🧮 algebra

1. مسئله: تبدیل عدد اعشاری 1.083 به کسر عام مارت. 2. ابتدا عدد را به صورت جمع عدد صحیح و قسمت اعشاری می‌نویسیم: $$1.083 = 1 + 0.083$$

1. **Problem statement:** We have a line with equation $y = mx + c$ and a curve with equation $xy = 16$.

1. **Problem 9:** For each function, find the greatest domain, range, and whether it is one-to-one or many-to-one. **a) Function:** $f(x) = 4x - 5$

1. **Problem:** For the function $f(x) = 4x - 5$, find: i) The greatest possible domain

1. **State the problem:** Solve the equation $x + 1 = \sqrt{7x + 15}$. 2. **Understand the equation:** The left side is linear, and the right side is a square root function. To sol

1. **State the problem:** Solve the equation $$(2x)^{\frac{3}{4}} + 2 = 10$$ for $x$. 2. **Isolate the term with the exponent:** Subtract 2 from both sides:

1. **State the problem:** Solve the equation $$\sqrt[3]{x} - 9 = 2$$ for $x$. 2. **Isolate the cube root:** Add 9 to both sides to isolate the cube root term.

1. **State the problem:** We are given a system of inequalities: $$5x + y \leq 10$$

1. **State the problem:** We need to graph the inequality $3x + 4y \geq 12$ on the Cartesian plane. 2. **Rewrite the inequality as an equation to find the boundary line:**

1. **State the problem:** We are given a one-to-one function $$f(x) = \frac{5x - 7}{7x + 5}$$ and need to find its inverse function $$f^{-1}(x)$$.

1. **State the problem:** Solve the quadratic equation $$6(-4m - 5)^2 + 1(-4m - 5) - 1 = 0$$ for $m$. 2. **Substitute:** Let $x = -4m - 5$ to simplify the equation.

1. **State the problem:** Solve the quadratic equation $$(3x + 3)^2 + 6(3x + 3) + 5 = 0.$$\n\n2. **Use substitution:** Let $y = 3x + 3$. The equation becomes $$y^2 + 6y + 5 = 0.$$\

1. **State the problem:** Find the inverse function $g^{-1}(x)$ of the one-to-one function $g(x) = \frac{4x}{5x - 9}$ and determine the domain and range of $g^{-1}$. 2. **Find the

1. **State the problem:** Factor the linear expression $56w + 35x$. 2. **Recall the factoring rule:** To factor an expression, find the greatest common factor (GCF) of all terms an

1. **State the problem:** Factor the linear expression $20x - 90$. 2. **Recall the factoring rule:** To factor an expression, find the greatest common factor (GCF) of all terms and

1. **State the problem:** Evaluate the expression $$-12 \div (-3) - (-6)$$. 2. **Recall the order of operations:** Division and subtraction are performed from left to right.

1. **State the problem:** Evaluate the expression $5 + 4 \times (-9)$. 2. **Recall the order of operations:** Multiplication is performed before addition.

1. **State the problem:** We need to graph the system of equations and determine the solution for the system: $$6x - 3y = 3$$

1. **State the problem:** We are given two systems of equations and asked to graph them and choose the correct graph. The first system is:

1. **State the problem:** Find an expression equivalent to $\left(2x\right)^{-3}$. 2. **Recall the negative exponent rule:** For any nonzero number $a$, $a^{-n} = \frac{1}{a^n}$.

1. **Problem statement:** The product of two whole numbers is 72. We need to find the largest possible sum $A$ and the smallest possible sum $B$ of these two numbers, then calculat