4. You go to the cafeteria for lunch and have a choice of 4 entrees, 5 sides, 5 drinks, and 4 desserts Assuming you have one of each category, how many different lunches could you make?

4 different lunches

Step-by-step explanation:

If you have one of each, you can't make 5 lunches because you will have 4, 5, 5, and 4

So considering you have an equal amount of each category, you can only make 4 lunches!

Hope I helped! :3

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

answers

\3. yes the presentation (i.e. odd numbers being written as differences of two squares) is possible for all odd natural number however the presentation may not be unique. for example,  57=112−82=292−28257=112−82=292−282.

\4. 2 can't be written as a difference of two squares because 4-1=3 and 1-1=0 and the difference of squares grows to integers larger that 3.

can i get some in proving questions 1 and 2?