🧮 algebra

1. The user mentions a problem involving only variables $x$ and $y$ but does not specify the exact problem. 2. To assist effectively, please provide the full problem statement or e

1. The problem states that every variable \(m\) or \(n\) should be replaced by \(x\).\n2. This means wherever you see \(m\) or \(n\) in an expression, equation, or function, substi

1. Planteamos el problema: Encontrar la ecuación explícita de la recta que pasa por dos puntos dados $A(x_1,y_1)$ y $B(x_2,y_2)$.\n\n2. La fórmula para la pendiente $m$ es: $$m=\fr

1. **Stating the problem:** We are given inequalities involving the function $E$ applied to variables $m$, $n$, $y$, and expressions involving sums like $m + y$. The goal is to und

1. **State the problem:** Simplify the complex nested fraction: $$1 + \frac{2 - \frac{1}{3}}{1 - \frac{\frac{1}{4}}{-1 + \frac{1}{2}}}$$

1. **State the problem:** We have a rectangular lot with perimeter 252 feet. The width is 26 feet shorter than the length. We need to find the dimensions (length, width). 2. **Defi

1. **State the problem:** We need to find the break-even point where revenue equals cost. 2. **Define variables:** Let $x$ be the number of items.

1. **State the problem:** Tomas’ Mexican Restaurant wants to mix extra hot salsa (\$12 per pound) and medium salsa (\$8 per pound) to create 40 pounds of spicy salsa selling at \$9

1. **State the problem:** Simplify the complex fraction $$\frac{3 - \frac{1}{2}}{1 + \frac{\frac{1}{4}}{-1 + \frac{1}{3}}}$$

1. The problem asks to solve questions 3c, 4, and 10 from exercise 3.4 on page 37 of Essential Mathematics, SS2. 2. Since the exact questions are not provided, I will solve typical

1. The problem asks to solve exercise 3.4 from Essential Mathematics page 37. Since the exact question is not provided, I will assume it involves algebraic manipulation or solving

1. The problem asks to solve or simplify parts 3c and 4a from Essential Mathematics Exercise 3.4. 2. Since the exact questions are not provided, I will demonstrate typical algebrai

1. **State the problem:** Simplify the expression $$1 - \frac{\frac{1}{2} - 3}{1 - \frac{1}{4} \div \left(1 - \frac{1}{3}\right)}$$. 2. **Simplify the numerator:** Calculate $$\fra

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 $x$