🧮 algebra

1. **State the problem:** Jason wants to know how many days it will take for a machine costing 9000 to produce enough silverware to pay for itself. 2. **Calculate the number of pie

1. نبدأ بكتابة التعبير المعطى: $$H \times \frac{1}{5} - H \cdot \frac{1}{5}$$. 2. نلاحظ أن كلا الحدين متشابهان، حيث كلاهما يساوي $$H \times \frac{1}{5}$$.

1. **بيان المسألة:** نريد إثبات أن $B = A$ حيث:

1. Let's denote Fanny's age as $x$ years. 2. Since Fanny is younger than her uncle by 16 years, the uncle's age is $x + 16$ years.

1. **State the problem:** We need to evaluate the expression $$r = \frac{8 - 10}{8 - 10 + 1}$$. 2. **Calculate the numerator:** $$8 - 10 = -2$$.

1. **Problem 11:** Given points $a=0$, $b=1$, $c$ on a number line and expressions $\frac{1}{a+2}$, $\frac{1}{b-3}$, $\frac{1}{c+3}$, determine the order of these fractions. - Calc

1. প্রথম সমস্যায়, $p(x) = x^3 + 5x^2 + 6x + 8$ কে $(x - a)$ ও $(x - b)$ দ্বারা ভাগ করলে একই ভাগশেষ থাকে। অর্থাৎ, $p(a) = p(b)$ যেখানে $a \neq b$। 2. তাই, $p(a) = a^3 + 5a^2 + 6a +

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:**