🧮 algebra

1. مسئله: مقایسه کسرهای $\frac{1}{7}$، $\frac{3}{14}$، $\frac{5}{2}$ و $\frac{3}{7}$ است. 2. برای مقایسه کسرها، ابتدا باید آنها را به مخرج مشترک تبدیل کنیم یا به صورت اعشاری مقادیر

1. **State the problem:** Find the inverse of the function $f(x) = 2x + 16$. 2. **Recall the formula and rule:** To find the inverse function $f^{-1}(x)$, we swap $x$ and $y$ in th

1. The problem is to calculate the percentage of $5,758,148$ out of $39,545,959$. 2. The formula to calculate percentage is:

1. **State the problem:** Calculate the percentage of $5,758,148$ out of $39,545,959$. 2. **Formula:** Percentage is given by $$\text{Percentage} = \left(\frac{\text{Part}}{\text{W

1. **State the problem:** Solve for $x$ in the equation $x - 3 = 2$. 2. **Formula and rules:** To isolate $x$, add 3 to both sides of the equation to cancel out the $-3$.

1. **State the problem:** We are given the function $f(x) = 3 - 5x$ and asked to find the value of its inverse function at $-27$, i.e., find $f^{-1}(-27)$. 2. **Recall the formula

1. **Problem statement:** (a) Given the assessed annual value of a house is 20000 and the municipal council charges 8% as rates per annum. Monthly rent is 12000.

1. The problem asks to find the values of the inverse function $f^{-1}$ at $0$ and $8$, i.e., $f^{-1}(0)$ and $f^{-1}(8)$. It also provides a point $(7,8)$ on the function $f$. 2.

1. Stwierdzenie problemu: Obliczyć sumy i różnice podanych par macierzy. 2. Wzory i zasady: Suma macierzy $A$ i $B$ o tych samych wymiarach to macierz, której elementy są sumą odpo

1. **State the problem:** We need to find the ratio of the change in $x$ to the change in $y$ between the points $(2,1)$ and $(4,7)$ on the line. 2. **Recall the formula for change

1. The problem is to calculate the percentage value of $\frac{5,364,761}{41,218,881} \times 100\%$. 2. The formula for percentage is $\text{Percentage} = \frac{\text{Part}}{\text{W

1. The problem is to calculate the value of the expression $\frac{5,364,761}{41,218,881} \times 100$. 2. The formula used here is to divide the numerator by the denominator and the

1. **State the problem:** We are given a function $f(x)$ whose graph is a straight line passing through the origin and points $(-3,-3)$ and $(3,3)$. We need to find the equation of

1. Problem: Identify the function for the top-left graph. This is a straight line with positive slope passing through the origin.

1. **State the problem:** We want to find how much the ticket sales fall below the goal of 2350 when 300 tickets are sold.

1. **State the problem:** We need to find how many adult tickets ($d$) and student tickets ($s$) were sold to fill 500 seats and raise exactly 2350.

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

1. **State the problem:** Solve the linear equation $3x + y = 25$ for $y$ in terms of $x$. 2. **Formula and rules:** To isolate $y$, subtract $3x$ from both sides of the equation.

1. **State the problem:** We need to find values of $x$ and $y$ that satisfy the system of equations: $$3x + y = 25$$

1. **State the problem:** Simplify the expression $$\frac{5}{(x-7)(x+5)} + \frac{2}{(x-7)(x+3)}$$ and express the answer in factored form. 2. **Find a common denominator:** The den

1. The problem asks for the least common denominator (LCD) of the two fractions $\frac{3}{10x^3}$ and $\frac{y}{14x^5}$.\n\n2. The LCD is the smallest expression that both denomina