Answer:
<h2>2. D. 64</h2><h2>5. B. 1, -3/2</h2><h2>6. C. 0, 2</h2>
Step-by-step explanation:
![2.\\(a-b)^2=a^2-2ab+b^2\\\\x^2-16x=-8\\\\x^2-2(x)(8)=-8\\\\\text{We have}\ 2ab=2(x)(8).\ \text{Therefore}\ b=8.\\\\x^2-2(x)(8)=-8\qquad\text{add}\ 8^2=64\ \text{to both sides}\\\\x^2-2(x)(8)+8^2=-8+64\\\\(x-8)^2=56](https://tex.z-dn.net/?f=2.%5C%5C%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2%5C%5C%5C%5Cx%5E2-16x%3D-8%5C%5C%5C%5Cx%5E2-2%28x%29%288%29%3D-8%5C%5C%5C%5C%5Ctext%7BWe%20have%7D%5C%202ab%3D2%28x%29%288%29.%5C%20%5Ctext%7BTherefore%7D%5C%20b%3D8.%5C%5C%5C%5Cx%5E2-2%28x%29%288%29%3D-8%5Cqquad%5Ctext%7Badd%7D%5C%208%5E2%3D64%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5C%5C%5Cx%5E2-2%28x%29%288%29%2B8%5E2%3D-8%2B64%5C%5C%5C%5C%28x-8%29%5E2%3D56)
![5.\\2x^2+x-1=2\qquad\text{subtract 2 from both sides}\\\\2x^2+x-3=0\\\\2x^2+3x-2x-3=0\\\\x(2x+3)-1(2x+3)=0\\\\(2x+3)(x-1)=0\iff 2x+3=0\ \vee\ x-1=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-\dfrac{3}{2}}\\\\x-1=0\qquad\text{add 1 to both sides}\\\boxed{x=1}](https://tex.z-dn.net/?f=5.%5C%5C2x%5E2%2Bx-1%3D2%5Cqquad%5Ctext%7Bsubtract%202%20from%20both%20sides%7D%5C%5C%5C%5C2x%5E2%2Bx-3%3D0%5C%5C%5C%5C2x%5E2%2B3x-2x-3%3D0%5C%5C%5C%5Cx%282x%2B3%29-1%282x%2B3%29%3D0%5C%5C%5C%5C%282x%2B3%29%28x-1%29%3D0%5Ciff%202x%2B3%3D0%5C%20%5Cvee%5C%20x-1%3D0%5C%5C%5C%5C2x%2B3%3D0%5Cqquad%5Ctext%7Bsubtract%203%20from%20both%20sides%7D%5C%5C2x%3D-3%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5Cboxed%7Bx%3D-%5Cdfrac%7B3%7D%7B2%7D%7D%5C%5C%5C%5Cx-1%3D0%5Cqquad%5Ctext%7Badd%201%20to%20both%20sides%7D%5C%5C%5Cboxed%7Bx%3D1%7D)
![6.\\2x^2-4x=0\qquad\text{divide both sides by 2}\\\\x^2-2x=0\\\\x(x-2)=0\iff x=0\ \vee\ x-2=0\\\\\boxed{x=0}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}](https://tex.z-dn.net/?f=6.%5C%5C2x%5E2-4x%3D0%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5Cx%5E2-2x%3D0%5C%5C%5C%5Cx%28x-2%29%3D0%5Ciff%20x%3D0%5C%20%5Cvee%5C%20x-2%3D0%5C%5C%5C%5C%5Cboxed%7Bx%3D0%7D%5C%5C%5C%5Cx-2%3D0%5Cqquad%5Ctext%7Badd%202%20to%20both%20sides%7D%5C%5C%5Cboxed%7Bx%3D2%7D)
<h3>
Answer: B.) it is a one-to-one function</h3>
Explanation:
It's a function because it passes the vertical line test. It's also one-to-one because it passes the horizontal line test.
The vertical line test is where we try to draw a single line through more than one point on the blue curve. Such a task isn't possible in this case, and we consider the curve passing the vertical line test. The horizontal line test is nearly identical, but we're dealing with horizontal lines of course.
Answer:
8 parties
Step-by-step explanation:
First, find how much of her paycheck was from working 30 hours:
7.50(30)
= 225
Then, subtract this from 265, to find how much money was from bonuses:
265 - 225
= 40
To find how many parties she scheduled, divide 40 by 5, since each party she schedules gives her a $5 bonus:
40/5
= 8
So, she scheduled 8 parties
Answer: 30%
Step-by-step explanation:
Let A be the probability of a student opting for mathematics - it consists of either boy opting for mathematics or girl opting for mathematics. As there is "or" we need to sum these probabilities.
![P(A) = P(B)* P(M|G) + P(G)*P(M|G)](https://tex.z-dn.net/?f=P%28A%29%20%3D%20P%28B%29%2A%20P%28M%7CG%29%20%2B%20P%28G%29%2AP%28M%7CG%29)
![P(A) = \frac{1}{2} * \frac{20}{100} + \frac{1}{2} * \frac{40}{100}](https://tex.z-dn.net/?f=P%28A%29%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20%5Cfrac%7B20%7D%7B100%7D%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20%5Cfrac%7B40%7D%7B100%7D)
![P(A) = 3/10 = 0.3](https://tex.z-dn.net/?f=P%28A%29%20%3D%203%2F10%20%3D%200.3)
=> 30%
Answer:
B. It represents 0.0000075540794
Step-by-step explanation:
If the contents of a cell in a spreadsheet are as shown below. 7.5540794E-6, the content of the cell will represent 0.0000075540794.
The standard form 7.5540794E-6 was converted to decimal number by shifting the decimal point to the back 6times since the power of the multiple of 10 is a negative number (-6) hence the reason for shifting the decimal point to the back 6times to have 0.0000075540794.