Questions in mathematics

Questions in mathematics

📝 Answered - 1. Two functions f(x) = 3 - 3x and g(x) = x (a) Find the value of g(-3). (b) Find f'(x). 2. f(x) = 8 - 3x and g(x) = 10/(x+1) (a) Write down the value of x for which g(x) is undefined. (b) Find f(8/3). 3. Functions f and g are given, such that f(x) = 3 - 4x and g(x) = x (a) Find gf(2). (b) Solve the equation f(x) = 5 - x. 4. It is given that p(x) = 4x - 7 and q(x) = x (a) Find p(-2). (b) Find x when q(x) = 2197.

📝 Answered - 18. \( \int \frac{x \, dx}{\sqrt[2012]{(1 + x^2)^{1012} (2 + x^2)^{3012}}} = \frac{\alpha}{2\beta} (1 - f(x))^{\beta/\alpha} + c \), where \( \alpha \) and \( \beta \) are coprime numbers. (A) \( f(\sqrt{2}) = \frac{1}{\beta - \alpha} \) (B) \( f(\sqrt{2}) = \frac{1}{\alpha - 2\beta} \) (C) \( f(1) = \frac{1}{\alpha - 2\beta} \) (D) \( f(\sqrt{3}) = \frac{1}{\alpha - \beta} \)

📝 Answered - Graph the solution set for this inequality: $-6x - 3y \leq -18$ Step 1: Identify the $x$- and $y$-intercepts of the boundary line. When $x=0, y=$ $\square$ When $y=0, x=$ $\square$

📝 Answered - What is the solution to the inequality [tex]$28>4-2 p$[/tex]? A. {p | p>-12} B. {p | p<-12} C. {p | p>12} D. {p | p<12}

📝 Answered - Show, by means of calculations, that a cow with a girth of 70 inches and a body length of 78 inches has a weight of [tex]$577,88 kg$[/tex]. You may use the formula: Animal weight in pounds [tex]$=\frac{(\text { girth })^2 \times \text { body length }}{300}$[/tex] Note: [tex]$1 kg=2,2046$[/tex] pounds

📝 Answered - For what value of $c$ is the relation a function? $\left\{(2,8),(12,3),(c, 4),(-1,8),(0,3)\right\}$

📝 Answered - Which equation represents a line that is perpendicular to the line passing through $(-4,7)$ and $(1,3)$? A. $y=-\frac{5}{4} x-2$ B. $y=\frac{5}{4} x+8$ C. $y=\frac{4}{5} x-3$ D. $y=-\frac{4}{5} x+6$

📝 Answered - What is the slope of a line that is perpendicular to the line shown on the graph? -4 1 1/4 1/4 4

📝 Answered - Write the following expression in simplified radical form: [tex]$\sqrt[3]{40 x^{10} z^{18}}$[/tex]

📝 Answered - Select the correct answer. Consider the following system of equations. [tex]\begin{aligned} -2 x+5 y & =19 \\ y & =-\frac{5}{6} x-\frac{1}{6} \end{aligned}[/tex] Use this graph of the system to approximate its solution. A. [tex]\left(\frac{5}{2},-\frac{13}{4}\right)[/tex] B. [tex]\left(-\frac{13}{4}, \frac{5}{2}\right)[/tex] C. [tex]\left(\frac{13}{4},-\frac{5}{2}\right)[/tex] D. [tex]\left(-\frac{5}{2}, \frac{13}{4}\right)[/tex]