🧮 algebra

1. **Problem 1:** In a G.P., the sum of the 3rd and 4th terms is $-\frac{4}{3}$ and the sum of the 4th and 5th terms is $-\frac{4}{9}$. Find (a) the first term $a$, and (b) the com

1. **State the problem:** We have a geometric progression (G.P.) where the sum of the 3rd and 4th terms is $-\frac{4}{3}$, and the sum of the 4th and 5th terms is $-\frac{4}{9}$. W

1. **State the problem:** Three girls paid 100 each, totaling 300, for a motel room. The correct charge was 250, so 50 was to be returned. The attendant gave 10 back to each girl (

1. **State the problem:** Factor the quadratic expression $x^2 + 5x + 6$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=5$, and $c=6$.

1. State the problem. We are given six functions and must compute $f(-x)$ and $-f(-x)$ for each, then compare with $f(x)$ to decide whether the function is even, odd, or neither.

1. **State the problem:** We are given the function $f(x) = 2x^2 - 5x + 1$ and need to evaluate the difference quotient $$\frac{f(a+h) - f(a)}{h}$$ where $h \neq 0$. 2. **Find $f(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. The attendant gave

1. **Stating the problem:** Amar wants to find the dimensions (length and width) of a rectangular lot. The perimeter is 2300 feet. 2. **Identify variables:** Let the length be $x$

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