🧮 algebra

1. **State the problem:** Solve the equation $$\frac{3x + 1}{5} + \frac{x - 2}{2} = \frac{47}{10}$$. 2. **Find a common denominator:** The denominators are 5, 2, and 10. The least

1. **State the problem:** Simplify the expression $10147x^2 - 624.5x - 1$ or analyze it as a quadratic expression. 2. **Recall the quadratic form:** A quadratic expression is gener

1. The problem asks us to fully factorise the expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form: $$20 + x - x^2 = -x^2 + x + 20$$

1. The problem is to fully factorise the quadratic expression $20 + x - x^2$. 2. First, rewrite the expression in standard quadratic form:

1. **State the problem:** We need to factor the function $$f(x) = -27x^5 - 18x^4 - 3x^3$$ to find all its x-intercepts. 2. **Recall the rule for x-intercepts:** The x-intercepts oc

1. **State the problem:** We are given the quadratic expression $$2x^2 - 6x - 20$$ and asked to fill in the gaps in the expression $$2x^2 - 6x - 20 = [ ] (x^2 - [ ] x - [ ])$$.

1. **State the problem:** We need to find all x-intercepts of the function $$f(x) = -4x^4 + 2x^3 + 12x^2$$. The x-intercepts occur where $$f(x) = 0$$. 2. **Set the function equal t

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: $$a X b = \begin{cases} 2a + b, & \text{if } a \leq b \\ a^2 - b^2, & \text{if } a > b \end{cases}$$