🧮 algebra

1. **State the problem:** Given the equations $x + y = 8$ and $x^2 + y^2 = 34$, we need to find: - $x^2 + 2xy + y^2$

1. **State the problem:** Solve the equation $$2x - 1 = \sqrt{8 - x}$$ and find any extraneous solution obtained by squaring both sides. 2. **Square both sides:** To eliminate the

1. We start with the equation \(\sqrt{8 - x} = 2x + d\) and want to find \(d\) such that \(x = -1\) is an extraneous solution. 2. An extraneous solution is a root of the squared eq

1. Problem: Simplify and manipulate algebraic expressions as needed. 2. Since no specific expression was given, here are general steps to manipulate algebraic expressions:

1. Soal pertama menanyakan persamaan kuadrat yang akar-akarnya adalah -7 dan 5. Kita tahu rumus dari persamaan kuadrat dengan akar-akarnya $x_1$ dan $x_2$ adalah

1. Stating the problem: Solve the equation $x^2 + 1 = 0$ for $x$. 2. Move the constant term to the other side: $$x^2 = -1$$

1. **Problem 1: Sketch the line with y-intercept -4 and slope 5/3.** - The line equation in slope-intercept form is $y = mx + b$ where $m=\frac{5}{3}$ and $b=-4$.

1. **Problem:** Find the domain and range of the function $f(x) = 1 + 3x + x^2$. 2. The function is a quadratic polynomial which is defined for all real $x$, so the domain is all r

1. We are given the formula for compound interest: $A = P(1 + i)^n$. Here, $A$ is the amount after interest, $P$ is the principal, $i$ is the interest rate per period, and $n$ is t

1. Diketahui akar-akar persamaan kuadrat adalah -7 dan 5. 2. Bentuk umum persamaan kuadrat jika diketahui akar adalah $$x^2 - (x_1 + x_2)x + x_1x_2 = 0$$.

1. The term "simple sollications" is unclear. Assuming you meant "simple solutions" for an algebraic problem, please provide the specific equation or problem you want to solve. 2.

1. State the problem. Solve the quadratic equation $2x^2 - 7x + 1 = 0$.

1. Stating the problem: Solve the quadratic equation $$2x^{2}-7x+1=0$$. 2. Identify coefficients: Here, $a=2$, $b=-7$, and $c=1$.

1. Evaluate $24 - (7 + 4)$: Calculate inside parentheses first: $7 + 4 = 11$

1. The problem is to understand the relationship between fractions and decimals and how to convert between them. 2. A fraction represents a part of a whole and is written as $\frac

1. Problem: Evaluate $$[25 - 3(6+1)] \div 4 + 9$$. Step 1: Calculate inside the parentheses: $$6+1=7$$.

1. Stated problem: We have the equation $A + B + C = 1$. 2. This is a linear equation relating three variables $A$, $B$, and $C$.

1. The problem provides several piecewise functions and evaluates them at specific points. We will verify each. 2. Problem 49:

1. Problem 1: Three friends have their marks in the ratio $3 : 4 : 5$ in the mid-term examination. They increased their marks by $10\%$, $5\%$, and $20\%$ respectively in the final

1. Problem: Analyze $f(x) = x^{2} + 10x + 24$. 2. Find the vertex:

1. The problem is to solve for $x$ in the equation $3.9x - 8 = -7$. 2. Start by adding 8 to both sides to isolate the term with $x$: $$3.9x - 8 + 8 = -7 + 8$$ which simplifies to $