Questions in mathematics

Questions in mathematics

📝 Answered - Let [tex]f(x) = \sqrt{x-3}[/tex] and [tex]g(x) = 9[/tex]. Find the domain of the composite function [tex](g \circ f)(x)[/tex]. A company uses a pricing function given by [tex]f(x) = 2x+5[/tex], where x is the number of items purchased and [tex]f(x)[/tex] is the total cost in dollars. (a) Find the inverse function [tex]f^{-1}(x)[/tex]. (b) Interpret the meaning of [tex]f^{-1}(25)[/tex] in this context.

📝 Answered - What is the slope of a line that is perpendicular to [tex]y=7 x+12[/tex]?

📝 Answered - Write an inequality for the statement: the difference between four times a number and fourteen is at most 10. A. [tex]$4 x-14 \geq 10$[/tex] B. [tex]$4 x-14 \leq 10$[/tex] C. [tex]$4(x-14) \leq 10$[/tex] D. [tex]$4(x-14) \geq 10$[/tex]

📝 Answered - Find the distance between the pair of points [tex]$\left(\frac{9}{2}, \frac{1}{5}\right)$[/tex] and [tex]$\left(\frac{1}{2}, \frac{6}{5}\right)$[/tex]. If necessary, express the answer in simplified radical form and then round to two decimal places. The distance between the given points is $\square$ units. (Simplify your answer. Type an exact answer, using radicals as needed)

📝 Answered - Review the table of values for function [tex]g(x)[/tex]. | x | g(x) | | :----- | :----- | | 28.9 | -3.751 | | 28.99 | -3.76 | | 28.999 | -3.9 | | 29 | undefined | | 29.001 | -4.1 | | 29.01 | -4.24 | | 29.1 | -4.249 | What is [tex]\lim _{x \rightarrow 29} g(x)[/tex], if it exists? A. -4.25 B. -4 C. -3.75 D. DNE

📝 Answered - Solve: [tex]$|2 x-1| < 11$[/tex] Express the solution in set-builder notation. A. [tex]$\left{x \mid 5 < x < 6\right}$[/tex] B. [tex]$\left{x \mid-5 < x < 6\right}$[/tex] C. [tex]$\left{x \mid x < 6\right}$[/tex] D. [tex]$\left{x \mid-6 < x < 6\right}$[/tex]

📝 Answered - What is the solution to the system of equations below? [tex]y=-\frac{1}{4} x+2[/tex] and [tex]3 y=-\frac{3}{4} x-6[/tex] A. no solution B. infinitely many solutions C. [tex](-16,6)[/tex] D. [tex](-16,-2)[/tex]

📝 Answered - For what value of [tex]$k$[/tex] do the equations [tex]$3x - 2y = 5$[/tex] and [tex]$x + y = k + 2$[/tex] have [tex]$P_x = 15$[/tex]?

📝 Answered - A submarine was 200 feet below sea level. It rose to the surface and then dove again to four times its initial depth. The submarine then descended another 300 feet. What was the sub's final depth? Steps: $-200+200+4(-200)+(-300)$ 1. Write an expression to model the situation. 2. Evaluate the expression. feet

📝 Answered - Solve for $n$. $11(n-1)+35=3n$