Correct Solution is: B. Since $12x-8=28$ by factoring 4 in the left side of the equation we get $4(3x-2)=28$ or $3x-2=7$

Correct Solution is: A. Solving for $x$ by multiply entire equation by least common denominator $5x$.

Correct Answer is B. Combining the given inequalities $x > 2$ and $x < 3$ yields $2 < x < 3$. So, $x$ lies between 2 and 3. Hence,
$x-2$ is positive and $x-3$ is negative. Hence, the product $(x-2)(x-3)$ is negative. I is false.
$2-x$ is negative and $x-3$ is negative. Hence, the product $(x-2)(x-3)$ is positive. II is true.
$2-x$ is negative and $3-x$ is positive. Hence, the product $(2-x)(3-x)$ is negative. III is false.
Hence, the answer is (B), II only is correct.

Correct Answer is A. The product $ab$ is positive when both $a$ and $b$ are positive or when both $a$ and $b$ are negative; in either case, $a/b$ is positive. Hence, choice (A) is always positive.

Correct Answer is A. The constant term $331.4$ in $S(T) = 0.6T + 331.4$ is the value of $S$ when $T = 0$. The value $T = 0$ corresponds to a temperature of $0^{\circ}C$. Since $S(T)$ represents the speed of sound, $331.4$ is the speed of sound, in meters per second, when the temperature is $0^{\circ}C$.

Correct Answer is B. Number 5 represent the slope but since it is negative it means that the tank loses 5 gallons of water each hour.

Correct Answer is C. Use the slope formula $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$ with the two given points $(3,2)$ and $(0,k)$ to get an equation involving $k$ which is $\displaystyle \frac{2-k}{3-0}=\frac{-1}{2}$.
Solving for $k$. $\displaystyle \frac{2-k}{3-0}=\frac{-1}{2}$ $\Rightarrow$ $\displaystyle \frac{2-k}{3}=\frac{-1}{2}$ $\Rightarrow$ $4-2k=-3 \Rightarrow 7=2k \Rightarrow \displaystyle k=\frac{7}{2}$

Correct Answer is A. The equation $y=kx+4$ is already in slope-intercept form, so we know the slope of the line is $k$. We also know that the line contains the point $(c,d)$ which means we can substitute those variables for $(x,y)$ in the equation. This gives us $d=kc+4$. Solving for this equation for the slope, $k$, gives us $k=\frac{d-4}{c}$

Transform each equation in slope intercept form: $$ y=\frac{5}{2}x-\frac{3}{2}$$ $$ y=-\frac{a}{b}x+\frac{6}{b}$$ Since this system of equations has infinitely many solutions, this means that the two lines must have the same slope and same $y$-intercept, therefore $$\frac{5}{2}=-\frac{a}{b} \ \text { and } -\frac{3}{2}=\frac{6}{b}$$ Solving for $b$ we get $-3b=12$ or $b=-4$. Solving for $a$ we get $5b=-2a$ or $-20=-2a$ so $a=10$ and $a+b=6$

Correct Answer is C. Transform each equation in slope intercept form $$y=\frac{2}{5}x-\frac{a}{5}$$ $$y=-\frac{b}{10}x-\frac{8}{10}$$ Since the system of equation has no solutions we have that the two equation must have the same slope and the same $y$ intercept therefore we get that $\displaystyle -\frac{a}{5}=-\frac{8}{10}$ or $10a=40$ or $a=4$