🧮 algebra

1. Pernyataan masalah: Diberikan fungsi kuadrat $Z = f(U) = -aU^2 + bU + c$ dengan $a > 0$. Tentukan bentuk kurva dan apakah kurva memotong sumbu horizontal. 2. Rumus dan aturan pe

1. The problem is to verify the calculation of the expression $$180 : (0.022 \times 2) = 180 : (0.022 \times 1.1) = 180 : 0.0242 = 7438.01$$. 2. The colon ":" here represents divis

1. The problem is to verify the calculation of the ratio $180:(0.022 \times 2)$ and $180:(0.022 \times 1.1)$ and check if it equals 7438.01. 2. The formula used is division and mul

1. **Problem statement:** A sum of money doubles itself in 3 years at compound interest. We need to find in how many years it will amount to 64 times the original sum. 2. **Formula

1. **State the problem:** We want to use trigonometric substitution to express the algebraic expression $$4 = \sqrt{25x^2 + 9}$$ as a function of $$\sec(\theta)$$, given that $$5x

1. **State the problem:** We want to use trigonometric substitution to express the algebraic expression $$\sqrt{25x^2 + 9}$$ as a function of $$\sec(\theta)$$, given the substituti

1. **State the problem:** We want to express the algebraic expressions $4 = 25x^2 + 9$ and $5x = 3\tan\theta$ as functions of $\sec\theta$ where $0 \leq \theta \leq \frac{\pi}{2}$.

1. The problem is to find the answer to the user's query "answer" which is ambiguous, so let's interpret it as solving a simple algebraic expression or equation. 2. Since no specif

1. The problem is to solve the equation $0/7$. 2. Division by any nonzero number of zero is always zero, so $0/7 = 0$.

1. The problem appears to involve evaluating or simplifying an expression with numbers and possibly Arabic text mixed in. 2. Since the input is unclear and contains mixed symbols a

1. **Stating the problem:** Solve a linear equation, which is an equation of the form $ax + b = 0$ where $a$ and $b$ are constants and $x$ is the variable. 2. **Formula and rules:*

1. **State the problem:** Express the sum $$\frac{1}{x^3} + \frac{1}{2xy} + \frac{1}{x^2 y^2}$$ as a single fraction. 2. **Find the common denominator:** The denominators are $$x^3

1. **State the problem:** Simplify the expression $$\left( \frac{2x^2 y^3}{x^3 y} \right)^3$$. 2. **Apply the quotient rule for exponents:** When dividing like bases, subtract the

1. **State the problem:** Find the vertical asymptotes of the function $$f(x) = \frac{3x - 7}{x^2 + 5x}$$. 2. **Recall the rule for vertical asymptotes:** Vertical asymptotes occur

1. **State the problem:** Find the domain of the function $$f(x) = \frac{\sqrt{x - 2}}{x^2 - 4}$$. 2. **Recall domain rules:**

1. **State the problem:** Find the equation of the line with slope $\frac{1}{2}$ passing through the point $(2, 3)$. 2. **Formula used:** The point-slope form of a line is given by

1. **State the problem:** Given the circle equation $$x^2 + y^2 - 4x + 6y + 4 = 0$$, find the centre and radius. 2. **Formula and rules:** The general form of a circle is $$ (x - h

1. The problem asks to simplify the expression $$\sqrt{x^2 + y^2}$$ and find which option it equals. 2. Recall that $$\sqrt{a^2} = |a|$$ for any real number $$a$$ because the squar

1. **State the problem:** Solve for $y$ in the equation $$4y^2 - 2 = 9y - 4$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. The problem asks to simplify the expression $$\sqrt{x^2 + y^2}$$ and find which option it equals. 2. Recall that $$\sqrt{x^2} = |x|$$ because the square root function returns th

1. **State the problem:** We need to find the exact value of $y$ given the equation $$7^{2y} = 3^{4}.$$ 2. **Recall the logarithm property:** To solve for $y$, we can take the loga