🧮 algebra

1. **State the problem:** Betty paints twice as fast as Dan. Together, Dan and Betty paint 2400 square feet in 4 hours. Sue joins them, and all three paint 3600 square feet in 3 ho

1. נתחיל מהביטוי הנתון: $5y^{29} - 20m^4$ 2. נבדוק אם יש גורם משותף לשני האיברים. נראה כי $5$ הוא גורם משותף.

1. **State the problem:** A baker starts with $\frac{3}{4}$ cup of water. 2. He pours half of the water into the batter, so the amount poured is:

1. נתחיל מהביטוי הנתון: $125y^2 - 180m^4$ 2. נזהה גורם משותף למקדמים: $125$ ו-$180$ שניהם מתחלקים ב-$5$.

1. **State the problem:** Annie bought 17 articles consisting of books and pens for a total cost of 25000. Each book costs 2000 and each pen costs 1000. We need to find the fractio

1. **State the problem:** We have three types of bags: wheat (W), corn (C), and oats (O). The problem gives us relationships between their weights and asks for the weight of one ba

1. The problem asks us to find which box of pens has the cheapest cost per pen. 2. We calculate the cost per pen for each box by dividing the total cost by the number of pens:

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: $$a+b=21$$