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Questions in mathematics

[Done] Graph the line. y=-\frac{2}{3} x+3

[Done] Which applies the power of a power rule properly to simplify the expression $\left(7^{10}\right)^5 ?$ A. $\left(7^{10}\right)^5=7^{10+5}=7^2$ B. $\left(7^{10}\right)^5=7^{10-5}=7^5$ C. $\left(7^{10}\right)^5=7^{10+5}=7^{15}$ D. $\left(7^{10}\right)^5=7^{10 \cdot 5}=7^{50}$

[Done] In the derivation of the formula for the volume of a cone, the volume of the cone is calculated to be [tex]$\frac{\pi}{4}$[/tex] times the volume of the pyramid that it fits inside. Which expression represents the volume of the cone that is [tex]$\frac{\pi}{4}$[/tex] times the volume of the pyramid that it fits inside? [tex]$\frac{\pi}{4}\left(2 r^2 h\right)$[/tex] [tex]$\frac{\pi}{4}\left(4 r^2 h\right)$[/tex] [tex]$\frac{\pi}{4}\left(\frac{r^2 h}{3}\right)$[/tex] [tex]$\frac{\pi}{4}\left(\frac{4 r^2 h}{3}\right)$[/tex]

[Done] The cube of [tex]$m$[/tex] varies inversely as the square root of [tex]$n$[/tex]. Which two equations model this relationship? [tex]$m^3=\frac{k}{\sqrt{n}}$[/tex] [tex]$\frac{m^2}{\sqrt{n}}=k$[/tex] [tex]$m=\frac{k}{n}$[/tex] [tex]$m^3=k n^{\frac{1}{3}}$[/tex] [tex]$m^3 n^{\frac{1}{2}}=k$[/tex] [tex]$m n=k$[/tex]

[Done] Solve the equation using square roots. Select the solution(s). [tex]4 x^2-351=20[/tex] A. [tex]x=-15[/tex] B. [tex]x=-16[/tex] C. [tex]x=-14[/tex] D. [tex]x=-8[/tex] E. [tex]x=-6[/tex] F. [tex]x=-1[/tex] G. [tex]x=2[/tex] H. [tex]x=4[/tex] I. [tex]x=0[/tex] J. [tex]x=12[/tex] K. [tex]x=14[/tex] L. [tex]x =16[/tex] M. [tex]x=-12[/tex] N. [tex]x=-2[/tex] O. [tex]x=8[/tex] P. [tex]x=18[/tex] Q. [tex]x=-10[/tex] R. [tex]x=0[/tex] S. [tex]x=10[/tex] T. no real solution

[Done] Calculate each difference: 75306 - 52451 72484 - 41777 98757 - 45957 92071 - 63125 38422 - 32165 52749 - 27521 90275 - 22581 27662 - 18028 66046 - 21401 88908 - 51942 83807 - 56656 81884 - 31951

[Done] Q.2: Change the mixed fractions into improper fractions. (Use Loose Sheets) a) 2 3/10 b) 2 6/8 c) 5 1/4 d) 1 5/12 Q.3: Change these into mixed fractions. (Use Loose Sheets) a) 15/4 b) 7/3 c) 22/10 d) 35/6

[Done] Evaluate the factorial expression. \(\left(\frac{8}{4}\right)!\) \(\left(\frac{8}{4}\right)! = \boxed{ }\)

[Done] 1. Five thousand seven is written in figures as 5070. 2. The answer obtained after adding the numbers is called the sum. 3. The predecessor of 7890 is 7889.

[Done] Without drawing a graph, calculate the [tex]$y$[/tex]-intercept for the equation: [tex]$y=x^2+9$[/tex]