🧮 algebra

1. **Problem b:** Elena has 75 pounds. How many foam fingers can she buy if each costs 10 pounds? 2. To find the number of foam fingers Elena can buy, divide her total money by the

1. Stating the problem: Solve the equation $$\frac{x}{2} - 6 = 8 - \frac{2x}{3}$$ for $x$. 2. Eliminate the fractions by multiplying every term by the least common denominator (LCD

Problem: Solve the equation $x/2 - 6 = 8 - 2x/3$. 1. Move terms to combine like terms.

1. Problem: Determine the domain, range, and whether the relation \{(3,1),(5,2),(7,3),(9,4),(12,4)\} is a function. - Domain: The set of all first elements (x-values): $\{3,5,7,9,1

1. **State the problem:** Solve the system of equations using the elimination method to eliminate $y$: $$\begin{cases} 2x + 3y + z = 13 \\ 3x + 2y + 4z = 17 \\ 4x + 5y + 2z = 24 \e

1. The problem asks to convert the mixed number $2 \frac{4}{9}$ into a decimal. 2. First, convert the fraction $\frac{4}{9}$ to a decimal. Since $9$ is a denominator that produces

1. **Identify whether the functions are injective, surjective, or bijective:** a) $f : \mathbb{R} \to \mathbb{R}, f(x) = x^2 + 4$

1. **State the problem:** Expand and simplify the expression $2(x + 4) + 1$. 2. **Expand the expression:** Use the distributive property to multiply 2 by each term inside the paren

1. Problem: Find the determinant of matrix $$A = \begin{pmatrix} 2 & -1 & 4 \\ -4 & 3 & 0 \\ 5 & -2 & 1 \end{pmatrix}$$. Step 1: Use the formula for the determinant of a 3x3 matrix

1. Skriv tallene i stigende rekkefølge: $\frac{3}{4}, \sqrt{8}, \frac{2}{3}, 3^0, 2^{-1}, 3, \frac{7}{3}$. - Først, regn ut eller skriv om alle tallene som desimaltall eller enkler

1. The problem is to find the value of the distance given by the formula $$\text{distance} = \frac{1}{\sqrt{0.3}}$$. 2. First, calculate the square root of 0.3:

1. **State the problem:** Solve the equation $$4(11 - x) = 24$$ for $x$. 2. **Distribute the 4:** Multiply 4 by each term inside the parentheses:

1. State the problem: Solve the equation $$\frac{5 - x}{7} = 4$$ for $x$. 2. Multiply both sides of the equation by 7 to eliminate the denominator:

1. The problem is to evaluate the expression for distance given as $\frac{1}{\sqrt{0.1}}$ and verify the approximation. 2. Start by calculating the square root of 0.1:

1. Énoncé du problème : Étudier la nature de la suite $(u_n)$ définie par $u_0 \in \mathbb{R}$ avec $u_0 \geq 4$ et la relation de récurrence $u_{n+1} = 2u_n - 3$ pour tout $n \in

1. Let's analyze the expression $4x - 2x$. 2. Combine like terms: $4x - 2x = (4 - 2)x = 2x$.

1. **State the problem:** We need to find the solutions to the equation $$-\frac{1}{2}x^2 - x + 8 = x + 3$$ which means finding the values of $x$ where the quadratic function and t

1. **Simplify the expression** $4x^2 - 3x + 8 - 2x^2 + x - 2$ by combining like terms. Combine the $x^2$ terms: $4x^2 - 2x^2 = 2x^2$.

1. The problem is to solve the equation $3x - x = 2$ for $x$. 2. First, combine like terms on the left side: $3x - x = (3 - 1)x = 2x$.

1. **Simplify the first expression:** Given: $4x^2 - 3x + 8 - 2x^2 + x - 2$

1. The problem is to calculate $\left(-\frac{1}{2}\right)^7$. 2. When raising a fraction to a power, raise both numerator and denominator to that power: $$\left(-\frac{1}{2}\right)