🧮 algebra

1. The problem is to understand the function $\varphi(|x|)$ where the input is the absolute value of $x$. 2. The absolute value function $|x|$ outputs $x$ if $x\geq0$ and $-x$ if $

1. The problem involves simplifying the expression given and solving the equation: $$x^2 + \frac{x}{2} = \left(x + \frac{x}{1}\right)^2 - 2 = 16^2 - 2 = 256 - 2 = 254$$

1. Problem (i): Given the equation $x + yi = 12i + 5i$, simplify the right side. Since $12i + 5i = 17i$, the equation becomes $x + yi = 17i$.

1. The problem asks about the expression "0imesy". 2. In mathematics, "imes" often symbolizes multiplication.

1. Stating the problem: Calculate the value of the expression $$7[(-15)-(-3)] \div 4 + \left(\frac{28-8}{4}\right)^2$$. 2. Simplify inside the brackets and parentheses:

1. Simplify inside the bracket: $$(-15) - (-3) = -15 + 3 = -12$$ 2. Multiply by 7: $$7 \times (-12) = -84$$

1. The problem is to find the number of roots of the equation $$\left(x^3 - \frac{1}{x}\right)^2 = 0$$. 2. Since the square of an expression equals zero, that expression itself mus

1. State the problem: We are given the equation $3x = 7$ and need to express it in the form $ax + by + c = 0$ and find the values of $a$, $b$, and $c$. 2. Rewrite the equation $3x

1. **Stating the problem**: We have a binary operation $*$ on $\mathbb{R}$ defined by $a * b = a + b + 3$. 2. **Find the identity element $e$ if it exists:** The identity element s

1. State the problem: Solve for $x$ in the equation $$\frac{3x + 1}{x - 1} = -2.$$\n\n2. Multiply both sides by the denominator $x - 1$ to eliminate the fraction:\n$$3x + 1 = -2 (x

1. Stating the problems: Solve the systems of equations given for each case. **Part 1:**

1. Problem Statement: (ii) Find an expression for the $i^{th}$ term: Given the sequence terms as $7i$.

1. Mari kita bahas pernyataan Kayla bahwa "daerah himpunan penyelesaian dari sistem pertidaksamaan masalah tersebut berada di atas garis $$2x + 3y = 40$$". 2. Persamaan garis yang

1. Stating the problems: (a) Find the value of $\left( \frac{1}{4} \right)^{0.5}$.

1. Evaluate expression $8-2[4+8\div(-2)-2]-(2\times3)^2$. Calculate inside brackets: $8\div(-2)=-4$.

1. **State the problem:** We need to find the mean number of magazines purchased by six customers with purchases: 1, 7, 3, 2, 3, and 4. 2. **Add all the purchases together:**

1. The problem asks to find the sum of the first $n$ terms of several geometric progressions (G.P.). The sum of the first $n$ terms of a G.P. is given by $$S_n = a \frac{1-r^n}{1-r

1. Evaluate $-(+7) - (-10) - 3 + (+4)$. Step 1: Simplify each term using signs.

1. State the problem: Evaluate the expression $$9 \cdot (8 - 3 \times 4) \cdot \left[7 + \frac{10}{-2} - 3\right]^2 + 4$$. 2. Simplify inside the first parentheses:

1. Problem 3 (1979): Find the value of \(\alpha\) so that the sequence \(a_n = \alpha n + 5\) satisfies a given condition.\n\nSince no other condition is stated, we assume the prob

1. ចំណាត់ថ្នាក់សំណួររបស់អ្នកគឺ ស្វែងរកសារៈបំផុតនៃអនុគមន៍តាងប្រត្យរីយៈសម្រាប់ស្វេតផ្តើមនីតិវិធី៖ ក. 1, 3, 5, 7, ...