🧮 algebra

1. **State the problem:** We have a farm with chickens and cows. Chickens have 2 legs each, cows have 4 legs each. There are 50 animals total and 140 legs total. We want to find ho

1. The problem asks to find the actual range of the function based on the graph and given options. 2. From the graph description, the function approaches a horizontal asymptote nea

1. The problem asks for the range of the function shown in the graph. 2. From the description, the function behaves like an exponential function that starts near $y = -2$ for $x <

1. **State the problem:** A student buys notebooks and pens. Each notebook costs $4 and each pen costs $1. The student buys 18 items in total and spends 54 in total cost. We need t

1. **State the problem:** Solve the system of linear equations: $$2x + 3y = 13$$

1. **State the problem:** A delivery company uses vans and trucks to deliver boxes. Each van carries 10 boxes, each truck carries 25 boxes, and the company uses 14 vehicles to deli

1. **State the problem:** A movie theater sells adult tickets at 12 each and child tickets at 8 each. On one night, 120 tickets were sold for a total of 1200. We need to find how m

1. **State the problem:** We need to find how many Combo A and Combo B lunches were sold given the total sandwiches and juices sold. 2. **Define variables:** Let $x$ be the number

1. The problem asks to find the rate of change (slope) for the lines $x=5$ and $y=-2$. 2. The line $x=5$ is a vertical line where $x$ is always 5 regardless of $y$.

1. **State the problem:** We have a linear function $f(x)$ passing through points $(2,5)$ and $(-1,10)$. We need to find the slope of a line perpendicular to $f(x)$. 2. **Formula f

1. **State the problem:** We need to find all values of $x$ such that $$f(x) = \log_2 x + \log_2 (x - 2) = 3.$$ 2. **Recall the logarithm property:** The sum of logarithms with the

1. **Stating the problem:** We are given two functions related to sound intensity and decibels: $$d(Y) = 10 \log_{10}(Y \cdot 10^{12})$$

1. **State the problem:** Given the arithmetic progression (A P) 3, x, y, 18, find the values of $x$ and $y$. 2. **Recall the formula for an arithmetic progression:** The differenc

1. **State the problem:** Simplify the expression $$\frac{2}{3}(21x + 15) + 7 + 8 + 3x + 1$$. 2. **Use the distributive property:** Multiply $$\frac{2}{3}$$ by each term inside the

1. **State the problem:** Simplify the expression $\left(5 \frac{7}{3}\right) \times \left(5 \frac{8}{3}\right)$ and express it in the form $5k$ where $k$ is a number. 2. **Convert

1. **State the problem:** A magician can now hold his breath for 41 seconds, which is 0% more than when he first tried. We need to find how long he could hold his breath originally

1. **State the problem:** The PTA raised 16750 this year, which is 0% less than last year. We need to find how much was raised last year.

1. Сформулюємо задачу: знайти точки екстремуму функції $$y = x^4 - 2x^2 + 1$$. 2. Для знаходження точок екстремуму потрібно знайти похідну функції та прирівняти її до нуля, оскільк

1. **State the problem:** Solve the equation $$3| -10 + x | = 21$$ for $x$. 2. **Recall the absolute value equation rule:** For $|A| = B$, where $B \geq 0$, the solutions are $A =

1. **Problem:** Find the absolute value of the complex number $2 - 10i$. 2. **Formula:** The absolute value (or modulus) of a complex number $a + bi$ is given by

1. **State the problem:** Find the equation of the line passing through points $(3, -4)$ and $(-2, 6)$ in gradient-intercept form $y = mx + b$. 2. **Formula for slope:** The slope