🧮 algebra

1. **State the problem:** Solve the system of equations using elimination: $$-5x + 6y = 5$$

1. The problem states that Shadow's medicine bottle starts with 100 milliliters and each dose is 5 milliliters. 2. The function $M(d)$ represents the amount of medicine left after

1. The problem is to calculate the value of $$\frac{11!}{3! \times 3! \times 2! \times 2!}$$ using a calculator. 2. Recall that the factorial of a number $n$, denoted $n!$, is the

1. **Stating the problem:** We need to solve the expression involving factorials: $\frac{11!}{3! \times 3! \times 2! \times 2!}$. 2. **Recall the factorial definition:** For any po

1. El problema es resolver la ecuación $2 = 3x^5 - 4x$ para encontrar el valor de $x$. 2. La ecuación es un polinomio de grado 5: $$3x^5 - 4x = 2$$

1. **State the problem:** We need to trace the curve given by the equation $$y^2(a^2 + x^2) = x^2(a^2 - x^2)$$ where $a$ is a constant. 2. **Rewrite the equation:** The equation re

1. Diberikan sistem persamaan linear: $$4a + 2b = 6$$

1. Masalah pertama adalah menjumlahkan pecahan $\frac{2}{5} + \frac{2}{4}$.\n\n2. Untuk menjumlahkan pecahan, kita harus menyamakan penyebutnya terlebih dahulu. Penyebut dari 5 dan

1. **State the problem:** Calculate the sum of the fractions $\frac{2}{5} + \frac{2}{4}$. 2. **Formula and rules:** To add fractions, find a common denominator, then add the numera

1. The problem is to find the 57th term of the Wu sequence (assuming it is a known sequence or arithmetic progression). 2. The general formula for the $n$th term of an arithmetic s

1. We are given the sequence $a_n = \frac{100n^3}{n^2 + 4}$ and asked to analyze or simplify it. 2. The formula for the sequence is already given: $a_n = \frac{100n^3}{n^2 + 4}$.

1. The problem is to solve the equation $y = a^x$ where $a > 0$ and $a \neq 1$, and to graph it. 2. The general form of an exponential function is $y = a^x$, where $a$ is the base

1. **State the problem:** We are given a matrix $$H = \begin{bmatrix} 1 & -3 \\ 2 & 4 \end{bmatrix}$$ and need to find $$H^2 = H \times H$$. 2. **Recall matrix multiplication:** To

1. The problem asks to solve part 3c, but no specific details are given. Assuming it refers to a typical algebraic problem, let's consider a generic example: solve for $x$ in $3x +

1. **State the problem:** Simplify the expression $$(uv^3)(-2u^3vw^4) - 3$$ and write the answer using only positive exponents. 2. **Use the distributive property and laws of expon

1. **State the problem:** We need to find the length of the seesaw. The pivot (midpoint) is 13.5 feet from the swing set, and the swing set is 8 feet from the edge of the seesaw wh

1. The problem is to expand all the terms in an expression (not specified by the user). 2. To expand terms means to multiply out all factors and remove parentheses.

1. Problem: Expand the algebraic expression $-3(-1 + 4e)$. 2. Formula: Use the distributive property $a(b + c) = ab + ac$.

1. Problem: Expand the algebraic expressions by distributing the multiplication over addition or subtraction. 2. Formula: Use the distributive property $a(b+c) = ab + ac$.

1. Problem: Expand the algebraic expressions given. 2. Formula: Use the distributive property $a(b+c) = ab + ac$ to expand each expression.

1. The problem asks us to write an exponential equation modeling Isabella's weekly sales, where sales increase by 20% each week after the first week. 2. The general form of an expo