🧮 algebra

1. **State the problem:** A warehouse starts with 460 boxes and ships out 65 boxes every week. We want to find after how many weeks the number of boxes remaining will be less than

1. **State the problem:** Simplify the expression $$12a^5 b^3 \div 9a^3 b^5$$. 2. **Write the division as a fraction:**

1. The problem states that AB is not equal, which suggests we need to understand or prove something about the inequality of AB. 2. To analyze this, we need to clarify what AB repre

1. **State the problem:** Megan wants to buy a cell phone costing 220. She has saved 175 so far and wants to buy it in 4 weeks. 2. **Define variables:** Let $x$ be the amount Megan

1. **State the problem:** Find the range of the function $F(x) = 2x^2 + 1$. 2. **Recall the formula and properties:** The function is a quadratic function in the form $ax^2 + bx +

1. The problem is to find the domain of the function $F(x) = 2x^2 + 1$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined.

1. **Problem:** Write two equivalent rational numbers for $-\frac{5}{4}$. 2. **Formula:** Equivalent rational numbers are found by multiplying numerator and denominator by the same

1. **State the problem:** Convert the line equation $4x + 7y - 2 = 0$ into three forms: slope-intercept form, two-intercept form, and normal form. 2. **Slope-intercept form:** This

1. **State the problem:** We have a map scale of 1cm : 4 kilometres.

1. The problem is to simplify the algebraic expression $3uv \times v^2 \times 5u^2$. 2. The formula for multiplying terms with the same base is $a^m \times a^n = a^{m+n}$.

1. **State the problem:** We are given the expression $8x^2$ and need to find the number of terms, the degree, the leading coefficient, and the constant term. 2. **Number of terms:

1. **State the problem:** Multiply the expressions $6pq^2$ and $2qr^2$. 2. **Recall the multiplication rule for algebraic expressions:** Multiply the coefficients (numbers) and the

1. **State the problem:** Find the equation of a circle passing through points $(2,3)$ and $(-1,2)$ with its center on the line $2x - 3y + 1 = 0$. 2. **Formula and rules:** The gen

1. **Stating the problem:** We need to graph the equations \(y = -3x\) and \(y = \frac{1}{3}x\). 2. **Formula and rules:** Both are linear equations in the form \(y = mx\), where \

1. **State the problem:** Find the equation of a circle passing through points $(2,3)$ and $(-1,2)$ with its center on the line $2x - 3y = 0$. 2. **General form of circle equation:

1. **State the problem:** Solve the quadratic equation $x^2 + 9x + 14 = 0$. 2. **Recall the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by

1. **Stating the problem:** Given the system of equations: $$18 = a^3 + x^3$$

1. **State the problem:** Simplify the expression $p^3 q^2 \times p^2 q$. 2. **Recall the rule for multiplying powers with the same base:** When multiplying powers with the same ba

1. **Problem:** Solve the equation $7x + 15 = 5$ using the bar model method. 2. **Formula and rules:** To solve linear equations like $ax + b = c$, we isolate $x$ by performing inv

1. **Déterminer une primitive de** $f(x) = 4x(2x^2 + 5)^3$. - Posons $u = 2x^2 + 5$, alors $\frac{du}{dx} = 4x$.

1. **State the problem:** We are given the equation $$(3 - X)(3 + X) = a + x^2$$ and need to find the value of $a$. 2. **Recall the formula:** The expression on the left is a produ