🧮 algebra

1. **Problem Statement:** Find the roots of the quadratic equation $$x^2 - 5x + 6 = 0$$. 2. **Formula Used:** The roots of a quadratic equation $$ax^2 + bx + c = 0$$ are given by t

1. **State the problem:** We need to find a two-digit number whose digits sum to 8 and when the digits are interchanged, the new number is 36 greater than the original. 2. **Define

1. **Nyatakan masalah:** Diberi bahawa $p$ berubah secara langsung dengan punca kuasa dua $q$ dan secara songsang dengan kuasa dua $r$. Kita perlu ungkapkan $p$ dalam sebutan $q$ d

1. Diketahui 75% siswa dari suatu sekolah adalah 150 siswa yang mengikuti kegiatan kunjung museum. 2. Kita diminta mencari jumlah keseluruhan siswa sekolah tersebut.

1. **Problem Statement:** We need to find the length of a rectangular plot where the length and width are in the ratio 4:3, and the total cost of fencing the plot is 1680. The cost

1. **Problem Statement:** We need to find the length of a rectangular plot where the length and width are in the ratio 4:3, and the total cost of fencing the plot is 1680. The cost

1. **State the problem:** The present ages of Anmol and Supriya are in the ratio $2:3$. After 10 years, their ages will be in the ratio $3:4$. We need to find the present age of An

1. **Problem statement:** We are given 6 consecutive odd numbers whose sum is 204. We need to find the fourth number in this sequence. 2. **Formula and approach:** Let the first od

1. **Problem statement:** We need to find the second number in a sequence of 3 consecutive even numbers whose sum is 78. 2. **Define variables:** Let the first even number be $x$.

1. **State the problem:** We need to find the second number in a sequence of 3 consecutive odd numbers whose sum is 183. 2. **Define variables:** Let the first odd number be $x$. S

1. **State the problem:** We are given 6 consecutive integers whose sum is 393, and we need to find the third number in this sequence. 2. **Set up variables:** Let the first intege

1. **State the problem:** Solve the equation $9 + 3.5g = 11 - 0.5g$ for $g$. 2. **Write down the equation:**

1. **State the problem:** Solve the equation $$12 - \frac{1}{5}r = 2r + 1$$ for $r$. 2. **Write down the equation:** $$12 - \frac{1}{5}r = 2r + 1$$

1. **State the problem:** Simplify the expression $$3^{n+1} \times 9^n \div 27^{\frac{2}{3}n}$$. 2. **Recall the base conversions:**

1. The problem asks where the function $m(p) = \sqrt{p}$ is continuous. 2. The square root function $\sqrt{p}$ is defined only for $p \geq 0$ because the square root of a negative

1. **State the problem:** Solve the equation $$(0.25)^x = 16$$ using indices. 2. **Rewrite the bases as powers of the same number:** Note that $0.25 = \frac{1}{4} = 4^{-1}$ and $16

1. **Problem Statement:** We are given the function $$h(x) = 3x^2 + 5$$ and asked to determine where this function is continuous. 2. **Recall the continuity rule:** Polynomial func

1. **State the problem:** Solve the equation $$(0.25)^x = 16$$ for $x$. 2. **Recall the formula and rules:** We use the property of exponents that if $$a^x = a^y$$, then $$x = y$$,

1. **Problem statement:** We are given the function $$g(t) = \frac{t}{2}$$ and asked to determine where this function is continuous. 2. **Recall the continuity rule:** A function i

1. **Stating the problem:** Solve the equation $x^{\frac{1}{3}} = 3$ for $x$. 2. **Formula and rules:** The equation involves a cube root. Recall that $x^{\frac{1}{3}}$ means the c

1. **Stating the problem:** Simplify the expression $16x^3 - 2x^{-6}$ using the laws of indices. 2. **Recall the laws of indices:**