🧮 algebra

1. **State the problem:** Scarlett has 44 m of blue ribbon and 110 m of red ribbon. She wants to cut both ribbons into smaller pieces of the same length with no ribbon left over. W

1. The problem involves simplifying the expression $6 \times \frac{4}{5}$.\n\n2. Start by multiplying the whole number by the numerator of the fraction:\n$$6 \times \frac{4}{5} = \

1. **State the problem:** Solve by factorization the expression $$315 \times \frac{2}{7} - 112 \times \frac{2}{7} + \frac{2}{7} \times 35$$. 2. **Identify the common factor:** Noti

1. **Problem statement:** Factorise the quadratic expression $x^2 - 12x + 20$. 2. **Formula and rules:** To factorise a quadratic of the form $x^2 - bx + c$, we look for two number

1. **State the problem:** Factorise the quadratic expression $$x^2 + 10x + 21$$. 2. **Recall the formula and rules:** To factorise a quadratic of the form $$x^2 + bx + c$$, we look

1. **State the problem:** Solve the equation $$2(x + 1)(x - 4) - (x - 2)^2 = 0$$ for $x$. 2. **Expand and simplify:**

1. **State the problem:** We want to find the values of $A$ and $B$ in the expression $$A \times B^n$$ that models the amount of money in a savings account after $n$ years, given c

1. Stating the problem: Evaluate the expression $40 \div (5 \times 2) + 6$. 2. Use the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (lef

1. The problem asks to write down the two inequalities that describe the unshaded region on the graph. 2. First, find the equations of the two lines.

1. **State the problem:** Simplify the expression $(-2 - x)^2$. 2. **Recall the formula:** The square of a binomial $(a + b)^2 = a^2 + 2ab + b^2$.

1. **State the problem:** Simplify the expression $2(-2 - x)$. 2. **Use the distributive property:** Multiply $2$ by each term inside the parentheses. The distributive property sta

1. **State the problem:** Calculate the value of the expression $$\frac{3.56 \times 10^{-5} \times 5.87 \times 10^{12}}{4.03 \times 10^{3}}$$ and express the answer in standard for

1. **State the problem:** Calculate $$\frac{4.67 \times 10^{-5} \times 6.98 \times 10^{12}}{5.04 \times 10^{3}}$$ and express the answer in standard form to 3 significant figures.

1. The problem defines a custom operation $X$ in equation I: $$a X b = \begin{cases} 2a + b, & \text{if } a \leq b \\ a^2 - b^2, & \text{if } a > b \end{cases}$$

1. **State the problem:** Calculate $$\frac{4.67 \times 10^{-5} \times 6.98 \times 10^{12}}{5.04 \times 10^{3}}$$ and express the answer in standard form to 3 significant figures.

1. **State the problem:** Simplify the expression $$\frac{2x + 4y}{9x - 18y} \times \frac{3x - 6y}{4x + 8y}$$. 2. **Identify common factors:**

1. The problem asks us to find the equation of a line parallel to the line $y = -\frac{1}{3}x + 1$ that passes through the point $(1, -2)$. 2. Recall that parallel lines have the s

1. The problem asks us to find the equation of a line parallel to the line given by $$y = -\frac{1}{3}x + 1$$ that passes through the point $(1, -2)$.\n\n2. Important rule: Paralle

1. **State the problem:** We have two sets defined by equations: Set A: $y=\frac{2x-1}{x}$

1. The problem asks to write the number 0.00654 in standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq a < 10$ and

1. The problem asks to write the number 0.00654 in standard form. 2. Standard form (also called scientific notation) expresses a number as $a \times 10^n$ where $1 \leq |a| < 10$ a