Isolating quantities

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~y-57=px\\
&\text{The given equation relates the positive numbers }p,x,\text{ and }y.\text{ Which equation correctly }\\
&\text{expresses }y\text{ in terms of }p\text{ and }x?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{1}{7b}=\frac{11x}{y}\\
&\text{The given equation relates the positive numbers }b,~x,\text{ and }y.\text{ Which equation correctly }\\&\text{expresses }x\text{ in terms of }b \text{ and }y?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~14j+5k=m\\&\text{The given equation relates the numbers }j,~k, \text{ and } m.\text{ Which equation correctly }\\&\text{expresses }k\text{ in terms of }j\text{ and }m?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~P=N(19-C)\\
&\text{The given equation relates the positive numbers }P,~N,\text{and }C\text{. Which equation correctly }\\&\text{expresses }C \text{ in terms of }P\text{ and }N?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p=\frac{k}{4j+9}\\&\text{The given equation relates the distinct positive numbers }p,~k,\text{ and }j.\text{ Which equation correctly}\\&\text{expresses }4j+9\text{ in terms of }p\text{ and }k?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7m=2(n+p)\\&\text{The given equation relates the positive numbers }m,n,\text{~and~}p.\text{ Which equation correctly }\\
&\text{gives }m\text{ in terms of }n\text{ and }p?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~x=2a(b+5)\\
&\text{The given equation relates the positive numbers }a,~b,\text{ and }x.\text{ Which equation correctly}\\&\mathrm{expresses~}a\text{ in terms of }b\mathrm{~and~}x?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ak=\frac{b}{12}(7+m)\\&\text{The given equation relates the positive variables~}a,~b,~k,\text{ and }m.\text{ Which equation correctly }\\&\text{expresses }m\text{ in terms of }a,~b,\text{ and }k?
\end{aligned}\)

\(\begin{aligned}&\text{The line }y=kx+4,\text{where }k\text{ is a constant, is graphed in the }xy\text{-plane. If the line contains }\\
&\text{the point }(c,d),\text{ where }c\neq0\text{ and }d\neq0,\text{ what is the slope of the line in terms of }c \text{ and }d?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~7x+16=\frac{4}{y}\\&\text{The given equation relates the distinct positive numbers }x\text{ and }y.\text{ Which equation correctly}\\&\text{expresses }y\text{ in terms of }x?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~v=-\frac{w}{130x}\\&\text{The given equation relates the distinct positive numbers }v,~w\text{ and }x.\text{ Which equation correctly}\\&\text{expresses }w\text{ in terms of }v\text{ and }x?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~h=-16t^{2}+v t+k\\&\text{The equation above gives the height }h, \text{in feet, of a ball }t\text{ seconds after it is thrown straight }\\&\text{up with a initial speed of }t\text{ feet per second from a height of }k\text{ feet. Which of the following }\\&\text{gives }v\text{ in terms of }h,~t,\text{ and }k?\end{aligned}\)

\(\begin{aligned}
&\text{The formula below is often used by project managersto compute }E\text{, the estimated time } \\
&\text{to complete a job, where }O\text{ is the shortest completion time, }P\text{ is the longest completion }\\
&\text{time, and } M\text{ is the most likely completion time.}\\\\
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~E=\frac{O+4M+P}{6}\\
&\text{Which of the following correctly gives }P\text{ in terms of }R,~O\text{ and }M?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{12}{n}-\frac{2}{t}=-\frac{2}{w}\\
&\text{The given equation relates the variables }n, ~t, \text{ and } w,\text{ where }n>0,~t>0,\text{ and }w>t.\\&\text{Which expression is equivalent to }n?
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{2}{c}-\frac{7}{d}=5\\
&\text{The given equation relates the variables }c\text{ and }d,\text{ where }c\text{ and }d\text{ are greater than }1.\\
&\text{Which equation correctly expresses }d\text{ in terms of }c?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{46}{p}=\frac{46}{q}-\frac{46}{r}-\frac{46}{s}\\
&\text{The given equation relates the positive variables }p,~q,~r,\text{ and }s.\text{ Which of the following}\\
&\text{is equivalent to }q?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~PC=N(44-C)\\
&\text{The given equation relates the variables }P,~N,\text{ and }C.\text{ Which expression represents the value }\\
&\text{of }C\text{ for distinct positive values of }P\text{ and }N?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~10yz-9xz=10xy-z\\
&\text{The given equation relates the real numbers }x,~y,\text{ and }z,\text{ where }x < 0\text{ and }y > 0 .\text{ Which}\\&\text{equation correctly expresses }z\text{ in terms of }x\text{ and }y?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~18qrt-2qrs+10rst=0\\
&\text{In the given equation, }q,~r,~s,\text{ and }t\text{ are positive, and }\frac{q}{t}\text{ is greater than }5.\text{ Which expression }\\&\text{is equivalent to }s?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~R=\frac{F}{N+F}\\
&\text{A website uses the formula above to calculate a seller’s rating, }R\text{, based on the number of favorable}\\
&\text{reviews, }F\text{, and unfavorable reviews, }N.\text{ Which of the following expresses the number of favorable}\\
&\text{reviews in terms of the other variables?}\end{aligned}\)

