🧮 algebra

1. **State the problem:** Find the slope of the line passing through the points $(-8, -4)$ and $(4, 2)$ on the coordinate plane. 2. **Formula for slope:** The slope $m$ of a line t

1. **State the problem:** Factorise the quadratic equation $Sx^2 + 19x + 12 = 0$. 2. **Recall the factorisation formula:** For a quadratic $ax^2 + bx + c = 0$, factorisation involv

1. **State the problem:** Solve the quadratic equation $$5x^2 + 19x + 12 = 0$$ for $x$. 2. **Formula used:** The quadratic formula is $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ whe

1. **Problem statement:** Given four numbers $a < b < c < d$ such that their product is $a \times b \times c \times d = 35$, find the value of $a \times b + c \times d$. 2. **Under

1. **State the problem:** Solve for $Y$ in the equation $$\frac{50 - 1.75Y}{1.5} = x.$$\n\n2. **Isolate the numerator:** Multiply both sides by 1.5 to eliminate the denominator:\n$

1. The problem is to find the total number of pages in Liam's and Mason's books combined. 2. Liam's book pages are given by the expression $2x + 10$.

1. **State the problem:** Simplify the expression $$3(4x^2 + x) - (3x^2 + 3x - 1)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the factor

1. **State the problem:** We need to find the values of $x$ for which the expression $\sqrt{3x+36}$ is defined. 2. **Recall the rule for square roots:** The square root function $\

1. **State the problem:** We want to find the values of $x$ for which the expression $\sqrt[4]{56x^3}$ is defined. 2. **Recall the rule for even roots:** The fourth root (an even r

1. **State the problem:** Find the equation of the line given by the point-slope form: $$y + 3 = \frac{1}{2}(x - 4)$$ 2. **Recall the point-slope form formula:**

1. **State the problem:** Find the equation of the line with slope $\frac{1}{3}$ and y-intercept 5. 2. **Recall the slope-intercept form:** The equation of a line is given by $$y =

1. Problem Q11: If 5 workers can complete a task in 4 days, how many days will it take 10 workers, assuming the same efficiency? 2. Formula: The work done is constant, so $\text{Wo

1. **State the problem:** Simplify the expression $21x + 14$. 2. **Identify the common factor:** Both terms $21x$ and $14$ have a common factor of $7$.

1. Problem Q9: Write the ratio of repeat customers to new customers. Given: Total customers = 200, Repeat customers = 80

1. **State the problem:** Factor the cubic polynomial expression $$24x - 2x^2 - 2x^3$$ completely. 2. **Write the polynomial:** $$24x - 2x^2 - 2x^3$$

1. **State the problem:** Factor the cubic polynomial $$x^3 - 15x^2 + 50x$$ completely. 2. **Identify common factors:** Notice that each term contains an $$x$$, so factor $$x$$ out

1. **State the problem:** Simplify the expression $$(2a^2b)^3 (4b^5)^2$$. 2. **Recall the exponent rules:**

1. **Problem Q6:** Write the ratio of full-time staff to part-time staff in simplest form. Given: Full-time staff = 12, Part-time staff = 18.

1. **Problem Q9:** Out of 200 customers, 80 are repeat customers and the rest are new customers. Write the ratio of repeat customers to new customers. 2. **Step 1:** Calculate the

1. **State the problem:** Solve the system of equations: $$x - y = 2$$

1. **State the problem:** We need to find the average number of visits per day given that a company website receives 2,400 visits in 8 days. 2. **Formula used:** The average (mean)