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.
The answer is 3x- I just took the text
Answer:
The student added the discount instead of subtracting the discount.
They also did not calculate the tax correctly.
Step-by-step explanation:
Original price is 499
Discount = original price * percent off
Discount = 499 * .18
=89.82
The sale price = original price minus the discount
sale price = 499-89.82
sale price = 409.18
Sales tax = sale price * tax rate
= 409.18 * 8.875%
=409.18*.08875
=36.314725
Rounding to the nearest cent
36.31
Final cost = sale price + sales tax
=409.18+36.31
445.49
The student added the discount instead of subtracting the discount.
They also did not calculate the tax correctly.
Answer:
the answer is c because it can be either greatly increased or decreased
Answer:
x=0.875
Step-by-step explanation:
3x-6=2-5x
Add 6 on both sides (6+2)
2x=8-5x
Add 5x on both sides
7x=8
Divide 7 from both sides
x=0.875
