🧮 algebra

1. The problem is to understand and use the delta symbol, often represented as $\Delta$, which means "change in" or "difference in" a quantity. 2. The delta symbol is commonly used

1. **State the problem:** We need to find the numerator of the expression using the FOIL method. The numerator is:

1. Problema: Să înțelegem ce este o funcție injectivă. 2. Definiție: O funcție $f:A \to B$ este injectivă dacă pentru orice $x_1, x_2 \in A$, dacă $f(x_1) = f(x_2)$ atunci $x_1 = x

1. **Stating the problem:** Simplify the expression $$(x^2 - 2x + 3)(\Delta x^2 + 2x \Delta x - 2 \Delta x)(x^2 + 2x - 3)(x^2 + 2x - 3)(\Delta x^2 + 2x \Delta x + 2 \Delta x) \frac

1. **Problem statement:** We have a sequence defined by the recurrence relation $$u_0 = 11$$

1. **State the problem:** Solve the equation $x - 10 = 20$ for $x$. 2. **Formula and rules:** To isolate $x$, add 10 to both sides of the equation. This uses the addition property

1. **State the problem:** We want to find the percentage contribution of each person to the total contribution and understand the interest distribution. 2. **Given data:**

1. Let's start by stating the problem: we want to understand how to divide fractions and rewrite the entire expression accordingly. 2. The general rule for dividing fractions is: $

1. We are asked to solve the system of linear equations using the elimination method. Given the first system:

1. **State the problem:** We need to solve for the numerator of the expression using the FOIL method. The numerator is given as:

1. **State the problem:** We are given a 2x2 matrix $$B = \begin{bmatrix} 3 & 9 \\ 2 & x - 1 \end{bmatrix}$$ and we want to analyze or solve for properties involving this matrix.

1. **State the problem:** Simplify the expression $$\frac{\frac{12.5}{s(s + 1 + 12.5k)}}{1 + \frac{12.5}{s(s + 1 + 12.5k)}}.$$\n\n2. **Rewrite the expression:** Let $$A = s(s + 1 +

1. The problem asks to find the value of $m$ such that $m + m = 11$. 2. We start by writing the equation: $$m + m = 11$$

1. **Problem statement:** Solve the linear equation $$2X + 6 = 2(5X - 1)$$ for $X$. 2. **Recall the distributive property:** $$a(b + c) = ab + ac$$. Apply it to the right side:

1. **State the problem:** Two numbers have a sum of 11. One of the numbers is $m$. Find the other number. 2. **Write the equation:** Let the other number be $x$. The sum of the two

1. **State the problem:** We are given a system of linear equations:

1. Diberi fungsi $f(x) = x^2 - 3$ dan fungsi gubahan komposit $fg(x) = 4x^2 - 4x - 2$. Kita diminta mencari fungsi $g(x)$. 2. Ingat bahawa $fg(x) = f(g(x))$, maka kita gantikan $g(

1. **Problem:** Given matrices $$A=\begin{bmatrix}-2 & 1 & \frac{3}{2} \\ 0 & 3 & 2\end{bmatrix},\quad B=\begin{bmatrix}1 & 2 & 3 \\ 3 & 2 & 1\end{bmatrix}$$

1. **Énoncé du problème :** Décomposer le polynôme $P(x) = 2x^3 - 5x^2 + 3x - 1$ en facteurs, identifier les coefficients des termes, et donner la forme canonique.

1. **Problem Statement:** Translate the polygon with vertices D(0,4), E(-3,-1), F(1,-5), and G(1,0) 3 units right and 3 units up. 2. **Translation Matrix:** Translation moves point

1. **State the problem:** Simplify the expression $$(-192k)^{20}$$. 2. **Recall the rule for powers:** When raising a product to a power, raise each factor to that power: $$ (ab)^n