Awesomeguy

The minutes hand would be on the 6, and the hours hand would be halfway between 2 and 3, because 30 is half of 60.

A circle is 360 degrees, so each gap between the numbers is 30 degrees each.

$30 \cdot 3.5 = 105$, so the answer is 105 degrees

Putting the equations into slope-intercept form,

\(y = -\frac{Ax}{B} + \frac{3}{B}\)

\(y = -\frac{x}{3} - \frac{5}{3}\)

Both lines are parallel, so \(-\frac{x}{3} = -\frac{Ax}{B}\). Simplify to find that \(\frac{A}{B} = \frac{1}{3}\), meaning that the slope is \(-\frac{1}{3}\).

\(y = -\frac{x}{3} + \frac{3}{B}\)

Plug in (-7, 2).

\(2 = -\frac{-7}{3} + \frac{3}{B}\)

\(6B = 7B + 9\)

\(B = -9\)

Because A and B are in ratio \(\frac{A}{B} = \frac{1}{3}\), B = -9 and A = -3. So B - A = -9 - (-3) = -6

Rewrite it with simplified radicals,

\(5\sqrt{2} + 3\sqrt{2}\)

They both have a radical of 2, so we can combine them to get \(8\sqrt{2}\)

To find the bases, we can plug in our known values with x being the smaller base,

\(\frac{2x+9}{2}\cdot 8 = 60\)

\(\frac{2x+9}{2}=7.5\)

\(2x+9 = 15\)

\(x = 3\)

The smaller base is 3, and the larger is 12. The median of a trapezoid is just the average of the bases. So (3+12)/2 = 7.5 which is our answer.

oh shoot lol

We can find a pattern in the exponents. Because we are only looking for units, let's find a pattern in 3s.

3^1, 3^2, 3^3, 3^4, 3^5

3, 9, 7, 1, 3

So every 4th multiple will have a units digit of 1. 120 is divisible by 4, meaning 123^120 has a units digit of 1, so 123^123 will have a units digit of 7.

Think of the perfect squares around 300. 17^2 = 289, 18^2 = 324. \(\sqrt{324} = 18\) as we know, so 18 is the least integer greater than $\sqrt{300}$

This means y = 100

\(-6t^2+51 = 100\)

\(-6t^2+51 =100 = 0\)

Apply quadratic formula to get the positive solution of \(\frac{17}{4}+\frac{\sqrt{201}}{12}\)

Plugging in the values,

\(\sqrt{7} \cdot \sqrt{13} \cdot \sqrt{91} \cdot \sqrt{97}\)

\(\sqrt{91} \cdot \sqrt{91} \cdot \sqrt{97}\)

So we get \(91\sqrt{97}\) as the answer

Let's put this into equations,

\(m + 4t = 13\)

\(m + 7t = 19\)

Subtracting the equations we get,

\(3t = 6\)

\(t = 2\)

Now we know the cost of a towel, we can plug it back into one of the equations.

\(m + 8 = 13\)

\(m = 5\)

So a mug costs 5 dollars.