🧮 algebra

1. **State the problem:** Simplify the expression $$\frac{15bc^2 \times 2b}{6b^2}$$. 2. **Write the expression:** $$\frac{15bc^2 \times 2b}{6b^2}$$.

1. **State the problem:** We have the matrix equation $$\begin{bmatrix}9 & 3x+1 \\ 2y-1 & 10\end{bmatrix} = \begin{bmatrix}9 & 16 \\ -5 & 10\end{bmatrix}$$ and need to find values

1. **State the problem:** Simplify each expression and match it to one of the simplified forms: $10c$, $5c^2$, or $5c$. 2. **Expression 1:** $\frac{15bc}{3b}$

1. The problem asks to find 2.5% of 3,400. 2. To find a percentage of a number, use the formula: $$\text{Percentage of a number} = \frac{\text{percentage}}{100} \times \text{number

1. Planteamos el problema: Tenemos las matrices $$ A = \begin{pmatrix} 2 & -3 \\ -3 & 5 \end{pmatrix}, \quad B = \begin{pmatrix} 1 & -4 \\ -9 & 5 \end{pmatrix} $$

1. **State the problem:** We need to find the percentage of students in band at Deer Creek Middle School. 2. **Identify the given values:** Total students = 1249, Students in band

1. **State the problem:** We are given fractions and their decimal and percent equivalents in a table, with some blanks to fill.

1. **State the problem:** Factor the polynomial completely: $$8x^2 + 50$$. 2. **Identify common factors:** First, look for the greatest common factor (GCF) of the terms 8x^2 and 50

1. The problem asks to find the geometric mean of $\sqrt{6}$ and $\sqrt{216}$. 2. The formula for the geometric mean of two numbers $a$ and $b$ is:

1. The problem is to find the Highest Common Factor (HCF) of given numbers. 2. The HCF of two or more numbers is the largest number that divides all of them without leaving a remai

1. **State the problem:** We are given that $\log 17 = k$ and need to find an expression for $\log 170$ in terms of $k$. 2. **Recall the logarithm property:** The logarithm of a pr

1. The problem asks to find the geometric mean of 4 and 21. 2. The formula for the geometric mean of two numbers $a$ and $b$ is:

1. **Problem statement:** Given that $\log 17 = k$, find an expression for $\log 170$.\n\n2. **Recall the logarithm property:** $\log(ab) = \log a + \log b$. This means the logarit

1. **Planteamiento del problema:** Tenemos las matrices $$A=\begin{pmatrix}2 & -1 \\ 3 & 2\end{pmatrix}, \quad B=\begin{pmatrix}0 & 1 \\ 4 & -2\end{pmatrix}$$

1. The problem appears to involve simplifying or manipulating the expression $A^2 - B$. 2. To proceed, we need to clarify the operation or goal, but assuming simplification or fact

1. **State the problem:** Simplify the expression $$\frac{(2xr)^0}{x - 2y^3 - 2xr^3}$$. 2. **Recall the rule:** Any nonzero number or expression raised to the power 0 equals 1, i.e

1. **State the problem:** Simplify the expression $$\left( \frac{2x^3 y^2}{x^3 y^7 x^4} \right)^{-3}$$. 2. **Rewrite the expression inside the parentheses:** Combine like terms in

1. **State the problem:** Solve the equation $$2^{x+4} = 2^{(x+5)3}$$ for $x$. 2. **Recall the property of exponents:** If $$a^m = a^n$$ and $$a > 0, a \neq 1$$, then $$m = n$$.

1. The problem is to express 7% as a fraction and a decimal. 2. Recall that percent means per hundred, so 7% can be written as \(\frac{7}{100}\).

1. **State the problem:** Simplify the expression $4\sqrt{112}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sqrt{a \time

1. El problema es calcular el producto de dos matrices: $A = \begin{pmatrix}4 & 2 \\ 3 & 2\end{pmatrix}$ y $B = \begin{pmatrix}2 & 4 \\ -1 & 2\end{pmatrix}$. Queremos encontrar $(A