🧮 algebra

1. The problem is to solve the equation $$|x+4| = 0$$. 2. Recall that the absolute value of a number is zero only when the number itself is zero.

1. The problem is to determine the condition under which the equation $|x| = a$ has two solutions. 2. Recall that the absolute value function $|x|$ outputs the distance of $x$ from

1. The statement says "2 2/3 is an improper fraction." Let's first understand what an improper fraction is. 2. An improper fraction is a fraction where the numerator (top number) i

1. The problem asks whether $\frac{2}{3}$ is the reciprocal of $-\frac{2}{3}$. 2. Recall that the reciprocal of a number $x$ is defined as $\frac{1}{x}$.

1. **State the problem:** We need to find the value of $$(a+b)^2$$ given that $$a+b=3$$ and $$ab=-2$$. 2. **Recall the identity:** The square of a binomial sum is given by

1. Start by stating the problem: Simplify the expression $$\frac{(4a^3b^2)^2}{(a^2b)^2}$$. 2. Apply the power of a product rule to both numerator and denominator:

1. **Evaluate** $\log_9 27$: Recall $\log_a b = c$ means $a^c = b$.

1. The problem is to simplify the expression $\sqrt{x}$ raised to the power 3. 2. We start with the expression $\left(\sqrt{x}\right)^3$.

1. Evaluate i) $\frac{1}{4} \times 10^{-5}$. Recall that $10^{-5} = \frac{1}{10^5} = \frac{1}{100000}$.

1. The problem asks to find 46 percent of the mixed number 2 whole 1 over 2. 2. Convert the mixed number to an improper fraction: $$2 \ \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \fr

1. We are given the sequence: 1, 2, 4, 7, 11, \ldots, 821, and we need to find the term number (position) of 821 in this sequence. 2. First, observe the differences between consecu

1. Let's analyze the given equations and expressions:\n\n- $Q = 10\sqrt{KL}$\n- $K + 4L = 16$\n- $Y = 150T^{0.5} S^{0.5}$\n- $C = 10T + 8S$\n\n2. The problem seems to involve under

1. The problem asks to increase 5400 by 20%. 2. To increase a number by 20%, multiply it by $1 + 0.20 = 1.20$.

1. ප්‍රශ්නය: දළ වශයෙන්, $y = f(x)$ යනු ඉහළට විවෘත වන වර්ග කළමනාකරණයක් (parabola) වේ. එහි මුලස්ථානය (vertex) $A(1, -9)$ පවා ඇත. 2. (i) ලක්ෂ්‍ය සටහන: A ලක්ෂය $A(1, -9)$ සහ පෙර ලක්ෂය

1. Stated problem: Solve the equation $2 - \frac{1}{\alpha+1} = 0$ for $\alpha$. 2. Move the fraction to the other side:

1. Problem: You are struggling to understand Problem 2. We will explain it both mathematically and graphically. 2. First, please provide the exact mathematical expression or equati

1. The problem is to write a compound inequality based on a number line graph. 2. The graph shows a line segment from approximately -619 to -614 with an open circle at -617 and a c

1. The problem asks for a compound inequality representing the given graph. 2. The number line has a hollow circle at 137, meaning $x \neq 137$ but values just less than 137 are in

1. **Problem:** Write a compound inequality that describes a number line graph with two filled points at 50 and 52, with a leftward arrow from 50 and a rightward arrow from 52.

1. The problem asks us to describe the given graph as a compound inequality. 2. The graph shows a number line from -4 to 6.

1. The problem asks for a compound inequality that describes the graph given. 2. The graph shows a number line with a thick magenta line segment starting at -3 (filled-in dot) to -