🧮 algebra

1. The problem is to analyze the equation of the form $3x^2 + 2y^2 = 11$. 2. This is an equation of an ellipse because it is a sum of squared terms equal to a constant.

1. The problem states that the parabola is given by the parametric equations $x=at^2$ and $y=2at$. 2. We want to show that these parametric equations represent the parabola $y^2=4a

1. The problem states that the parabola is given by the parametric equations $x=at^2$ and $y=2at$. 2. We want to show that these parametric equations represent the parabola $y^2=4a

1. The problem is to find the values of $x$ and $y$. 2. Since no equations or additional information are provided, we cannot determine unique values for $x$ and $y$.

1. The problem involves understanding ratios, formulas, and their solutions. 2. A ratio is a comparison of two quantities expressed as $a:b$ or $\frac{a}{b}$.

1. The problem is to understand and solve ratio formulas. 2. A ratio compares two quantities and is often written as $a:b$ or $\frac{a}{b}$.

1. समस्या को समझते हैं: हमें -2 के गुणज (multiples) लेने हैं और फिर प्रत्येक के बाद एक विषम संख्या (odd number) का वर्ग (square) जोड़ना है। 2. -2 के गुणज: $-2, -4, -6, -8, \dots$

1. **State the problem:** Solve the system of equations by substitution method: $$x + y = 2$$

1. The problem is to find the missing number in the sequence: 13, 11, 20, 16, ?, 35. 2. Let's analyze the pattern by looking at the differences between consecutive terms:

1. The problem is to solve the equation $$\sqrt{}\left(\;\right)w^2 - w + 3\left(\;\right) = 2w$$. 2. Notice that the expression $$\sqrt{}\left(\;\right)$$ and $$3\left(\;\right)$$

1. The user asks about the absence of $x$ in an equation. 2. To clarify, an equation without $x$ means it is either a constant or involves other variables.

1. The problem is to simplify and solve the equation $$\sqrt{x} \cdot w^2 - w + 3 = 2w$$ for $w$ in terms of $x$. 2. Start by rewriting the equation:

1. Stating the problem: Simplify and solve the equation $$\sqrt{x} \cdot wx^2 - w + 3 = 2w$$ for $x$ or $w$ if possible. 2. Rewrite the equation clearly: $$\sqrt{x} \cdot wx^2 - w

1. The problem involves simplifying and understanding expressions with square roots and variables $a$, $b$. 2. First expression: $$\sqrt{15 \times 2\sqrt{15} + 2\sqrt{15} + \ldots}

1. We are given the inequality $-x^2 - 6x - 5 < 0$ and need to find the values of $x$ that satisfy it. 2. First, rewrite the inequality by multiplying both sides by $-1$ to make th

1. Let's clarify the terms: The x-intercept is where the graph crosses the x-axis, so $y=0$ at this point. 2. The y-intercept is where the graph crosses the y-axis, so $x=0$ at thi

1. We are asked to solve the inequality $-x^2 - 6x - 5 < 0$. 2. First, multiply the entire inequality by $-1$ to make the quadratic coefficient positive. Remember to reverse the in

1. The problem appears to involve understanding the formula with symbols +, =, and -. 2. Typically, in algebra, the symbols +, =, and - represent addition, equality, and subtractio

1. The problem is to simplify the expression $- + + = -$. 2. This expression appears to be a sequence of signs without numbers or variables, so let's interpret it as a sequence of

1. The problem is to simplify the expression $\sqrt{56} + 14\sqrt{7}$.\n\n2. Start by simplifying $\sqrt{56}$. Note that $56 = 7 \times 8$, so:\n$$\sqrt{56} = \sqrt{7 \times 8} = \

1. The problem is to simplify the expression: $1 + \frac{1}{2} + \frac{1}{1} + \sqrt{2}$. 2. First, rewrite the expression clearly: