Awoman has 21 total coins in her pocket, all of which are either dimes or quarters. if the total value of her change is $3.90, how many dimes and how many quarters does she have? write the number of dimes, then the number of quarters separated by a comma.

Step-by-step explanation:

Givens

With this information we can construct a system of equations, where is dimes and is quarters.

, because there are 21 coins between dimes and quarters.

Now, we know that one dime values 10 cents, and one quarter values 25 cents.

, because the woman has $3.90 in total.

Then, we isolate in the first expression

And we substitute it in the second expression

Then, we use this value to find the other one

Therefore, the woman has 12 quarters and 9 dimes.

answer: standard form is ax^2 + bx + c = 0

step-by-step explanation:

standard form is ax^2 + bx + c = 0

(2x + 1)(x - 2) = 0

distribute to get into standard form

2x^2 - 4x + x - 2 = 0

2x^2 - 3x - 2 = 0

a = 2, b= -3, c = -2

a is your answer

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.