🧮 algebra

1. **State the problem:** We are given the equation $y = x + 6$ and a table of values for $x$ and $y$:

1. **State the problem:** Elsie, Ruby, and Alfred drove a total of 320 miles. Elsie drove \(\frac{1}{4}\) of the distance, Ruby drove \(\frac{5}{8}\) of the distance, and we need t

1. **State the problem:** Simplify each algebraic expression involving exponents. 2. **Recall exponent rules:**

1. **State the problem:** Find the inverse function of $f(x) = -\frac{4}{5}x + 8$ in slope-intercept form $y = mx + b$. 2. **Recall the formula and rules:** To find the inverse fun

1. **State the problem:** Find the inverse function of \( f(x) = \frac{3}{5}x - 12 \) in slope-intercept form \( y = mx + b \). 2. **Recall the formula and rules:** To find the inv

1. The problem is to evaluate the expression: \( \div 4 \times + 2 \).\n2. However, the expression is incomplete or unclear as it lacks numbers or variables before the division and

1. **State the problem:** A student has 72 music files divided into four folders: techno, hip hop, reggae, and classic rock. The fractions of songs in techno, hip hop, and reggae a

1. **State the problem:** We have the function $g(x) = a \times b^x$ where $a$ and $b$ are constants. We know $g(0) = 8$ and $g(3) = 343$. We need to find $g(1)$.

1. **State the problem:** Solve the rational number operation $-1 \frac{1}{3} - 2 \frac{4}{5}$. 2. **Convert mixed numbers to improper fractions:**

1. **Problem:** Calculate $-1 \frac{1}{3} - 2 \frac{4}{5}$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** We have three types of tickets: child ticket costing $c$, adult ticket costing $c+4$, and senior ticket costing $c+3$.

1. Il problema chiede di trovare il dominio della funzione $$f(x) = \frac{x^{2} - 2x - 3}{x^{2} - 6x + 9}$$ e di mostrarne il grafico. 2. Il dominio di una funzione razionale è l'i

1. **State the problem:** We want to rewrite radicals as products of radicals and simplify them.

1. **State the problem:** We need to find out if Amelia's family and Manuel's family pay the same amount for tickets to the corn maze, given the costs of child, adult, and senior t

1. **State the problem:** We are given the first 5 terms of a quadratic sequence: 4, 11, 20, 31, 44. We need to find an expression for the nth term of this quadratic sequence.

1. The problem asks to find the first term of a Fibonacci-type sequence where the first two terms can be any numbers, and each subsequent term is the sum of the two previous terms.

1. **State the problem:** Simplify the expression $$\frac{x^7 y^4}{x^2 y}$$. 2. **Recall the exponent rules:** When dividing like bases, subtract the exponents: $$\frac{a^m}{a^n} =

1. **State the problem:** We are given the function $F(t) = -50t$ and need to understand or analyze it. 2. **Formula and explanation:** This is a linear function where $F(t)$ depen

1. **State the problem:** Simplify the square root expression $\sqrt{387}$. 2. **Recall the formula and rules:** To simplify a square root, find the largest perfect square factor o

1. The problem is to simplify $\sqrt{216}$.\n\n2. Recall that $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and that we want to find perfect square factors of 216.\n\n3. Factor 21

1. **State the problem:** Máiréad can clean a window in 9 minutes, Diarmuid in 12 minutes. (i) They start cleaning at the same time and finish a window simultaneously. Find after h