🧮 algebra

1. The problem asks to find the next two terms in the sequence of triangular numbers: 1, 3, 6, 10, 15, ... 2. Triangular numbers are given by the formula $$T_n = \frac{n(n+1)}{2}$$

1. **State the problem:** You and your friend run at different constant speeds. After 1 minute, your friend is 45 meters ahead. After 3 minutes, your friend is 105 meters ahead. We

1. **State the problem:** Simplify or factor the quadratic expression $x^2 + x - 12$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers

1. The problem asks for the range of the function $f$, which means we need to find all possible $y$-values (outputs) that $f(x)$ can take. 2. From the graph description, the functi

1. The problem asks for the domain of the function $g$ based on the graph description. 2. The domain of a function is the set of all possible $x$-values for which the function is d

1. **State the problem:** We have a bag with three types of counters: green triangles, green circles, and yellow circles. We know: - 70% of the green counters are circles.

1. **State the problem:** We want to find the starting value of George's house given that after one year it increased by 9%, and after the second year it decreased by 4%, ending at

1. The problem asks if analytic methods can be used to solve the equation $$f(E) = M - Et - e \sin E = 0$$. 2. This is a transcendental equation because it involves both the variab

1. Let's start by understanding the problem: You want to find the square root of 5.8. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** We are given that Paloma's ratio of seconds to feet is 1:10, meaning she travels 10 feet in 1 second. 2. **Given:** Paloma's speed ratio is seconds:feet =

1. **State the problem:** Paloma rides a scooter traveling 10 feet every 1 second. Hannah claims the ratio of seconds traveled to feet traveled is 10:1. We need to check if Hannah

1. **State the problem:** Simplify or analyze the expression $X + 1 + \ln(X)$. 2. **Recall the components:** The expression consists of a variable term $X$, a constant term $1$, an

1. **State the problem:** Solve for $x$ in the equation $5^{3x} = 125$. 2. **Rewrite the right side as a power of 5:** Since $125 = 5^3$, the equation becomes:

1. **State the problem:** Simplify the expression $ (3+2i) - (8-5i) $. 2. **Recall the rule for subtraction of complex numbers:**

1. **State the problem:** Simplify the expression $$(3+2i)-(8-5i)$$. 2. **Recall the rule for subtraction of complex numbers:** Subtract the real parts and the imaginary parts sepa

1. نبدأ بكتابة الدالة المعطاة: $$f(x) = \frac{3x+7}{x+3}$$. 2. المطلوب هو حساب قيمة الدالة عند العدد 0، أي حساب $$f(0)$$.

1. **State the problem:** Solve the system of equations using the elimination method: $$2x + y = 7$$

1. The problem is to find the fourth root of 0.0016, which means we want to find a number $x$ such that $$x^4 = 0.0016.$$ 2. Recall the definition of the fourth root: $$\sqrt[4]{a}

1. The problem is to analyze the population growth over the years given the data points: (1970, 10), (1980, 20), (1990, 40), and (2000, 50) where population is in thousands. 2. We

1. **State the problem:** Solve for $x$ in the equation $$2^{2x+2} = 2^{3x}$$. 2. **Use the property of exponents:** If $a^m = a^n$ and $a > 0$, $a \neq 1$, then $m = n$.

1. مسئله: مقایسه دو مقدار یا دو عبارت ریاضی است. 2. برای مقایسه، ابتدا باید هر دو مقدار را به صورت عددی یا جبری ساده کنیم.