🧮 algebra

1. **State the problem:** Combine like terms in the expression $$6x + 4 - 3x + 5$$. 2. **Identify like terms:** Like terms are terms that have the same variable raised to the same

1. **State the problem:** Jaylen picks $x$ strawberries. The number of blueberries he picks is 4 less than half the number of strawberries. 2. **Write the expression:** Half the nu

1. **State the problem:** Simplify the expression $$(-\frac{1}{4}) + 2(9.75 - 0.75)$$ using the order of operations. 2. **Recall the order of operations:** Parentheses first, then

1. The problem asks us to find the expression that means "15 less than an unknown number." 2. Let the unknown number be represented by the variable $x$.

1. **State the problem:** Ahana swims $x$ laps on Tuesday.

1. The problem asks for the expression that means "2 more than the quotient of a number and 3". 2. "Quotient of a number and 3" means dividing the number by 3, which is written as

1. The problem asks to identify which of the given options is not an expression. 2. An expression is a combination of numbers, variables, and operations without an equality sign.

1. **State the problem:** We need to determine the correct statement about the domain and range of the function $$f(x) = \sqrt{-x}$$. 2. **Recall the domain rule for square root fu

1. **State the problem:** Find the vertex of the parabola given by the equation $$y = - \frac{4}{9} x^2 + \frac{8}{3} x$$ using the method of completing the square. 2. **Recall the

1. **State the problem:** We need to calculate the value of the expression $$\frac{(11-9)^3}{2}$$. 2. **Understand the expression:** The numerator is the cube of the difference bet

1. The problem is not fully specified, so let's assume you want to know how to solve a general algebraic equation. 2. To solve an equation means to find the value(s) of the variabl

1. Problema cere să găsim resturile împărțirii lui $2^{1000000}$ la $35$ și $7^{2025}$ la $1000$. 2. Vom folosi teorema lui Euler și proprietăți ale congruențelor pentru a simplifi

1. **Enunțul problemei:** Avem un număr natural $n$ care, împărțit la 6, 8, 9, 12 și 16, dă același rest 5. 2. **Ce înseamnă asta?** Dacă împărțim $n$ la fiecare dintre aceste nume

1. **State the problem:** We are given a line $2y=2x+29$ and a quadratic equation $x^2 - 2ky + 32k = 0$ where $k \neq 0$. The line is tangent to the quadratic, and we need to find

1. **State the problem:** Simplify the expression $$\sqrt{9 + 4\sqrt{5}}$$. 2. **Recall the formula:** Expressions of the form $$\sqrt{a + b}$$ where $$b$$ involves a square root c

1. Το πρόβλημα ζητά να εκφράσουμε το $\sqrt{a + b\sqrt{c}}$ με απλούστερη μορφή. 2. Υποθέτουμε ότι υπάρχει μια μορφή $\sqrt{a + b\sqrt{c}} = \sqrt{x} + \sqrt{y}$, όπου $x$ και $y$

1. **Problem 4:** Find $f(-8)$ when $f(x) = -2x + 3$. 2. **Formula:** To find $f(a)$, substitute $x = a$ into the function: $$f(a) = -2a + 3$$

1. **Problem:** Find the product $f(n) \cdot g(n)$ where $f(n) = -3n^2 - 2$ and $g(n) = 4n - 5$. 2. **Formula:** To multiply two polynomials, use the distributive property: $(a+b)(

1. **Problem Statement:** Find the composite functions $f \circ g$, $g \circ f$, $f \circ f$, and $g \circ g$ for $f(x) = 2x - 1$ and $g(x) = x^2$. Also, state the domain of each c

1. **State the problem:** We are given two functions:

1. **State the problem:** We are given two functions $$f(x) = 2\sqrt{x}$$ and $$g(x) = 7x$$ and need to evaluate the compositions: (a) $$(f \circ g)(4)$$