🧮 algebra

1. **State the problem:** Solve the equation $0.88 = \frac{558 + x}{700 + x}$ for $x$. 2. **Use the formula:** To solve for $x$, multiply both sides by the denominator to eliminate

1. **State the problem:** We are given the function $f(x) = 3x^2 - 2x + \frac{1}{2}$ and want to understand its properties. 2. **Formula and rules:** This is a quadratic function o

1. **State the problem:** We need to find the equation of a line parallel to line A that passes through point P(0, 3). 2. **Find the slope of line A:** The slope $m$ is given by th

1. **Nyatakan masalah:** Cari punca-punca bagi persamaan kuadratik $$x^2 + 8 = 6 + 3x$$. 2. **Susun semula persamaan supaya berbentuk $$ax^2 + bx + c = 0$$:**

1. The problem is to find the greatest value of $t$ where two given functions are equal. 2. To solve this, we set the two functions equal to each other: $$f(t) = g(t)$$

1. **State the problem:** We are given two functions: $$f(x) = \frac{x + 3}{\sqrt{x^2 - 1}}$$

1. **State the problem:** Simplify the expression $$\frac{5p^{4} \times (3q^{3})^{2}}{15p^{6}q^{4}}$$. 2. **Apply the exponent rule:** Recall that $ (a^m)^n = a^{m \times n} $. So,

1. **State the problem:** We need to analyze and draw the graph of the function $$f(x) = 3 - \sqrt{2 - x}$$. 2. **Understand the domain:** The expression under the square root must

1. **Nyatakan masalah:** Kita perlu menyederhanakan ekspresi $$\frac{(2x^5 y^{-3})^4}{(x^2 y)^5}$$. 2. **Gunakan hukum pangkat:** Untuk pangkat pada perkalian, gunakan $$ (ab)^n =

1. **State the problem:** Find the domain and range of the function $$f(x) = \frac{3}{\sqrt{9 - x^2}}$$. 2. **Understand the domain constraints:** The expression under the square r

1. **State the problem:** We need to find the possible values of $k$ such that the constant term in the expansion of $\left(x^2 + x^k\right)^{12}$ has a coefficient of 495. 2. **Re

1. The problem asks to identify the pattern of the decay sequence and then find the total decay in the first 5 seconds. 2. The given decay numbers are 24300, 8100, 2700, ...

1. **State the problem:** Solve the equation $x^2 + 9x + 7 = -x^2 - 2$ for $x$. 2. **Bring all terms to one side:** Add $x^2$ and $2$ to both sides to combine like terms:

1. The problem is to solve the equation shown in question 3 (assuming it is a typical algebraic equation). Since the exact equation is not provided, let's consider a common example

1. **State the problem:** Solve the system by substitution: $$y = 6x - 11$$

1. **State the problem:** Simplify the expression $$\frac{(11 \times 2 \times 3) \times 12 \times 11 \times 9 \times \sqrt{9}}{2 \times 7 \times (12 \times 1) \times 2 \times 11 \t

1. **State the problem:** Simplify the expression $$\frac{(11 \frac{1}{2})^{12} \times 11^{19} \times \sqrt{9}}{27 \times 12^2 \times 11^{11}}$$. 2. **Rewrite mixed number:** Conve

1. **Stating the problem:** Mark and Tony had the same weight before vacation. Mark's weight increased by $\frac{1}{16}$ and Tony's by $\frac{1}{20}$. Together, their combined weig

1. Stated problem: Izračunajte izraz $-81 - \frac{5}{3}$.\n\n2. Prvo, izrazimo oba broja u zajedničkom obliku da bismo mogli da ih saberemo ili oduzmemo. Broj $-81$ možemo napisati

1. **Stating the problem:** You have 18,000,000 Rp and want to convert all of it into Ge, then find out how much $ it would take to buy that amount of Ge. 2. **Given:**

1. Postavimo problem: Neka je broj $x$. Sabiranjem tog broja sa 5 dobijamo $x+5$. 2. Zbir $x+5$ množimo sa $\frac{1}{3}$, što daje izraz $$\frac{1}{3}(x+5)$$.