Let’s start this off by assigning some variables. Let’s have q stand for the amount of quarters while n stands for the amount of nickels.
To start this problem, you need to utilize a system of equations. First, we know that there’s a certain number of quarters and a certain number of nickels and together there’s 63 quarters and nickels.
q + n = 63
We also know that there’s $13.15 in the jar. Since we know the value of the quarters and nickels, we can turn this into another equation.
.25q + .05n = 13.15
And there’s are two equations. Next, we have to solve for one of the variables. Either one works, but I’m going to be using q. I’m going to take the first equation since it’s easier to work with and isolate the q on one side by subtracting n from both sides.
q = 63 - n
Using that new definition for the q variable, we can substitute that into the second equation by replacing q there.
0.25(63 - n) + .05n = 13.15
Now we just need to simplify and solve for n. First we multiply both of the terms inside of the parenthesis by the .25 coefficient
15.75 - .25n + .05n = 13.15
Combine like terms
15.75 - .2n = 13.15
Add .2n to both sides to make the coefficient positive
15.75 = 13.15 + .2n
Subtract 13.15 from both sides to isolate the variable
2.60 = .2n
And finally divide both sides by .2 to solve for n.
13 = n
Now we have the amount of nickels that are in the jar. To solve for the amount of quarters is simple: Put the n value into the first equation and solve for q.
13 + q = 63
And then subtract 13 from both sides for the only step in solving for q.
q = 50.
Leaving us with a solution of 50 quarters and 13 nickels. Both of these variables can be inserted into the second equation to double check the work, but it comes out as even on both sides proving that this is the correct answer.
Hope this helped!
Answer: 30 feet per second
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x = diameter, y = speed of water
y varies inversely with respect to x, so, y = k/x for some constant k
If x = 0.6 and y = 5 pair up, then y = k/x turns into 5 = k/0.6 which solves to k = 3 when you multiply both sides by 0.6
So the equation y = k/x turns into y = 3/x
Now plug in the diameter x = 0.1 to find the speed to be...
y = 3/x
y = 3/0.1
y = 30 feet per second
Answer:
D
Step-by-step explanation:
I don’t believe there is any work to show for this question
Answer:
Factoring: y2-900
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 900 is the square of 30
Check : y2 is the square of y1
Factorization is : (y + 30) • (y - 30)
