🧮 algebra

1. The given expression is $\frac{3^{6} \times 3^{5}}{3^{7}}$ and we need to write it in the form $n : 1$, where $n$ is an integer. 2. Using the properties of exponents, $3^{6} \ti

1. **State the problem:** Evaluate the expression $$(1 - w + w^2)(1 + w - w^2).$$ 2. **Expand the expression:** Use the distributive property (FOIL) to multiply each term in the fi

1. **Problem:** Find the general integral solutions of the Diophantine equation $$5x + 8y = 1$$. 2. **Step 1:** Check if the equation has any integer solutions by verifying that $$

1. First, we solve the simultaneous equations:\nGiven: \n$$5x + 3y = 2 \quad \text{and} \quad \frac{2}{x} - \frac{3}{y} = 1.$$\n\n2. From the first equation, express $x$ in terms o

1. Diketahui matriks \( \begin{pmatrix} -1 & 2 \\ x & 2 \end{pmatrix} \) dengan determinan sebesar 8. 2. Rumus determinan matriks \( 2 \times 2 \) adalah \( \text{det} = ad - bc \)

1. **Problem:** Calculate the expressions: i) $32^{3/5}$

1. **State the problem:** Simplify or perform operations with the expression $$\frac{3}{3x + 3} + \frac{x - 1}{2x + 2}$$. 2. **Factor denominators:** Note that $3x + 3 = 3(x + 1)$

1. The problem is to understand and simplify the expression $2x + 2$. 2. This expression is a linear polynomial with two terms: $2x$ and $2$.

1. The problem is to simplify or analyze the expression $3x+3$. 2. Notice that both terms have a common factor of 3.

1. We are asked to write an equation relating $p$, the number of pages read, and $m$, the number of minutes spent reading. 2. From the problem, we know she reads 3 pages in 8 minut

1. The problem is to simplify $\sqrt{27a}$ where $a$ is positive. 2. First, factor 27 into its prime factors: $27 = 3^3 = 3 \times 3^2$.

1. The problem asks us to find the values of $h(x)$ at $x = 3.999$, $4$, $4.0001$, and $9$ based on the graph's description. 2. From the graph description:

1. Stating the problem: Simplify the expression $\frac{8x}{9} + \frac{4x}{6}$.\n\n2. Find a common denominator for the fractions.\nThe denominators are 9 and 6. The least common de

1. Stating the problem: Simplify the expression $$(\sqrt{2} + \sqrt{3})(\sqrt{2} - \sqrt{3})$$. 2. Use the difference of squares formula: $$(a+b)(a-b) = a^2 - b^2$$.

1. **State the problem:** We want to find which expressions are equivalent to $$\frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5} \cdot \frac{1}{5}$$ and choose the correct two from

1. Diberikan matriks \( A = \begin{pmatrix}-1 & 3 & 2 \\ 2 & 1 & 3 \\ 1 & 2 & 1\end{pmatrix} \). \n2. Kita diminta mencari determinan matriks \( A \). \n3. Determinan matriks 3x3 d

1. The problem is to convert $\frac{15}{150} \times 100$ to a percentage. 2. Start by simplifying the fraction $\frac{15}{150}$:

1. The problem is to simplify the expression $$\frac{3x + 6}{x + 2}$$. 2. First, factor the numerator: $$3x + 6 = 3(x + 2)$$.

1. **Part A: Find local minima and maxima of f(x)** The function is given as $$f(x) = -5(x - 2)(x - 4)(x + 1)$$

1. **Problem 1:** Graph the linear function $y = 4x + 3$. - The slope of the line is the coefficient of $x$, which is $4$.

1. The user provided a decimal number: 0.176. 2. We can express this decimal as a fraction by recognizing the place value of the digits.