🧮 algebra

1. Problem: For each pair of functions, identify one characteristic they share and one characteristic that distinguishes them. 2. a) Functions: $f(x) = \frac{1}{x}$ and $g(x) = x$

1. **State the problem:** Three girls paid 100 each, totaling 300, for a motel room. The correct charge was 250, so the clerk gave 50 to the attendant to return to the girls. The a

1. **State the problem:** Three girls paid 100 each, totaling 300, for a motel room. The correct charge was 250, so the clerk gave 50 to the attendant to return to the girls. The a

1. **State the problem:** Three girls paid $100 each, totaling $300, for a motel room. The correct charge was $250, so the clerk gave $50 to the attendant to return to the girls. T

1. **State the problem:** Three girls paid $100 each, totaling $300, for a motel room. The clerk later realizes the correct charge should be only $250, so he gives $50 to the atten

1. Let's start by understanding the problem. Three girls initially pay $100 each, totaling $300.

1. **State the problem:** Three girls paid $100 each, total $300, for a motel room.

1. **Stating the problem:** Three girls paid 100 each, totaling 300, for a motel room. The correct charge was 250, so the clerk gave 50 to the attendant to return. The attendant ga

1. Simplify each expression as requested. **a)** $3\sqrt{17} + 6\sqrt{7} - 5\sqrt{17} - 5\sqrt{7}$

1. Énoncé du problème : Calculer $$\frac{(2a+3b)^2-(2a-3b)^2}{4b}$$ et expliquer les étapes. 2. Utiliser l'identité remarquable de la différence de carrés : $$x^2 - y^2 = (x-y)(x+y

1. The problem is to "Add another 7 to the bottom" which likely means to add 7 to the denominator of a fraction or an expression. 2. Suppose we have a fraction $\frac{a}{b}$ and we

1. State the problem: Simplify the expression $$\frac{7}{\frac{7}{7}}$$. 2. Simplify the denominator: The denominator is $$\frac{7}{7}$$, which equals $$1$$ because $$7 \div 7 = 1$

1. Let's first clarify the problem: "It’s have to be 49." If this means we need to find a number or expression that equals 49, we can start by considering simple squares since 49 i

1. **State the problem:** Simplify the expression $\frac{7}{\frac{7}{7}}$. 2. **Simplify the denominator:** Calculate $\frac{7}{7}$. Since 7 divided by 7 is 1, this simplifies to 1

1. **State the problem:** Solve the equation $$\frac{3x + 2}{x - 1} = 2\sqrt{x + 3} - 1$$ for $x$.

1. Stated problem: Solve the quadratic equation $3x^2 - 110x + 60 = 0$. 2. Identify coefficients: $a = 3$, $b = -110$, $c = 60$.

1. Problem: Simplify the expression $$\frac{x^2 - y^2}{x + y}$$. 2. Recognize that the numerator is a difference of squares: $$x^2 - y^2 = (x - y)(x + y)$$.

1. State the problem: Simplify the expression $$ A = \frac{12}{8} - \frac{6}{8} \div \frac{5}{4} $$.\n\n2. Simplify the first fraction: $$ \frac{12}{8} = \frac{3}{2} $$.\n\n3. Perf

1. We are given the system of inequalities: $$3x + y \geq 15$$

1. Evaluate the following complex number operations: i) \((2 + 3i) + (7 - 2i)\)

1. The problem asks us to simplify the expression $(x-120)^2$. 2. Recall that $(a-b)^2$ expands using the formula: $$ (a-b)^2 = a^2 - 2ab + b^2 $$