🧮 algebra

1. **Stating the problem:** We are given an expression involving logarithms with base 7: $$\log_7 174 = 7 \log_7 174 + 7 \log_7 174$$ and need to analyze or simplify it. 2. **Recal

1. **Problem statement:** Show that the equation $3x^2 - 4y^2 + 3x + 16y - 18 = 0$ represents a hyperbola. Then find its eccentricity and the equations of its asymptotes. 2. **Rewr

1. **Problem:** Solve the system of equations: $$\begin{cases} 4x - 3y = 20 \\ 2x - y = 5 \end{cases}$$

1. **Stating the problem:** Given matrices

1. The problem is to find 10% of 78. 2. The formula to find a percentage of a number is: $$\text{Percentage value} = \frac{\text{percentage}}{100} \times \text{total value}$$

1. **State the problem:** Calculate the retail price given the cost and mark-up percentage using the formula: $$\text{Retail Price} = \text{Cost} + (\text{Cost} \times \text{Mark-u

1. **State the problem:** We want to find the number of miles $m$ you can drive a Gambelli Agency car so that the total cost is less than renting from McDougal Rental.

1. **State the problem:** We need to find the percentage of women in a cycling club with 1254 members, where 342 are women. 2. **Formula:** The percentage of women is given by

1. **State the problem:** Simplify the expression $$2 \frac{5}{8} - \left(-\frac{1}{5}\right) \div \left(-\frac{8}{5}\right) + \frac{1}{4}$$. 2. **Convert mixed number to improper

1. **State the problem:** Solve the expression $\frac{1}{2} \times (6k+1) \times 3k$. 2. **Write the expression clearly:**

1. **Problem statement:** Solve the system of equations: $$\begin{cases} s + c = m \\ s - c = 2 \end{cases}$$

1. **State the problem:** We are given values $e = 1$ and $f = 12$, and we need to find the value of the expression $$11e + 7f$$. 2. **Write the expression with given values:** Sub

1. **State the problem:** Evaluate the expression $$\frac{12d - e}{2}$$ given that $$d = 11$$ and $$e = 8$$. 2. **Write the formula and substitute values:** Replace $$d$$ and $$e$$

1. **State the problem:** Simplify the expression $1 \frac{3}{5} - 2 \frac{1}{3} + \frac{2}{5} \div 3$. 2. **Convert mixed numbers to improper fractions:**

1. **State the problem:** Find the equation of a line passing through the point $(-4,2)$ and perpendicular to the line given by $3x + 4y - 7 = 0$. 2. **Identify the slope of the gi

1. **State the problem:** Find the equation of a line passing through the point $(-4,2)$ and perpendicular to the line given by $3x + 4y = 0$. 2. **Rewrite the given line in slope-

1. The problem is to interpret the time given as "10h 40mn 45s" and understand the number 8 in the context. 2. The time is given in hours, minutes, and seconds: 10 hours, 40 minute

1. **State the problem:** We are given a table with values of $x$ and $y$: $$\begin{array}{c|cccc}

1. **State the problem:** We are given a table showing the baby's age $x$ in months and the corresponding average length $y$ in inches: | Age $x$ (months) | 0 | 1 | 2 | 3 |

1. **State the problem:** We need to solve the equation $$\frac{2x+4}{x-3} = 3$$ for $x$. 2. **Recall the formula and rules:** To solve a rational equation like this, multiply both

1. **Stating the problem:** We need to find the shape of the solution region for the system of inequalities: