🧮 algebra

1. The problem is to solve the equation $$\sqrt{48x - 5} = 3\sqrt{27x - 2}.$$\n\n2. We start by squaring both sides to eliminate the square roots. The rule is: if $a = b$, then $a^

1. The problem is to simplify the expression $A=2^{\frac{3}{-4^{17}}}$. 2. First, recognize the exponent: $\frac{3}{-4^{17}}$. This means $3$ divided by $-4$ raised to the 17th pow

1. **Stating the problem:** We are given three equations: - $y^2=4ax$

1. **Stating the problem:** Solve the system of equations: $$xy = 2 \quad \text{(Equation ①)}$$

1. The problem gives three equations: $$y^2=4ax$$,

1. **Stating the problem:** Solve the system of equations for $x$ and $y$: $$\begin{cases} xy = 3 \\ x^2 + y^2 = 10 \end{cases}$$

1. The problem asks us to identify the fractions represented by points A and B on a number line between 0 and 1. 2. Since the number line is divided into equal parts between 0 and

1. **State the problem:** We have a photograph with width $x$ inches and length $x + 3$ inches. The area is given by $x(x + 3)$ square inches. 2. **Write the equation for the area:

1. **State the problem:** Simplify the expression $$\sqrt[3]{108c^{17}}$$. 2. **Recall the formula and rules:**

1. **State the problem:** Simplify the complex fraction $$\frac{10}{1+2i}$$ and write the answer in the form $a + bi$. 2. **Formula and rules:** To simplify a complex fraction, mul

1. **State the problem:** Simplify the expression $$\frac{x+3}{x^2 - 5x + 6} + \frac{6}{x^2 - 7x + 12}$$. 2. **Factor the denominators:**

1. The problem asks us to find which number among 10, 60, 100, and 160 does NOT have the same prime factors as 40. 2. First, find the prime factors of 40.

1. **State the problem:** Evaluate the product of the fractions $\frac{37}{100}$ and $\frac{7}{10}$. 2. **Formula used:** To multiply two fractions, multiply the numerators togethe

1. **State the problem:** Simplify the expression $5 - 7 + 2(3 - 8)$. 2. **Apply the order of operations:** First, simplify inside the parentheses.

1. The problem is to calculate the division of two fractions: $\frac{3}{14} \div \frac{6}{7}$.\n\n2. The formula for dividing fractions is:\n$$\frac{a}{b} \div \frac{c}{d} = \frac{

1. **State the problem:** Calculate the product of the three fractions $$\frac{4}{21} \times \frac{7}{6} \times \frac{9}{11}$$. 2. **Formula and rules:** When multiplying fractions

1. **State the problem:** Calculate the product of the fractions $\frac{9}{10} \times \frac{2}{7} \times \frac{5}{6}$.\n\n2. **Formula and rules:** To multiply fractions, multiply

1. Masalah: Cari range dari fungsi $h(x) = 2x$ dengan domain $\{1, 2, 3, 4\}$.\n\n2. Formula: Range adalah himpunan nilai output fungsi ketika domain tertentu diberikan.\n\n3. Lang

1. **State the problem:** Factor the expression $$-2x(16x^2 - 40x - 25)$$ using the MT (Middle Term) Test Method. 2. **Recall the MT Test Method:** This method is used to factor qu

1. **Problem:** Solve for $p$ in the equation $5p^{-3} = 8 \times 5^{-2}$. 2. **Formula and rules:** Recall that $a^{-n} = \frac{1}{a^n}$ and properties of exponents allow us to ma

1. **State the problem:** Given the equation $5p^{-3} = 8 \times 5^{-2}$, find the value of $p$. 2. **Recall the rules:**