We use letters to represent the unknown coins.

P for pennies that worth 1 cents

N for nickels that worth 5 cents

D for dimes that worth 10 cents

Q for quarters that worth 25 cents.

<span>"He has twice as many nickels (N) as dimes (D)" So D=2N

</span><span>"and four times as many pennies (P) as quarters (Q)." So Q=4P

</span>

Number of coins equals P+N+D+Q=P+N+2N+4P (Dimes and quarters are written in terms of nickels and pennies, respectively)

So, number of coins is equal to 5P+3N=201. Thats is the first equation (I)

To write the second equation, use cents of coins. 12.10 $ in coins can be shown as

5P. 1 cent + 3N. 5 cent=1210 cents or simply 5P + 15N=1210 (Second equation)

We have two equations and two unknowns so it is soluble.

number of coins: 5P+3N=201 (I)

cents of coins: 5P+15N=1210 (II)

Use the substitution method. (II) - (I)=12N=1009

N=1009/12=84 ( Actually it is 84.08)

D=2N=168

P= -10

Q=-40

Number of pennies and quarters are <span>meaningless. They can't be negative. So they should be something wrong in the question.</span>

**Answer:**

<h3>If you had a line of x = 7, (or any time you have an equation where x equals a number) then you would have a vertical line. In every vertical line, the slope is undefined. In equations of lines that are in the format of y = mx + b, the slope is represented by the "m".</h3>

**Answer:**

**Step-by-step explanation:**

Using annuity, each sisters saving can be calculated.

Annuity formula:

Fv = PMT (( 1 + i)^n - 1) / i

where Fv is the future value (amount), PMT is the periodic payment ( $2000),

i is the rate per period ( 7%) and n is the number of payments.

Using the above formula to calculate each sister savings after their respective years of savings

Jane ( between 25 - 35, with n = 10 years)

Fv = 2000 (( 1 + 0.07)^10 - 1 ) / 0.07 = $ 27634.3

Joan ( between 35 - 65, with n = 30 years)

Fv = 2000((1 + 0.07)^30 - 1) / 0.07 = $ 188914

Joan actually have invested more since over 30 years she has invested $60000 while Jane on the other hand invested for 10 years which equals $20000 and Joan has more money after retirement. Going by the result it will make sense for Jane to emulate Joan or increase her number of years of saving in other to improve her retirement saving significantly close to Joan or even more.

**Answer and Step-By-Step-Explanation:**

Expanded form is stating all place values of a number and separating it.

So we have 3.611

3 is the ones place

3

There is a decimal point following before the number 6

Which is in the tenths place

3 + 0.6

After that, there is a 1

In the hundredths place

3 + 0.6 + 0.01

Lastly, there is another 1

In the thousandths place

<u>**3 + 0.6 + 0.01 + 0.01**</u>

<u></u>

An expressions obtained from the square of binomial expression is a perfect square trinomial . For example: x square+2x+1