🧮 algebra

1. **State the problem:** Solve the system of simultaneous equations: $$4x + 3y = 23$$

1. The user has provided multiple function definitions and asked for compositions $g \circ f(x)$, $g \circ h(x)$, and $f \circ h(x)$ where: $$ f(x) = \frac{x}{x-1}, \quad g(x) = 3x

1. The problem states that John and Mary share a sum of money in the ratio 4:1. 2. John received 600 dollars, and we need to find Mary's share.

1. **Problem statement:** Solve the equation $9^{4/3} = 3^n$ for $n$. 2. **Rewrite the bases:** Note that $9 = 3^2$, so the equation becomes $\left(3^2\right)^{4/3} = 3^n$.

1. Stating the problem: We are given the quadratic function $$y = 4x - x^2$$ and want to analyze its graph, find key points such as x-intercepts and the vertex, and understand the

1. The question appears to ask for a redo due to an incorrect answer on question one. 2. Since the original question content is not provided here, I'll illustrate the process on a

1. Let's analyze the pattern in the given triangles one by one. 2. Each triangle has a top number and two bottom numbers side-by-side.

1. **Solve the equation:** \(\frac{m}{2} + \frac{m}{3} + 3 = 2 + \frac{m}{6}\) Step 1: Get common denominator for the fractions on the left and right. The denominators are 2,3,6; c

1. The problem is to resolve the fraction \( \frac{4}{x(x-1)} \) into partial fractions. 2. Assume the partial fraction decomposition has the form:

1. প্রশ্নটি হচ্ছে: ৭ নাম্বার গণিতে আমরা কেন $k$ এর মান ৩ ধরি? 2. চলুন দেখি, $k$ সাধারণত একটি ধ্রুবক হিসেবে ব্যবহৃত হয়। এটি কোন নির্দিষ্ট মান ধরে নেওয়ার কারণ হচ্ছে সমস্যা বা সূত্রের

1. State the problem: We are asked to decompose the expression $\frac{1}{2x^2 + x}$ into partial fractions. 2. Factor the denominator: The denominator $2x^2 + x$ can be factored as

1. Stated the problem: Calculate the sum of $\frac{8}{7}$ and $\frac{4}{5}$.\n\n2. Find a common denominator for the fractions: The denominators are 7 and 5, so the least common de

1. The problem is to simplify the expression $\frac{1}{2}x^2 + x$. 2. Notice that the expression contains two terms: $\frac{1}{2}x^2$ and $x$.

1. The problem is to express the fraction $\frac{1}{9}$ in decimal form. 2. Recall that dividing 1 by 9 results in a repeating decimal.

1. Problem stated: Given $a - b = b - c = 2$, find the maximum sum of the four-digit number $ab2c$ and the three-digit number $ab4$. Since $a - b = 2$ and $b - c = 2$, we can expre

1. Let's start by writing down the given expression clearly: $$6(3g + h) - 4(3g - h)$$ 2. Next, distribute the numbers 6 and -4 into the parentheses:

1. Let's clarify the problem: you asked why the expression $12g - 4h$ can become an addition. 2. The original expression $12g - 4h$ involves subtraction, not addition. However, sub

1. Let's first state the problem: you asked why the expression \(12g - 4h\) would become a plus sign in some context. 2. The expression \(12g - 4h\) involves a minus sign between \

1. **State the problem:** Expand the expression $$6 (3g + h) - 4 (3g - h)$$. 2. **Distribute the coefficients:** Multiply each term inside the parentheses by the coefficient outsid

1. The problem is to divide two ordered pairs: $ (3, -7) \div (3, 2) $. 2. Division directly for ordered pairs is not defined as usual division. Instead, we divide corresponding co

1. Il problema è dividere il numero 210 in due parti tali che siano proporzionali a 8 e 27. 2. Definiamo le due parti come $x$ e $y$, rispettivamente proporzionali a 8 e 27, quindi