Answer:
Step-by-step explanation:
Area of square = area of triangle
![side*side = \dfrac{1}{2}b*h\\\\\\x*x=\dfrac{1}{2}*(x+1)(x+2)\\x^{2}=\dfrac{1}{2}[x*x +x*2+1*x+1*2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+2x+x+2]\\\\\\x^{2}=\dfrac{1}{2}[x^{2}+3x+2]\\\\\\Multiply \ both \ sides \ by \ 2\\\\2x^{2}=x^{2}+3x+2\\\\2x^{2}-x^{2}-3x-2 = 0](https://tex.z-dn.net/?f=side%2Aside%20%3D%20%5Cdfrac%7B1%7D%7B2%7Db%2Ah%5C%5C%5C%5C%5C%5Cx%2Ax%3D%5Cdfrac%7B1%7D%7B2%7D%2A%28x%2B1%29%28x%2B2%29%5C%5Cx%5E%7B2%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Bx%2Ax%20%2Bx%2A2%2B1%2Ax%2B1%2A2%5D%5C%5C%5C%5C%5C%5Cx%5E%7B2%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Bx%5E%7B2%7D%2B2x%2Bx%2B2%5D%5C%5C%5C%5C%5C%5Cx%5E%7B2%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Bx%5E%7B2%7D%2B3x%2B2%5D%5C%5C%5C%5C%5C%5CMultiply%20%5C%20both%20%5C%20sides%20%5C%20by%20%5C%202%5C%5C%5C%5C2x%5E%7B2%7D%3Dx%5E%7B2%7D%2B3x%2B2%5C%5C%5C%5C2x%5E%7B2%7D-x%5E%7B2%7D-3x-2%20%3D%200)
x² - 3x - 2 = 0
<h3>
Answer: Choice B</h3>
The set notation includes all values from -5 to 0, but the domain only includes the integer values
eg: something like -1.2 is in the second set, but it is not in the set {-5,-4,-3,-2,-1}
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Further explanation:
Let's go through the answer choices one by one
- A. This is false because 0 does not come before -5, but instead -5 is listed first. The order -5,-4,-3,-2,-1,0 is correct meaning that
is the correct order as well. - B. This is true. A value like x = -1.2 is in the set
since -1.2 is between -5 and 0; but -1.2 is not in the set {-5, -4, -3, -2, -1, 0}. So the distinction is that we're either considering integers only or all real numbers in this interval. To ensure that we only look at integers, the student would have to write
. The portion
means "x is in the set of integers". The Z refers to the German word Zahlen, which translates to "numbers". - C. This is false. The student used the correct inequality signs to indicate x is -5 or larger and also 0 or smaller; basically x is between -5 and 0 inclusive of both endpoints. The "or equal to" portions indicate we are keeping the endpoints and not excluding them.
- D. This is false. Writing
would not make any sense. This is because that compound inequality breaks down into
. Try to think of a number that is both smaller than -5 AND also larger than 0. It can't be done. No such number exists.
This can be mathematically expressed to
250 + X = 1075
where X represents the parts you produce before the shift ends
Transpose 250 to the other side by subtracting each side by 250
Thus, it goes like this
X = 1075 - 250
X = 825
You produced 825 parts in the middle of the shift.
4 times 4 which is 8 so 8 times 4 which is 32 so divide that by 138 but divide the 138 first and you will get 17.25?
Answer:
TRIANGLES
Step-by-step explanation: