $$ax^2 + bx + c$$, le signe dépend du discriminant $$\Delta

1. **State the problem:** Show that for the function $f(x) = 5^x$, the difference quotient is

1. **Problem:** Simplify the expression $(8a - 5a^3) + (4a^3 + a)$. 2. **Formula and rules:** Combine like terms by adding or subtracting coefficients of terms with the same variab

1. **State the problem:** Solve the equation $$\partial^2 \sqrt{5x} - 14 = 0$$. 2. **Interpret the problem:** The symbol $$\partial^2$$ usually denotes a second partial derivative,

1. **State the problem:** Simplify and solve the expression $ (x + y)^2 - 10(x + y) + 25 $. 2. **Recognize the formula:** This expression resembles a quadratic in terms of $ (x + y

1. Énonçons le problème : Étudier les variations de la fonction $f$ définie par $f(x) = e^{-2x + 3}$. 2. Rappelons la formule et les règles importantes :

1. **State the problem:** Calculate $\frac{1}{3} - \frac{1}{4}$ of $\frac{4}{3}$. 2. **Understand the expression:** The word "of" means multiplication, so the expression is $\frac{

1. Énonçons le problème : Résoudre l'inéquation $$\frac{4x + 7}{6x + 4} \geq \frac{\sqrt{15}}{6}$$. 2. Rappelons que pour résoudre une inéquation de la forme $$\frac{A}{B} \geq C$$

1. The problem is to understand if factoring out 2 from an equation is correct. 2. Factoring means taking a common factor from terms in an expression.

1. **State the problem:** Calculate the state income tax owed on a $70,000 salary using the given progressive tax rates. 2. **Understand the tax brackets and rates:**

1. **State the problem:** Calculate the state income tax owed on a 50000 salary using the given progressive tax rates. 2. **Understand the tax brackets:**

1. **State the problem:** Calculate the state income tax owed on a 70,000 salary using the given progressive tax rates. 2. **Understand the tax brackets:**

1. **State the problem:** Calculate the state income tax owed on a salary of $40,000 using the given progressive tax rates. 2. **Understand the tax brackets:**

1. **State the problem:** Calculate the total state income tax owed on a $60,000 salary using the given progressive tax rates. 2. **Given tax brackets and calculations:**