🧮 algebra

1. **State the problem:** Jason wants to know how many days it will take for the machine to produce enough silverware to cover its $9000 cost. 2. **Calculate the production rate:**

1. **Problem 21a:** Find the binomial expansion of $\left(1 - \frac{x}{4}\right)^5$ in ascending powers of $x$. Using the binomial theorem:

1. The problem is to analyze the function $y=2x^3 - x^2$. 2. First, identify the function type: it is a cubic polynomial.

1. The problem is to find the value of $x$ given an equation or condition (please provide the full equation or condition to solve for $x$). 2. Since the equation or condition is mi

1. The problem states that the numbers 40 and P are in the ratio 4:3, and their prime factors are represented in a Venn diagram. 2. First, express 40 as its prime factors: $$40 = 2

1. **State the problem:** ABC Company has 80 employees and currently has \(\frac{1}{4}\) fewer computers than employees. They plan to hire 5% more employees. We need to find how ma

1. **State the problem:** Scarlett has 44 m of blue ribbon and 110 m of red ribbon. She wants to cut all the ribbon into smaller pieces of the same length with no ribbon left over.

1. પ્રશ્ન: 10 અને 11 વાગ્યાની વચ્ચે ઘડિયાળના કલાક કાંટા અને મિનિટ કાંટા વચ્ચેનો ખૂણો 0° ક્યારે થાય છે તે શોધો. 2. ઘડિયાળના કલાક કાંટા અને મિનિટ કાંટા વચ્ચેનો ખૂણો 0° એટલે કે બંને ક

1. **State the problem:** We need to find how long the new computer will take to load a document containing 2 graphics and 1 paragraph, given that the new computer loads 17% faster

1. **State the problem:** Jack initially types at 80 words per minute (wpm). After two weeks, his speed increases by 3%. By the end of the course, he types a 1,680-word document in

1. نبدأ بكتابة الكسر الذي يمثل المسافة التي يقطعها سفيان سباحة. - المرحلة الأولى: يقطع \frac{3}{4} من المسافة على الدراجة.

1. The problem asks to find the sum of the sequence $1 + 2 + 3 + \dots + 1001$ and determine which of the given numbers it is divisible by. 2. The sum of the first $n$ natural numb

1. **State the problem:** Simplify the expression $$\left(1 - \frac{4}{9}\right)^2 - \frac{7}{25} - \left(\frac{1}{3}\right)^2$$. 2. **Simplify inside the parentheses:**

1. We are given the system of equations: $$a+b=21$$

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 +