Option B
There are 30 quarters
<em><u>Solution:</u></em>
Let "x" be the number of quarters
Let "y" be the number of dimes
We know that,
Value of 1 quarter = 0.25 dollars
Value of 1 dime = 0.10 dollar
<em><u>The counter said there were 180 total coins
</u></em>
Therefore,
number of quarters + number of dimes = 180
x + y = 180
y = 180 - x ------- eqn 1
<em><u>The coins were worth $ 22.50. Therefore, frame a equation as:</u></em>
number of quarters x Value of 1 quarter + number of dimes x Value of 1 dime = 22.50
0.25x + 0.1y = 22.50 -------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Substitute eqn 1 in eqn 2</u></em>
0.25x + 0.1(180 - x) = 22.50
0.25x + 18 - 0.1x = 22.50
0.25x - 0.1x = 22.50 - 18
0.15x = 4.5
x = 30
Thus there are 30 quarters
Answer:
He's correct.
Step-by-step explanation:
As long as there is no change in sign of the variables.
“Extraneous solutions are not solutions at all. They arise from outside the problem, from the method of solution. They are extraneous because they are not solutions of the original problem. ... To tell if a "solution" is extraneous you need to go back to the original problem and check to see if it is actually a solution.”
Basically, they are an answer you get when you solve a problem, but they don’t actually make the equation true so you disregard it.
Answer: 167
Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.
Since we want to determine the 76th term, we are going
to substitute 76 in for <em>n</em> in our explicit formula.
Then, 
will be our first term in our sequence which is 17.
Lastly, <em>d</em> is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.
So we have 
.
Now we have all the information we need. Just simplify from here.
Make sure to apply order of operations because this is where many
students make mistakes. Inside the parentheses first!
(76 - 1) is going to be 75.
So we have 
.
Then, we have to make sure we multiply before we add.
So (75)(2) is going to give us 150.
So we have 
.
Now just add to find that 
.
So the 76th term is 167.
