🧮 algebra

1. **State the problem:** Solve the equation $$\frac{8}{14} = \frac{5}{x}$$ for $x$. 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{a}{

1. **State the problem:** Solve for $x$ in the proportion $\frac{x}{1} = \frac{4}{7}$. 2. **Formula used:** In a proportion $\frac{a}{b} = \frac{c}{d}$, the cross products are equa

1. **State the problem:** Solve for $a$ in the equation $$\frac{a - 2}{4a + 2} = \frac{1}{2}.$$\n\n2. **Use the cross-multiplication rule:** When two fractions are equal, their cro

1. Problem: Simplify $4\sqrt{6} \cdot \sqrt{15}$. 2. Use the property of radicals: $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$.

1. **State the problem:** The grocer buys 620 kg of onions, correct to the nearest 20 kg, and packs them into bags each containing 5 kg of onions, correct to the nearest 1 kg. We n

1. **State the problem:** Find $\frac{2}{3}$ of $\frac{1}{5}$. This means multiply $\frac{2}{3}$ by $\frac{1}{5}$. 2. **Formula used:** To find a fraction of another fraction, mult

1. **State the problem:** Find half of one-fourth, i.e., calculate $\frac{1}{2}$ of $\frac{1}{4}$. 2. **Formula used:** To find a fraction of another fraction, multiply the two fra

1. **State the problem:** Multiply the fractions $\frac{1}{4}$ and $\frac{4}{5}$.\n\n2. **Formula:** To multiply fractions, multiply the numerators together and the denominators to

1. The problem asks us to multiply the fractions $\frac{1}{3}$ and $\frac{1}{2}$.\n\n2. The formula for multiplying fractions is:\n$$\frac{a}{b} \times \frac{c}{d} = \frac{a \times

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: