🧮 algebra

1. The problem asks to solve for the values 3 and 4 in the given context. 2. Since no specific equation or expression is provided, we interpret the request as evaluating or confirm

1. Convert the number systems: 1.1 Convert binary $10101110_2$ to denary:

1. **Problem:** Find the inverse of the function $f(x) = 5x - 4$. 2. To find the inverse, replace $f(x)$ with $y$:

1. Problema afirmă că pentru orice număr natural $n$, expresia $n^3 - n$ este divizibilă cu 3, adică $3 \mid n^3 - n$. 2. Se observă că $n^3 - n = n(n^2 - 1) = n(n-1)(n+1)$, adică

1. The problem is to simplify the expression $24 - 2(3 \times 1)$.\n\n2. First, evaluate the multiplication inside the parentheses: $3 \times 1 = 3$.\n\n3. Substitute back into the

1. **State the problem:** Solve the inequality $x(x-2) \ge 9 - 2x$. 2. **Expand and simplify:**

1. **State the problem:** Solve the equation $$\frac{y-1}{3} - \frac{y-2}{4} = 1$$ using the systematic method. 2. **Find a common denominator:** The denominators are 3 and 4, so t

1. **Difference between a relation and a function:** A relation is any set of ordered pairs, where each input (domain element) is related to one or more outputs (range elements).

1. Énoncé : Soient $a$, $b$ impairs, déterminer la parité de : a. $3a$

1. The problem is to solve the quadratic equation $$2x^2 - 4x - 6 = 0$$. 2. First, identify the coefficients: $$a = 2$$, $$b = -4$$, and $$c = -6$$.

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. The problem is to solve the equation $$2x + 3 = 11$$ for $x$. 2. Start by isolating the variable term $2x$ on one side. Subtract 3 from both sides:

1. The problem asks to evaluate the product \(\prod_{k=1}^{n} k\), which means multiplying all integers from 1 to \(n\).\n\n2. This product is known as the factorial of \(n\), deno

1. The problem asks to solve the equation $f(x) = -4$ where $f(x) = 2x^2 - 2x - 64$. 2. Set the function equal to $-4$:

1. **State the problem:** Solve the equation $$\frac{2}{3} \cdot (3x - 4) = -\frac{5}{3} - (2x + 3)$$ for $x$. 2. **Distribute the fraction on the left side:**

1. The problem is to evaluate the expression $120\% - 3 + 2 \times 0.75 + \frac{2}{3}$.\n\n2. Convert the percentage to a decimal: $120\% = 1.20$.\n\n3. Substitute the decimal back

1. Stating the problem: Solve the equation $$-2x + \frac{1}{2} = \frac{3}{2} + \frac{1}{3}\left(x - \frac{1}{2}\right)$$ for $x$. 2. Expand the right side: $$\frac{1}{3}\left(x - \

1. Solve the first equation: $$\frac{2}{3} \cdot (3x - 4) = -\frac{5}{3}$$ Multiply out the left side:

1. Calculer et simplifier $A = \frac{4725}{2625}$. - Trouvons le plus grand commun diviseur (PGCD) de 4725 et 2625.

1. The problem is to evaluate the expression $120\% - 3 + 2 \times 0.75 + 0.6$. 2. Convert the percentage to a decimal: $120\% = 1.20$.

1. Stating the problem: Solve the equation $$\frac{2}{3} x - 8 = 4 \cdot (x - 5)$$ for $x$. 2. Expand the right side: $$4 \cdot (x - 5) = 4x - 20$$.