xCorrosive

The slope of two points is $\frac{y_1-y_2}{x_1-x_2}$. In order for the slope to be $\frac{1}{7}$, this equation has to equal $\frac{1}{7}$. 

Plugging in values gives $\frac{4-y}{-3-4} = \frac{1}{7}$. Solving this equation gives $y = \boxed{5}$. 

I'm assuming the botched latex is $10$ for a large Pizza and a fixed cost of $8$ of the delivery charge. 

$18-8 = 10$ (subtracting the delivery charge.

$\frac{10}{10} = \boxed{1}$, so they ordered one large pizza. 

Thanks Guest!

I appreciate the help but I already solved it by myself 

$-3(1+4i) + i(-2-i) = -3 -12i -2i - i^2$.

We know that $i^2 = -1$, therefore, this equation is now $-14i - 3 - (-1) = \boxed{-2 -14i}$, which is our final equation. 

2.

The area of the parallelogram is $8$. Can't explain why because I gotta go. 

1.

From Point $B$ to Point $A$ you increase the x coordinate by $2$ and the y coordinate by $1$. Similarly, from point $C$ to point $D$ we use a similar method of increasing x by $2$ and y by $1$. Thus, the coordinates of point D are $(5+2, 1+1) = \boxed{(7, 2)}$

The expected amount of money you will win from this is 

$\frac{3}{4} \cdot 2 + \frac{1}{4} \cdot -1 = \boxed{\frac{5}{4}}$, which is the expected win amount of the coin flip. 

This is essentially multiplying the probability of each scenario (heads and tails), with the amount of money you would win theoretically if you flipped that scenario. 

Even if you will never win exactly $\frac{5}{4}$ dollars in a coinflip, it's essentially an average of how much you would profit on average for each coin flip. 

The special properties a cyclic quadrilateral has is that 

1. All 4 vertices lie on the edge of some circle. 

2. Opposite angles add up to $180°$ 

Thus, applying #2 here gives us $2x-50 + 3x+20 = 180 \rightarrow \boxed{x = 42}$, which is our answer. 

I also have a method to upload a picture using imgur. Here are the steps. 

1. Go to Imgur.com

2. Click the New Post button in the upper left-hand corner. 

3. Create a new post by dropping the image in or opening it from your computer. 

4. Drag the image into a new tab (like the image below). 

5. Copy the I.Imgur link into the insert image section on web2.0calc and adjust the height accordingly. 

Cross multiply (multiply the numerator and denominator of opposite sides and vice versa.)

This gives us $2x(x+4) = -6(x+2) \rightarrow 2x^2+8x = -6x-12 \rightarrow 2x^2+14x+12 = 0 \rightarrow x^2+7x+6 = 0$. 

Now we have to look for two numbers that add to $7$ and multiply to $6$. These numbers are clearly $1$ and $6$, so we can rewrite our equation as $(x+1)(x+6) = 0$. Thus, our answers are $\boxed{x = -1,-6}$.