\(\text{If }a^{-\large\frac{1}{2}}=x,\text{ where }a>0,\text{ what is }a\text{ in terms of }x?\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{14x}{7y}=2\sqrt{w+19}\\
&\text{The given equation relates the distinct positive real numbers }w,~x\text{ and }y.\text{ Which equation correctly}\\
&\text{expresses }w\text{ in terms of }x\text{ and }y?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p=\sqrt{12c}-25\\
&\text{The given equation relates the variables~}p\text{ and }c,\text{ where }c\text{ is positive. Which equation correctly }\\&\text{expresses }c\text{ in terms of }p?\end{aligned}\)

\(\begin{aligned}
&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b^{2}+5c=9d\\
&\text{The given equation relates the real numbers }b,~c,\text{ and }d,\text{ where }d>\frac{5}{9}c.\text{ Which equation correctly }\\&\text{expresses }b\text{ in terms of }c\mathrm{~and~}d?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~W=\frac{R^{2}}{R^{2}+S^{2}}\\
&\text{The given equation relates the variables }R,~S,\text{ and }W,\text{ where }R,~S,\text{ and }W\text{ represent positive}\\&\text{numbers. Which equation correctly }\text{expresses }S\text{ in terms of }R\text{ and }W?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r=\sqrt{5w-3}\\
&\text{The given equation relates the real number and }w,\text{ where }w>\frac{3}{5}.\text{ Which equation correctly }\\&\text{expresses }w\text{ in terms of }r?\end{aligned}\)

\(\begin{aligned}
&\text{The volume of a sphere is given by the formula }V=\frac{4}{3}\pi r^{3},\text{ where }r\text{ is the radius of the sphere. }\\
&\text{Which of the following gives the radius of the sphere in terms of the volume of the sphere?}\end{aligned}\)

\(\begin{aligned}
&\text{For a certain circuit, its power }P,\text{ in watts; current }C,\text{ in amperes; voltage }V,\text{ in volts; and}\\
&\text{resistance }R\text{, in ohms, are related as }\frac{CV^2}{P}=\sqrt{\phantom{\rule{0pt}{2ex}}\text{PR}} \text{, where }P,C,V\text{, and }R\text{ are positive.}\\&\text{When }R=18,\text{which equation correctly expresses }P\text{ in terms of }C\mathrm{~and~}V?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~49=\frac{2K}{v^{2}}\\
&\text{For an object with a mass of 49 kilograms, the given equation relates the kinetic energy }K,\\
&\text{in joules, }\text{of the object to the object’s speed }v,\text{ in meters per second, where }K\text{ and }v\text{ are }\\
&\text{positive. Which equation correctly expresses this object’s speed, in meters per second, in }\\&\text{terms of the object’s kinetic energy, in joules?}\\
\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~5a=\frac{4b^{2}}{a}-20a\\&\text{The given equation relates the positive variables }a\mathrm{~and~}b.\text{ Which equation correctly expresses }\\&a\text{ in terms of }b?\end{aligned}\)

\(\begin{aligned}&~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\frac{1}{5xy}+xyz=\frac{1}{4yz}\\
&\text{In the given equation, }x,~y,\text{ and }z\text{ are positive numbers. Which expression is equivalent to }y?\end{aligned}\)