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.
Answer:
12 ≤ a < 18 B is the letter
Step-by-step explanation:
i took the test
Answer: $2227.41
Step-by-step explanation:
A = P(1 + r/n)^nt
If there are 12 grams of protein in all, and 4 servings, in order to get the amount of grams per serving you must divide 12 by 4.
12 divided by 4 = 4.
Therefore, there are 4 grams per serving.
Answer: (x³ - 2x² - 11x + 12)
Step-by-step explanation:
Recall that zeroes can be transformed into factors by subtracting them from x. This gives us the following factors:
(x - 1)(x + 3)(x - 4)
Now, if you multiply the first two factors together, you get the following:
(x² + 2x - 3)
Multiply that by the last factor, (x - 4), and you get this:
(x³ + 2x² - 3x - 4x² - 8x + 12)
This can be simplified:
(x³ - 2x² - 11x + 12)
And there's your final answer. Hope this helped! (x³ - 2x² - 11x + 12)
