🧮 algebra

1. **State the problem:** A group of 10 people planned to pay equally for a pizza. One person left, so 9 people paid instead, each paying 60 cents more. We need to find the total b

1. **State the problem:** We need to determine the numerical value represented by each picture (bubblegum, wreath, blender, small character, handheld device, box shape) and identif

1. **State the problem:** We need to determine what number each picture represents and identify the operations used between them based on the connections described. 2. **Analyze gi

1. **State the problem:** We want to find which absolute value inequality corresponds to the intervals $x \leq -4$ or $x \geq 10$. 2. **Recall the absolute value inequality form:**

1. **State the problem:** Solve the quadratic inequality $$4x^2 + 8x - 21 > 0$$ and represent the solution set graphically. 2. **Find the roots of the quadratic equation:** To solv

1. **State the problem:** Solve the inequality $$(x + 2)(x - 3)(x - 5) \leq 0$$ and express the solution using inequality notation. 2. **Identify critical points:** The expression

1. **State the problem:** Calculate the value of the expression $$ (2) \times \frac{0.95 \times 0.76}{0.95 + 0.76} $$. 2. **Write the formula:** The expression involves multiplicat

1. **State the problem:** Calculate the value of the expression $$2 \times (0.95 \times 0.76) / (0.95 + 0.76)$$. 2. **Write the formula and explain:** The expression involves multi

1. Énonçons le problème : On affirme que dans l'exercice 2 de la page 6, la solution $x=\frac{1}{2}$ est fausse. 2. Vérifions cette solution dans l'équation donnée (non précisée ic

1. Il problema richiede di calcolare il cubo del trinomio $$2a+5b+3c$$, cioè $$ (2a+5b+3c)^3 $$. 2. La formula per il cubo di un trinomio $$ (x+y+z)^3 $$ è:

1. Diberikan persamaan kuadrat $$2x^2 - 8x + 6 = 0$$ dengan akar-akar $$p$$ dan $$q$$. 2. Kita ingin mencari nilai $$p^2 + q^2$$ dan membandingkannya dengan $$10$$.

1. **State the problem:** We need to find the average rate of change of the function $f$ from $x=3$ to $x=4$ using the graph. 2. **Formula for average rate of change:**

1. **State the problem:** We need to find the average rate of change of the function $f$ from $x=0$ to $x=3$ using the given points on the graph. 2. **Recall the formula for averag

1. **Problem:** Solve the simultaneous equations using the elimination method: $$X + 2Y = 7$$

1. **State the problem:** We are given the quadratic function $$f(x) = -4x^2 + 9x + 8$$ and need to find the vertex, direction of opening, axis of symmetry, y-intercept, and identi

1. **State the problem:** Identify which options are terms of the expression $$5x^2 + 9x + 6$$. 2. **Recall the definition of a term:** A term is a single part of an expression sep

1. **State the problem:** We have an initial ratio of purple to red sweets as $3:4$. After eating $40$ red sweets, the ratio changes to $5:4$. We need to find the original number o

1. **State the problem:** We are given $x+y=13$ and $xy=\frac{25}{4}$. We need to find the value of $x-y$. 2. **Recall the formula:** The identity for the square of a difference is

1. **Stating the problem:** We are given that the product $xy$ is 25 more than 4. 2. **Expressing the problem mathematically:** This means

1. **State the problem:** We are given two equations: $x+y=13$ and $xy=61 4$. We need to find the value of $x-y$.

1. نبدأ بتعريف القيمة المطلقة للعدد الحقيقي $x$: $$|x| = \begin{cases} x, & x \geq 0 \\ -x, & x < 0 \end{cases}$$