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Questions in mathematics

[Answered] In triangle ABC, angle B is a right angle. The length of side AB is 10√41 and the length of side BC is 24√41. What is the side length of AC? A. 14√41 B. 26√41 C. 34√41 D. 34√41

[Answered] [tex]\frac{4}{6} \div \frac{3}{12}[/tex]

[Answered] Solve $6 x+18=3 x+9$ for $x$.

[Answered] Which graph represents the piecewise-defined function [tex]f(x)=\left\{\begin{array}{ll}-1.5 x+3.5, & x\ \textless \ 2 \\ 4+x, & x \geq 2\end{array}\right.[/tex]?

[Answered] Solve the following inequalities: (a) [tex]x^2+6 x+8\ \textless \ 0[/tex] (b) [tex]4 x^2+x-3\ \textless \ 0[/tex] (c) [tex]6 x^2+7 x-3\ \textless \ 0[/tex] (d) [tex]x^2+5 x-14 \leq 0[/tex]

[Answered] A store has sales of $500 in their first month. If sales increase at a rate of $10 each month, they can be modeled by this equation: [tex]a_n=500+(k-1) 10[/tex] Use summation notation to model and evaluate the sales for the first ten years. Explain your steps.

[Answered] Use the arithmetic series [tex]S _5=\sum_{k=1}^5(1+3 k)[/tex] to answer each question. What are the terms of this arithmetic series? [tex]\begin{array}{l} a_1=\square \ a_2=\square \ a_3=\square \ a_4=\square \ a_5=\square \end{array}[/tex]

[Answered] Which equation is the equation of a line that is perpendicular to [tex]x+2 y=16[/tex]? A. [tex]y=-\frac{1}{2} x+6[/tex] B. [tex]y=\frac{1}{2} x-3[/tex] C. [tex]y=2 x-2[/tex] D. [tex]y=-2 x+8[/tex]

[Answered] The table shows the approximate height of an object [tex]$x$[/tex] seconds after the object was dropped. The function [tex]f(x) = -16x^2 + 100$[/tex] models the data in the table. Height of a Dropped Object | Time (seconds) | Height (feet) | | -------------- | ------------- | | 0 | 100 | | 0.5 | 96 | | 1 | 84 | | 1.5 | 65 | | 2 | 37 | For which value of [tex]$x$[/tex] would this model make the least sense to use? A. -2.75 B. 0.25 C. 1.75 D. 2.25

[Answered] The pair of parametric equations represent a line, parabola, circle, ellipse, or hyperbola. Name the type of basic curve that the pair of equations represents. [tex] \begin{array}{l} x=3 \sin (5 t) \\ y=3 \cos (5 t) \end{array} [/tex] A. line B. parabola C. circle D. ellipse E. hyperbola