A twelve inch pizza is cut into eight congruent pieces. What is the length of outer crust on each piece of pizza?

Solution:

A twelve inch pizza means:

 

is cut into eight congruent pieces means: 

 

 

outer crust is 4.71inches

After an 8% discount from the list price,the sale price of a key chain was $18.40. What was the list price of the key chain

Solution:

L-list price
S-sale price
D-discount 
D-8% of L so 
 

The sale price is how much it costs after the discount:

 

Now we substitute in the known values and solve for L:

 

so L=$20.00

A triangle is such that its medium side is three times as long as its shortest side, and its longest side is five inches longer than four times its shortest side. The perimeter of the triangle is 69inches. Find the length of the medium side of the triangle

Solution:

First we decide on names for our sides: 

s-short side
m-medium
l-long 

Next let's look at each statement carefully... 

medium side is three times as long as its shortest side means: 

 

longest side is five inches longer than four times its shortest side means: 

 

perimeter of the triangle is 69 inches means: 

 

Now we can substitute values: 

 

becomes 

 

Adding s-terms... 
 
 

so s=8 

Now 

Given f(x)= x^2 + 7 and g(x)= x^2 - 7, find f(g(x))

Solution:

f(g(x)) is a composition - we take a function as an input to another function. 

 

and 

 

g is the input of f so we replace g(x) with the expression - they are equal 

 

 

 

 

show me how to get the opposite of the polynomial 28x^2 - 7x + 5

Solution:

The opposite of a polynomial P usually refers to the polynomial -P. That is the polynomial that "adds" to P to make 0. 

 

leads us to 

 

so we reverse the sign or operation for each term: 

solve: 6m(m-1)=3(1-m)

Solution:

We'll solve by using grouping -it's actually more efficient... 
 

 

 

 

 

 

Next we use the zero product property 
 

or 
 

so... m=1 or m=-1/2

Solve by the square root property 25(y+5)^2=81

 

 

 

 

 

or 


 
Solving the two equations we get 

y=-16/5 or y=-34/5

A manufacturer sells watches for $23. The manufacturer has fixed costs of $5004 per month and variable costs of $11 per watch. How many watches must be sold to break even?

Break even occurs when revenue and cost are equal. In our case 

 

So we need to solve the equation: 

 

or... 

 

so x=417 watches

Find the remaining angles and sides of each triangle if it (they) exists. If no triangle exists, say “no triangle” A=10(degrees), B=40 (degrees), side c=2

A=10(degrees), B=40 (degrees), side c=2




Solution:

A=10deg, B=40deg, c=2 

First let's find the missing angle: 

 

We can solve this triangle by using the Law of Sines. 



 

which is approximately 0.453 
Similarly...

 

which is approximately 1.678