Jim has only dimes and nickels in his coin bank. He has 37 coins with a total value of $2.65.
2 answers:
Answer:
21
Step-by-step explanation:
Let x represent the number of dimes and y represent the number of nickels. The total number of coins is 37; this gives us the equation
x+y = 37
Each dime is worth ten cents, or 0.10, and each nickel is worth five cents, or 0.05. The total amount of money is given by
0.10x+0.05y = 2.65
This gives us the system
To solve this, we will use substitution. We will isolate x in the first equation:
x+y=37
Subtract y from each side:
x+y-y = 37-y
x = 37-y
Substitute this into the second equation:
0.10(37-y)+0.05y = 2.65
Using the distributive property,
0.10(37)-0.10(y)+0.05y = 2.65
3.70-0.10y+0.05y = 2.65
Combining like terms,
3.70-0.05y = 2.65
Subtract 3.70 from each side,
3.70-0.05y-3.70 = 2.65-3.70
-0.05y = -1.05
Divide both sides by -0.05:
-0.05y/-0.05 = -1.05/-0.05
y = 21
There were 21 nickels.
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Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
Please check the explanation.
Step-by-step explanation:
<u>Calculating the area of the outer rectangle:</u>
Given
- The length outer rectangle = l = 3x - 1
- The width of outer rectangle = w = 5x + 2
Thus,
The area of the outer rectangle:
<u>Calculating the area of the inner rectangle:</u>
Given
- The length inner rectangle = l = x + 7
- The width of inner rectangle = w = x
Thus,
The area of the outer rectangle:
A = wl
= x(x+7)
= x² + 7
<u>Calculating the area of the shaded region:</u>
As
The area of the outer rectangle = 15x² + x - 2
The area of the inner rectangle = x² + 7
- The area of the shaded region can be determined by subtracting the area of the inner rectangle from the area of the outer rectangle.
Thus,
shaded region Area = Outer Rectangle Area - Inner Rectangle Area
= 15x² + x - 2 - (x² + 7)
= 15x² + x - 2 - x² - 7
= 14x² + x - 9
Therefore, the Area of the shaded region is: 14x² + x - 9