🧮 algebra

1. **State the problem:** We want to find how many more unique users there were in APAC in 2020 compared to North America, given the number of connections per person in each region

1. Problema ne cere să găsim valoarea lui $x$ pentru care suma seriei $$\frac{1}{4} + \frac{1}{28} + \frac{1}{70} + \dots + \frac{1}{x^2 + 3x} = \frac{2027}{6084}.$$\n\n2. Observăm

1. The problem is to simplify the expression $\left(2^4\right)^2$. 2. According to the power of a power rule in exponents, $(a^m)^n = a^{m \times n}$.

1. The problem asks for the multiplicative inverse of $\frac{3}{2}$ raised to the power of $-4$ in exponential form. 2. The multiplicative inverse of a number $x$ is $\frac{1}{x}$.

1. The problem asks for the multiplicative inverse of $\frac{3}{2}$ raised to the power of $-4$ in exponential form. 2. The multiplicative inverse of a number $x$ is $\frac{1}{x}$.

1. The problem asks for the multiplicative inverse of $2^{-4}$ in exponential form. 2. Recall that the multiplicative inverse of a number $x$ is $\frac{1}{x}$.

1. The problem asks for the multiplicative inverse of $2$ raised to the power of $-4$. 2. First, calculate $2^{-4}$. By the rule of negative exponents, $a^{-n} = \frac{1}{a^n}$, so

1. Problem 4(a): Compare the natural domains of \(f(x) = \frac{x^2 + x}{x + 1}\) and \(g(x) = x\). - The domain of \(f\) excludes values that make the denominator zero.

1. Masalah ini menanyakan dari mana angka 2 dalam ekspresi $2x$ berasal. 2. Angka 2 biasanya muncul sebagai koefisien yang menunjukkan bahwa variabel $x$ dikalikan dengan 2.

1. The problem gives the equation of a line: $$4x - 5y = 80$$ and asks for the x- and y-intercepts. 2. To find the x-intercept, set $$y = 0$$ and solve for $$x$$:

1. The problem is to analyze the function $y=\sqrt{x^{2}+1}$.\n\n2. This function represents the square root of the expression $x^{2}+1$. Since $x^{2}$ is always non-negative and 1

1. The problem is to simplify or understand the expression $\sqrt{x^2 + 1}$.\n\n2. Inside the square root, we have $x^2 + 1$. Since $x^2$ is always non-negative and 1 is positive,

1. Simplify the expressions: (i) Simplify $\frac{\sqrt{3} + \sqrt{12} + \sqrt{108} - \sqrt{15}}{\sqrt{6} - \sqrt{96} + \sqrt{105}}$.

1. The problem asks for the coefficient of $x^2 y^3$ in the expansion of $(x + y)^5$. 2. Use the binomial theorem: $$(x + y)^5 = \sum_{k=0}^5 \binom{5}{k} x^k y^{5-k}$$

1. The problem asks for the coefficient of $x^3$ in the expansion of $(1 + x)^5$. 2. We use the binomial theorem, which states:

1. **State the problem:** Find the sum of the infinite geometric series $$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \cdots$$. 2. **Identify the first term and common ratio:** T

1. The problem asks to write the equation of a line in slope-intercept form, which is generally written as $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 2. From

1. Let's start by understanding that your request covers multiple units with formulas, questions, answers, and a test. 2. Since this is a broad request, I will provide a structured

1. The problem asks for the remainder when the polynomial $p(x) = x^3 - 4x^2 + 6x - 24$ is divided by $x - 2$. 2. According to the Remainder Theorem, the remainder of dividing a po

1. The problem is to find the square root of the discriminant of the quadratic equation $$2x^2 + 3x - 5 = 0$$. 2. Recall the discriminant formula for a quadratic equation $$ax^2 +

1. The problem states that we have a function $f : A \to B$ with sets $A = \{1, 2, 3\}$ and $B = \{4, 5, 6\}$. The function values are given as $f(1) = 4$, $f(2) = 5$, and $f(3) =