Questions in mathematics

Questions in mathematics

[Answered] Let $g$ be the piecewise defined function shown. $g(x)=\left\{\begin{array}{ll} x+4, & -5 \leq x \leq-1 \\ 2-x, & -1 < x \leq 5 \end{array}\right.$ Evaluate $g$ at different values in its domain. $\begin{array}{l} g(-4)=\square \\ g(-2)=\square \\ g(0)=\square \\ g(3)=\square \\ g(4)=\square \end{array}$

[Answered] $\begin{array}{l}x=0 . \overline{7} \\ x \cdot 10^1=0 . \overline{7} \cdot 10^1 \\ 10 x=5 \\ 10 x-x=\overline{7}-0.7\end{array}$

[Answered] Find the inverse of the given one-to-one function [tex]f[/tex]. Give the domain and the range of [tex]f[/tex] and of [tex]f^{-1}[/tex], and graph both [tex]f[/tex] and [tex]f^{-1}[/tex] on the same set of axes. [tex]f(x)=\frac{x+5}{x-3}[/tex] The inverse function, [tex]f^{-1}(x)=[/tex] [$\square$]. The domain of [tex]f[/tex] is [$\square$]. (Type your answer in interval notation.) The domain of [tex]f^{-1}[/tex] is [$\square$]. (Type your answer in interval notation.) The range of [tex]f[/tex] is [$\square$]. (Type your answer in interval notation.)

[Answered] For $f(x)=2 x+1$ and $g(x)=x^2-7$, find $(f-g)(x)$. A. $-x^2+2 x+8$ B. $2 x^2-15$ C. $-x^2+2 x-6$ D. $x^2-2 x-8$

[Answered] The equation for the future value of a deposit earning compound interest is [tex]V(t)=P\left(1+\frac{r}{n}\right)[/tex] where [tex]P =[/tex] the initial deposit [tex]t =[/tex] years invested [tex]r =[/tex] rate at which interest is compounded annually [tex]n =[/tex] number of times the interest is compounded per year After 10 years, a $2,000-dollar investment compounded annually has grown to $3600. What is the interest rate to the nearest whole-number percent?

[Answered] Which of the following is equivalent to $\frac{\sqrt[3]{32 x^3 y^6}}{\sqrt[3]{2 x^9 y^2}}$ , where $x \geq 0$ and $y \geq 0$ ? A. $\sqrt[3]{16 x^6 y^4}$ B. $\sqrt[3]{\frac{y^4}{16 x^6}}$ C. $\sqrt[3]{\frac{16 y^4}{x^6}}$

[Answered] Write an integer for the following: 1) Father deposits Rs. 2000 in bank. 2) Mother withdraws Rs. 1500 from ATM. 3) 300 calories are increasing by consuming junk food. 4) 400 calories are decreasing by doing exercise. 5) Difference between the boiling point of water and freezing point of water.

[Answered] A coordinate grid has a line labeled -3x + (1/2)y = -3 passing through the points (1, 0) and (0, -6). What value of b will cause the system to have an infinite number of solutions? The system is: y = 6x - b -3x + (1/2)y = -3 Possible values of b: 2, 4, 6, 8.

[Answered] Estimate the product by rounding the first factor up and the second factor down to the nearest tens: (a) 45 x 62 (b) 69 x 77 (c) 88 x 17 (d) 55 x 75 (e) 52 x 32 (f) 91 x 24

[Answered] An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?