🧮 algebra

1. **State the problem:** Solve the equation $2x + 6 = 0$ for $x$. 2. **Isolate the variable term:** Subtract 6 from both sides to get:

1. **State the problem:** Given that $2^A \times 3^B \times 5^C = 36000$, find the value of $3A + 4B + 6C$. 2. **Prime factorize 36000:**

1. **State the problem:** Given that $2^A \times 3^B \times 5^C = 36000$, find the value of $3A + 4B + 6C$. 2. **Prime factorize 36000:**

1. نبدأ بحساب مجموع الأعداد المعطاة: $\pi + 27 + 10$. 2. نعلم أن قيمة $\pi$ تقريباً تساوي 3.1416.

1. The problem is to find the greatest common divisor (GCD) of 10932 and 3150. 2. We use the Euclidean algorithm, which involves repeated division and taking remainders.

1. **State the problem:** Sketch the graph of the polynomial $$y = (x - 2)^2 (x + 1)^3$$ showing the y-intercept, x-intercepts, turning points, and the inflection point.

1. **Problem 1: Percent increase in Jack's typing speed** Jack's initial typing speed is 80 words per minute (wpm).

1. נתחיל מהביטוי הנתון: $75 - 3x^2$ 2. נוכל להוציא גורם משותף מחוץ לסוגריים, שהוא 3:

1. The problem gives us two equations: $$(a+b)^2=81$$ and $$(a-b)^2=1$$. 2. Expand both equations using the identity $$(x+y)^2 = x^2 + 2xy + y^2$$:

1. Given the problem: \((a+b)^2 = 81\) and \(ab = 18\). 2. We need to find the value of \(a^2 + b^2\).

1. We are given the equation $$\frac{19}{8} = 2 + \frac{1}{a + \frac{1}{b + \frac{1}{c}}}$$ and need to find the value of $a + b + c$. 2. First, subtract 2 from both sides:

1. The problem states: Let $$198 = 2 + 1a + 1b + 1c$$. We need to find the value of $$a + b + c$$. 2. Rewrite the equation clearly: $$198 = 2 + a + b + c$$.

1. نبدأ بكتابة المعادلة: $$x^2 - kx + 12 = 0$$. 2. نفرض أن جذري المعادلة هما $$x_1$$ و $$x_2$$.

1. **State the problem:** We need to find how many integers between 100 and 999 have an odd ones digit, an even tens digit, and an even hundreds digit. 2. **Analyze the digits:**

1. **State the problem:** We are given positive integers $a$, $b$, and $c$ such that $$2^{a} 3^{b} 5^{c} = 36000.$$ We need to find the value of $$3a + 4b + 6c.$$\n\n2. **Prime fac

1. The problem states: Let $$198 = 2 + 1a + 1b + 1c$$. We need to find the value of $$a + b + c$$. 2. Rewrite the equation clearly: $$198 = 2 + a + b + c$$.

1. The problem states: Let $$198 = 2 + 1a + 1b + 1c$$. We need to find the value of $$a + b + c$$. 2. Rewrite the equation clearly: $$198 = 2 + a + b + c$$.

1. Given the equations: $$a^2 - b^2 = 32$$

1. The problem asks us to list the numbers $\frac{1}{4}$, $\frac{4}{10}$, $\frac{41}{100}$, $0.04$, and $0.404$ from smallest to largest and find the middle number. 2. Convert all

1. **Problem statement:** A man starts at 0 on the number line and makes 101 moves. On the $n$th move, he moves $n$ units either left or right. We want to find how close to 0 his f

1. The problem is to expand the expression $ (a - b)^2 $. 2. Recall the formula for the square of a binomial: