🧮 algebra

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) =

1. **State the problem:** Simplify the rational expression $$\frac{x^2 - 16}{x^2 - 5x + 4}$$. 2. **Factor the numerator:** Recognize that $$x^2 - 16$$ is a difference of squares.

1. The problem asks for the degree of the polynomial $$p(x) = 3x^4 - 5x^3 + 7x^2 - 2x + 1$$. 2. The degree of a polynomial is the highest power of the variable $x$ with a nonzero c

1. The problem is to multiply $\frac{20}{100}$ by 10. 2. Write the multiplication as a fraction: $\frac{20}{100} \times 10$.

1. The problem asks to find the inverse function $f^{-1}(x)$ of the function $f(x) = 2x + 3$. 2. To find the inverse, start by replacing $f(x)$ with $y$: $$y = 2x + 3$$

1. Solve $8^{4x + 2} = 64$. Express bases as powers of 2: $8 = 2^3$, $64 = 2^6$.

1. **State the problem:** A number $w$ is decreased by 6, then the result is multiplied by 4. The final result is greater than the original number $w$. We need to write and solve a

1. The problem asks for the sum of the roots of the quadratic equation $$3x^2 - 5x = 2 = 0$$. 2. First, note that the equation as written is ambiguous because of the double equals

1. **State the problem:** Solve the inequality $$2(3x - 4) > 5(5 - x)$$ for $x$. 2. **Expand both sides:**