The three angles create a triangle. The sum of the angles of a triangle is always 180°.
Solving for x,
45° + 35° + x = 180°
x = 100°
Find the average of all the tests on the first and second test. You find the average by adding up all the test scores and dividing it by the number of test scores you added. Then you can see if she did better than the overal average on each of the tests
Take $360.00 and multiply by .944 and that equals $339.84
Answer: <em>0</em>
Step-by-step explanation:
<em>Simply the answer is </em><em>0</em><em> because anything multiplied by </em><em>0</em><em> will result in </em><em>0</em>
<em>4x(0) =</em><em> 0 </em>
ANSWER: 32 five-dollar bills
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EXPLANATION:
Let x be number of $5 bills
Let y be number of $10 bills
Since we have total of 38 bills, we must have the sum of x and y be 38
x + y = 38 (I)
Since the total amount deposited is $220, we must have the sum of 5x and 10y be 220 (x and y are just the "number of" their respective bills, so we multiply them by their value to get the total value):
5x + 10y = 220 (II)
System of equations:
![\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ 5x + 10y &= 220 && \text{(II)} \end{aligned} \right.](https://tex.z-dn.net/?f=%20%5Cleft%5C%7B%20%5Cbegin%7Baligned%7D%20x%20%2B%20y%20%26%3D%2038%20%26%26%20%5Ctext%7B%28I%29%7D%20%5C%5C%205x%20%2B%2010y%20%26%3D%20220%20%26%26%20%5Ctext%7B%28II%29%7D%20%5Cend%7Baligned%7D%20%5Cright.%20)
Divide both sides of equation (II) by 5 so our numbers become smaller
![\left\{ \begin{aligned} x + y &= 38 && \text{(I)} \\ x + 2y &= 44 && \text{(II)} \end{aligned} \right.](https://tex.z-dn.net/?f=%20%5Cleft%5C%7B%20%5Cbegin%7Baligned%7D%20x%20%2B%20y%20%26%3D%2038%20%26%26%20%5Ctext%7B%28I%29%7D%20%5C%5C%20x%20%2B%202y%20%26%3D%2044%20%26%26%20%5Ctext%7B%28II%29%7D%20%5Cend%7Baligned%7D%20%5Cright.%20)
Rearrange (I) to solve for y so that we can substitute into (II)
![\begin{aligned} x + y &= 38 && \text{(I)} \\ y &= 38 - x \end{aligned}](https://tex.z-dn.net/?f=%20%5Cbegin%7Baligned%7D%20x%20%2B%20y%20%26%3D%2038%20%26%26%20%5Ctext%7B%28I%29%7D%20%5C%5C%20y%20%26%3D%2038%20-%20x%20%5Cend%7Baligned%7D%20)
Substituting this into equation (II) for the y:
![\begin{aligned} x + 2y &= 44 && \text{(II)} \\ x + 2(38 - x) &= 44\\ x + 76 - 2x &= 44 \\ -x &= -32 \\ x &= 32 \end{aligned}](https://tex.z-dn.net/?f=%20%5Cbegin%7Baligned%7D%20x%20%2B%202y%20%26%3D%2044%20%26%26%20%5Ctext%7B%28II%29%7D%20%5C%5C%20x%20%2B%202%2838%20-%20x%29%20%26%3D%2044%5C%5C%20x%20%2B%2076%20-%202x%20%26%3D%2044%20%5C%5C%20-x%20%26%3D%20-32%20%5C%5C%20x%20%26%3D%2032%20%5Cend%7Baligned%7D%20)
We have 32 five-dollar bills
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If we want to finish off the question, use y = 38 - x to figure out number of $10 bills
![y = 38 - 32 = 6](https://tex.z-dn.net/?f=y%20%3D%2038%20-%2032%20%3D%206)
32 five-dollar bills and 6 ten-dollar bills