🧮 algebra

1. The problem is to evaluate the function $y = 3 \cdot 5^x$ for $x = 0$. 2. The formula given is $y = 3 \cdot 5^x$. Here, $5^x$ means 5 raised to the power of $x$.

1. Bài toán yêu cầu tìm các giá trị thực của tham số $k$ để phương trình $$x^2 + (k - 1)x + k^2 - 5k + 6 = 0$$ là phương trình bậc hai. 2. Phương trình bậc hai có dạng chung $$ax^2

1. **State the problem:** We need to evaluate the function $$y = 5 \cdot 2^x$$ for $$x = 3$$. 2. **Formula used:** The function is given by $$y = 5 \cdot 2^x$$.

1. **State the problem:** We have two lines, $D_1$ and $D_2$. We know $D_1$ cuts the y-axis at $(0, -5)$ and is parallel to $D_2$ given by $x - 2y - 1 = 0$. We also know $D_1$ cuts

1. **Тодорхойлолт:** Моторт завь A зогсоолоос B зогсоол руу явахдаа хоёр өөр хурдтай явсан үед цагийн зөрүү гарчээ. 2. **Өгөгдөл:**

1. **State the problem:** We need to find the width of a rectangle given its area and length. 2. **Given:**

1. The problem is to divide the fraction $\frac{7}{9}$ by the whole number 3. 2. Recall the rule for dividing fractions: dividing by a number is the same as multiplying by its reci

1. The problem is to solve for $h$ using a different method than previously used. 2. Suppose the original equation is $A = \frac{1}{2}bh$ (area of a triangle), and we want to solve

1. **State the problem:** You are rooting for the Warriors in a 10-game series against the Lakers.

1. The problem asks to verify if $\log 22 = (\log 2)^2$ is true or false. 2. Recall the properties of logarithms: $\log(ab) = \log a + \log b$ and $\log(a^b) = b \log a$.

1. The problem is to understand and apply the GEMDAS rule in mathematics. 2. GEMDAS stands for Grouping symbols, Exponents, Multiplication and Division (from left to right), Additi

1. **State the problem:** Simplify the expression $$(10+2^3) \times (9-5) \div 4 + 6$$. 2. **Recall order of operations:** Use PEMDAS (Parentheses, Exponents, Multiplication and Di

1. The user has listed multiple topics for a final exam review in MA 1000, including ratios, proportions, percents, linear and quadratic equations, interest problems, set theory, c

1. The problem asks to represent Maya's monthly internet cost as a function of connection time. 2. The total monthly cost consists of a fixed monthly access fee plus a variable con

1. **State the problem:** Sheri has $515.85 saved and saves $62 each week. We need to write a function for her total savings over time, discuss the domain, and find how many weeks

1. مسئله را بیان می‌کنیم: مقدار عبارت $$\frac{x^3}{1 + x + x^2 + x^3}$$ را وقتی که $$x=6$$ است، پیدا کنید. 2. فرمول و قواعد مهم: در این مسئله باید مقدار عبارت جبری را با جایگذاری م

1. Problem: Znajdź wzór funkcji $f$, która każdej liczbie naturalnej $n$ przyporządkowuje największą liczbę całkowitą $k$ spełniającą nierówność $$xk^2 - 2nk - 8nk^2 < 0.$$ 2. Najp

1. The problem states that a psychologist assessed 120 patients and 1/4 of them were diagnosed with anxiety disorder. 2. To find how many patients had anxiety disorder, we use the

1. The problem asks to find which set of three numbers are all perfect square numbers. 2. A perfect square number is an integer that can be expressed as $n^2$ where $n$ is an integ

1. **State the problem:** Solve for $x$ in the equation $$2(x-6) = 3(2x + 14)$$. 2. **Use the distributive property:** Multiply out the parentheses.

1. **Stating the problem:** We have a sequence $(U_n)$ with the conditions: