🧮 algebra

1. **Stating the problem:** Simplify the expression $\sqrt{6} \sqrt{42}$.\n\n2. **Recall the property of square roots:** The product of square roots can be combined as the square r

1. **State the problem:** Expand and simplify the expression $$(5x - 3)(2x - 7)$$ and write the result in the form $$ax^2 - bx + c$$. 2. **Apply the distributive property (FOIL met

1. The problem involves three parallelograms with algebraic expressions for their sides and diagonals. 2. For parallelogram SRUT, the sides are given as $2x + 15$ and $x + 15$. The

1. Diketahui deret geometri: 3 + 6 + 12 + ... + 192. 2. Tentukan rasio deret geometri: $r = \frac{6}{3} = 2$.

1. **State the problem:** Find the area between the ellipse given by $$\frac{x^2}{9} + \frac{y^2}{4} = 1$$ and the line $$x + y = 2$$. 2. **Rewrite the line equation:** Solve for $

1. The problem asks to find the interval on which the function defined by the equation $$2y^3 + 3x = 3x^{10} - x$$ is continuous. 2. First, rewrite the function explicitly if possi

1. **State the problem:** Find the area enclosed by the graphs of the circle $x^2 + y^2 = 4$, the ellipse $\frac{x^2}{9} + \frac{y^2}{4} = 1$, and the line $x + y = 2$. 2. **Analyz

1. **Stating the problem:** We are given a quadratic number pattern: -5, -4, -1, 4, ... We need to find the two consecutive terms in the first differences sequence whose product is

1. The problem is to simplify the expression $=$. 2. Since the expression is empty or invalid, there is nothing to simplify or solve.

1. **State the problem:** We have several questions about numbers, inequalities, and ordering on a number line. 2. **Question 1:** Classify the numbers \(-0.3, \frac{1}{5}, 0, -\fr

1. The problem is to find the value of $x$ that satisfies the equation $$\frac{2x+3}{5} = 7.$$\n\n2. Start by eliminating the denominator 5 by multiplying both sides of the equatio

1. **Problem statement:** Fatema's distance from Tomsville after $t$ hours is given by the function $$D(t) = 15.5 - 5t.$$ We are asked to find the inverse function $D^{-1}(x)$ and

1. **Problem 1(a)(i):** Find $s$ when $t=26.5$, $u=104.3$, and $a=-2.2$ using the formula $s = ut + \frac{1}{2}at^2$. 2. Substitute values:

1. لنبدأ بحساب \( \frac{144}{\sqrt{4}} \).\n\n2. نعلم أن \( \sqrt{4} = 2 \).\n\n3. إذن، \( \frac{144}{\sqrt{4}} = \frac{144}{2} = 72 \).\n\n4. الآن نحسب \( \sqrt{\frac{4}{81}} \cdo

1. The problem involves understanding how the fraction $\frac{4}{5}$ was obtained after dividing both sides of an equation by 625. 2. Suppose the original equation was $625x = 500$

1. Problem: Express $2x^2 - 8x + 1$ in the form $a(x+b)^2 + c$ where $a$ and $b$ are integers. Step 1: Factor out the coefficient of $x^2$ from the first two terms:

1. Let's first clarify the problem you are working on in Q4 to understand step 5 better. 2. Please provide the exact problem statement or the steps leading up to step 5.

1. The problem asks to find the value of $x$ that satisfies the equation $$\frac{2x+3}{4} = 5.$$\n\n2. To solve for $x$, first eliminate the denominator by multiplying both sides o

1. Write each expression as a single logarithm in the form $\log k$: g. $g \log 20 + \log(0.2) = \log(20^g) + \log(0.2) = \log(20^g \times 0.2)$

1. **State the problem:** Rationalize the denominator and simplify the expression $$\sqrt[4]{\frac{7}{8}}$$. 2. **Rewrite the expression:** We have $$\sqrt[4]{\frac{7}{8}} = \frac{

1. **State the problem:** Simplify the expression $$(2\sqrt{3} - 3)(2\sqrt{3} + 3).$$ 2. **Recognize the pattern:** This is a product of conjugates of the form $(a - b)(a + b) = a^