Question 21
Let's complete the square
y = 3x^2 + 6x + 5
y-5 = 3x^2 + 6x
y - 5 = 3(x^2 + 2x)
y - 5 = 3(x^2 + 2x + 1 - 1)
y - 5 = 3(x^2+2x+1) - 3
y - 5 = 3(x+1)^2 - 3
y = 3(x+1)^2 - 3 + 5
y = 3(x+1)^2 + 2
Answer: Choice D
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Question 22
Through trial and error you should find that choice D is the answer
Basically you plug in each of the given answer choices and see which results in a true statement.
For instance, with choice A we have
y < -4(x+1)^2 - 3
-7 < -4(0+1)^2 - 3
-7 < -7
which is false, so we eliminate choice A
Choice D is the answer because
y < -4(x+1)^2 - 3
-9 < -4(-2+1)^2 - 3
-9 < -7
which is true since -9 is to the left of -7 on the number line.
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Question 25
Answer: Choice B
Explanation:
The quantity (x-4)^2 is always positive regardless of what you pick for x. This is because we are squaring the (x-4). Squaring a negative leads to a positive. Eg: (-4)^2 = 16
Adding on a positive to (x-4)^2 makes the result even more positive. Therefore (x-4)^2 + 1 > 0 is true for any real number x.
Visually this means all solutions of y > (x-4)^2 + 1 reside in quadrants 1 and 2, which are above the x axis.
1. x^15
2. m^40
3. v^7/2
4. k^4
5. 1/x^14
6. 1/r^3/2
7. b^25
8. h^2
9. m^3n^1/7
10. x^12
11. 1/g^37
12. 1/100m^6
13. j^6/216
14. 1/125f^3
15. 3z^1/2
16. 1/100m^6
17. j^6/216
18.1/81d^20
19. 1
20. g^1/2 r^3
21. 16a^11
22. m^16n^21
23. 1
24. 1/y^10x^6
25. 343s^10/t^17/2
26.n^17/2 /m^10/2
27. 729/b^24c^9
28. 20y^2/x^33
The correct answer would be Choice B: 4 square units.
When the scale factor is 1/5, that means the lengths of the sides are 1/5 of the original size. So instead of having a base of 20 and height of 10, the new triangle has a base of 4 and a height of 2.
The area of the triangle is: (4 x 2) / 2 = 4
3,141......
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