🧮 algebra

1. Problem 3: Solve the system of inequalities $$4x + 8y \leq 640;

1. **State the problem:** We are given several matrices A, B, C, D, and E and asked to find their order (dimensions).

1. State the problem: Simplify the expression $6^2 - \left[\frac{2 + 2 \times 3^2}{10}\right]$. 2. Evaluate the exponents first:

1. The problem is to graph the function $y=(-2x+1)^3-6$. 2. This is a cubic function with a transformation. The base cubic function is $y=x^3$.

1. **State the problem:** Paul uses some number of trays A, B, and C to bake a total of 378 donuts. Tray A has 9 donuts, Tray B has 3 donuts, and Tray C has 6 donuts.

1. Diketahui fungsi $f(x) = x + 3$ dan $g(x) = 3x - 5$. Tentukan: 1.a. Cari invers fungsi $f^{-1}(x)$ dan $g^{-1}(x)$.

1. Given the equation $x - 3 = -\frac{1}{x}$, our goal is to find the value of $x^3 + \frac{1}{x^3}$. 2. First, rewrite the equation:

1. Stated problem: Solve the equation $4(a-2) - 3(a+5) = 7$ for $a$. 2. Expand the parentheses:

1. Problema 4: Encontrar la función inversa de $p(x) = 3(2x - 1)^2 + 3$. 2. Para hallar la inversa, empezamos intercambiando $p(x)$ por $y$:

1. The problem asks to calculate 26000 multiplied by 10%.\n2. Recall that 10% as a decimal is $\frac{10}{100} = 0.1$.\n3. Multiply 26000 by 0.1: $$26000 \times 0.1 = 2600.$$\n4. Th

1. **Stating the problem:** Simplify the algebraic expression $r - 5r - 6s + 8s - 15$. 2. **Combine like terms:** Group terms with $r$ and with $s$ separately.

1. State the problem: Find the x-intercepts of the function $$f(x)=3x^3+2x^2-5x-2$$. The x-intercepts occur where $$f(x)=0$$. 2. Set the equation to zero: $$3x^3+2x^2-5x-2=0$$.

1. Problema 7: El 2º término de una progresión geométrica (PG) es $a_2$, y el 5º término es $a_5$. Expresar la progresión. Paso 1: Sea $a_1$ el primer término y $r$ la razón común.

1. Diberikan sistem persamaan $$\frac{3}{x} + \frac{2}{y} = -7 \\

1. समस्या: दुई समसामयिक रेखीय समीकरणहरु 2x + y = 8 र x + y = 5 छन्। यी समीकरणहरुलाई ग्राफ प्रयोग गरेर समाधान गर्नूहोस्। 2. पहिलो समीकरणलाई y को रूपमा अभिव्यक्त गरौँ:

1. Let's clarify the problem: you are asking if the third term (or expression) is at least 2y greater than $\frac{1}{3}x$. 2. To analyze this, we need the exact expression for the

1. Planteamos la ecuación dada: $$\frac{5}{3x - 1} - \frac{1}{5x - 7} = \frac{11x - 1}{15x^2 - 26x + 7}$$

1. Let's translate each statement into a mathematical inequality. 2. "The sum of $x$ and $y$ is at most 10" means the sum cannot be greater than 10. This can be written as:

1. The problem is to solve the equation or expression given. 2. Since no explicit equation or expression was provided, please provide the details of the question you want solved.

1. Diketahui sistem persamaan: $$2^x - 5^y = 7$$

1. Problem: Solve the simultaneous linear equations $2x + y = 8$ and $x + y = 5$ by graphing. 2. Step 1: Identify the system type. These are simultaneous linear equations because t