🧮 algebra

1. **State the problem:** Solve the equation $$\frac{x}{3} + 7 = 9$$ for $x$. 2. **Isolate the term with $x$:** Subtract 7 from both sides to get $$\frac{x}{3} = 9 - 7$$

1. **Problem Statement:** Find the coordinates of the point that divides the segment joining $(-2,0)$ and $(3,4)$ in the given ratios from left to right. 2. **Formula:** The point

1. **State the problem:** Evaluate the expression $$\sqrt[3]{\frac{(0.07432)^2 \times 48.38}{8458}}$$ using logarithms. 2. **Recall the logarithm properties:**

1. **Problem:** Use logarithms to calculate $$\frac{\sqrt{6.019 \times 10^2} \times 10^{2.38}}{3.0 \times 5.8}$$. 2. **Formula and rules:**

1. **Problem Statement:** We need to explain a math problem with full equations and formulas in detail. 2. **General Approach:** To solve algebraic problems, we use formulas and ru

1. **State the problem:** Simplify the expression $X - 2 (x + 2) - 2 (x - 2)(x - 2)$. 2. **Rewrite the expression:**

1. State the problem. Problem: Multiply out and simplify the following expressions a) $x - 2(x + 2) - 2(x - 2)^2$ b) $x - 2(x + 2) - 2(x - 2)(x + 2)$ c) $(2a - 3)^2 - (2a - 3)(3a +

1. **State the problem:** Find the value of $k$ in the equation $$\frac{7}{18} \times \frac{k}{5} \times \frac{1}{3} = \frac{14}{45}.$$\n\n2. **Write the multiplication of fraction

1. **State the problem:** Simplify the expression $$\frac{1}{7} + \frac{4}{7} \div \frac{10}{11}$$ and write the answer in its simplest form. 2. **Recall the division rule for frac

1. **State the problem:** We want to find how many years it will take for the population of an island to double if it increases by 10% each year. 2. **Formula used:** The populatio

1. The problem is to simplify the expression with the addition of 4. 2. Since the original expression is not provided, we assume the problem is to add 4 to a given number or expres

1. **State the problem:** Solve the quadratic equation $$-2x^2 + 4x - 4 = 0$$ by completing the square. 2. **Rewrite the equation:** First, divide the entire equation by -2 to make

1. **Problem:** Simplify the expression $ (3x + 5) + (2x + 7) $. 2. **Formula and rules:** When adding polynomials, combine like terms by adding their coefficients.

1. **Problem statement:** We need to find the smallest number of fence pieces to surround a rectangular garden measuring 3 m by 6 m without cutting or bending any fence pieces. 2.

1. **State the problem:** We need to find the exponential function $f(x)$ that fits the given graph. 2. **Identify key points:** From the graph, the function passes through $(0,5)$

1. **State the problem:** We are given an exponential graph with a point (0,5) and asked to find the exponential function $f(x)$, including the initial value and constant ratio. 2.

1. **State the problem:** Find the value of each expression when $p=2$. 2. **Evaluate (a) $6p - 10$:**

1. **State the problem:** We want to find what percent the new value 200 is of the original price 10.

1. **Problem statement:** Given tables of values for two exponential functions, find the constant ratio, initial value, and write the exponential function $f(x)$ for each. ---

1. Muammo: Agar $2017a - 2018b = 1$ bo'lsa, $\gcd(a,b)$ ni toping. 2. Bu tenglama $2017a - 2018b = 1$ ko'rsatadiki, $a$ va $b$ sonlari $2017$ va $2018$ sonlari bilan lineer kombina

1. **State the problem:** Solve the equation $3 = 0$. 2. **Analyze the equation:** The equation $3 = 0$ is a simple equality statement.