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Questions in Grade College

[Done] Which of the following shows the extraneous solution to the logarithmic equation? $\log _4(x)+\log _4(x-3)=\log _4(-7 x+21)$ A. $x=-7$ B. $x=-3$ C. $x=3$ and $x=-7$ D. $x=7$ and $x=-3$

[Done] Find the median for $12,16,10,14,20,22,15,24$.

[Done] The colony of Georgia was originally founded by James Oglethorpe and others as a slave state. A. True B. False

[Done] Solve $7 f+12 \geq 5 f+4$

[Done] $z$ varies directly as the square of $x$ and inversely as the cube of $y$. If $z=171$ when $x=8$ and $y=9$, find $z$ if $x=9$ and $y=6$. Round your answer to two decimal places if necessary.

[Done] Find the amplitude and period of the function. [tex]y=\frac{1}{2} \cos 6 x[/tex] Give the exact values, not decimal approximations.

[Done] Select the correct answer. Evaluate the following expression when [tex]x=-4[/tex] and [tex]y=4[/tex]. [tex]\frac{x^6-x}{4 y}[/tex] A. [tex]\frac{1,023}{4}[/tex] B. [tex]\frac{1,025}{4}[/tex] C. [tex]-\frac{1,023}{4}[/tex] D. [tex]\frac{16,385}{4}[/tex]

[Done] Divide these two fractions: [tex]$\frac{4}{5}+\frac{2}{3}=?$[/tex]

[Done] The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let [tex]t=0[/tex] be 12:00 am. Write a cosine model, [tex]d=a \cos (b t)+k[/tex], for the depth as a function of time. This amplitude is [tex]1.5[/tex] meters. The period is hours. [tex]b=[/tex]

[Done] Select the correct answer from each drop-down menu. [tex] \begin{array}{l} y=x^2+2 x-1 \ y-3 x=5 \end{array} [/tex] The pair of points representing the solution set of this system of equations is [ ]. and [ ].