🧮 algebra

1. Stating the problem: Solve the quadratic equation $$x^2 + 2x + 1 = 0$$. 2. Recognize that this is a quadratic equation in standard form $$ax^2 + bx + c = 0$$ where $$a=1$$, $$b=

1. State the problem: Solve the quadratic equation $2x^2+4x=0$. 2. Factor the equation: Factor out the greatest common factor $2x$:

1. The problem is to solve the quadratic equation $x^2 + 3x = 0$. 2. To solve this, start by factoring the expression on the left side.

1. The problem is to expand and simplify the expression $ (a + 2)(a^2 - 2a + 4) $. 2. Use the distributive property (FOIL or expansion) to multiply each term in the first parenthes

1. Stating the problems: a. Evaluate 7 \(\frac{3}{5}\) - 8 \(\frac{2}{7}\)

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