🧮 algebra

1. **State the problem:** We need to find the linear equation in slope-intercept form $y = mx + b$ that fits the given table of points: $(4, 28)$, $(5, 29)$, $(6, 30)$, and $(7, 31

1. **State the problem:** Evaluate $$\left[ \left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}} \right]^7$$. 2. **Recall the exponent rule:** W

1. **State the problem:** Evaluate the expression $$\left[\left(-\frac{4}{11}\right)^{\frac{4}{5}} \cdot \left(-\frac{4}{11}\right)^{-\frac{4}{5}}\right].$$ 2. **Recall the exponen

1. The problem asks to find the 20th term of the sequence defined by $T_n = 3^n$. 2. The formula for the $n^{th}$ term of this sequence is $T_n = 3^n$, which means each term is 3 r

1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ and check the solution. 2. **Write the equation:**

1. **State the problem:** We need to evaluate each expression and then organize the results from least to greatest. 2. **Evaluate each expression:**

1. The problem asks us to show that the sequence $1, -1, 1, -1, 1, -1, \ldots$ defined by the general term $a_n = (-1)^{n+1}$ diverges. 2. Recall that a sequence converges if it ap

1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ and check the solution. 2. **Formula and rules:** To solve linear equations, isolate the variable on one side by perfo

1. **Problem Statement:** Show that the sequence $51, -1, 1, -1, 1, -1, c, (-1)^{n+1}, c_6$ diverges. 2. **Understanding the sequence:** The sequence appears to start with $51$, th

1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ for $x$. 2. **Write down the equation:**

1. The problem asks: What is $Rs \times Pr$? We need to find the product of $Rs$ and $Pr$. 2. From the given data, we have values for $Sr$, $Rr$, $Rp$, but no direct values for $Rs

1. The problem asks for the average rate of change of a function $g$ over the interval $[-3,3]$ using the given table values. 2. The average rate of change formula over an interval

1. **State the problem:** We need to graph the function $g(x) = 2^x + 5$ using transformations of the base function $f(x) = 2^x$. 2. **Recall the base function:** The base function

1. The problem is to evaluate the expression $\frac{1}{9} \times 6$ and solve the equation $| -10 + 4 | = -6$. 2. First, calculate $\frac{1}{9} \times 6$. Multiplying a fraction by

1. ปัญหา: สร้างแบบทดสอบแบบเขียนตอบสำหรับวิชาคณิตศาสตร์สมการหลายตัวแปร 1 ข้อ 2. ตัวอย่างสมการ: \(3x + 4y - 5z = 12\)

1. The problem asks for the value of the function $f$ at $x=4$, i.e., $f(4)$. 2. From the graph, we identify the point where $x=4$. This corresponds to point D with coordinates $(4

1. ปัญหา: แก้ระบบสมการเชิงเส้น 3 ตัวแปร สมการ: $$\begin{cases} 2x + y - z = 3 \\ x - 2y + 3z = -1 \\ 3x + y + 2z = 4 \end{cases}$$

1. **State the problem:** We are given three points representing the cost of owning a car based on kilometers driven: (200, 72), (700, 152), and (1000, 200). The relationship is li

1. The problem asks to complete the grid for the relation $y = 2x - 9$ and find the values of $b$ and $d$. 2. The formula given is $y = 2x - 9$. This means for any $x$, $y$ is twic

1. ปัญหา: สร้างแบบทดสอบสมการหลายตัวแปร 5 ข้อ พร้อมแนวทางการตอบละเอียดสำหรับนักศึกษาปริญญาตรีปี 3 2. ตัวอย่างข้อที่ 1: จงแก้ระบบสมการ \(\begin{cases} 2x + 3y - z = 7 \\ -x + 4y + 5z

1. **State the problem:** We need to analyze and graph the function $g(x) = -\frac{4}{x} + 3$. 2. **Identify key features:** This is a rational function with a vertical asymptote w