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:
y = -2/7x - 22/7
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Slope Formula: 
Slope-Intercept Form: y = mx + b
Step-by-step explanation:
<u>Step 1: Define</u>
Point (-4, -2)
Point (3, -4)
<u>Step 2: Find slope </u><em><u>m</u></em>
- Substitute:
- Add:
<u>Step 3: Find y-intercept </u><em><u>b</u></em>
- Define: y = -2/7x + b
- Substitute: -4 = -2/7(3) + b
- Multiply: -4 = -6/7 + b
- Isolate <em>b</em>: -22/7 = b
- Rewrite: b = -22/7
<u>Step 4: Write linear equation</u>
y = -2/7x - 22/7
Answer:
B. 4 and 6/10
Step-by-step explanation:
in order to find this answer i've always had a trick where i first off find an even number to divide these with and in this case that would be 4 and then the leftovers would be 6/10 and in this case your answer would be right there 4 and 6/10 but if needed to be simplified it would be 4 and 3/5
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Answer:
The trapezoid has a height of 3 inches, a shorter base measuring 2.75 inches, and a longer base measuring 4.25 inches. The total area of the entire figure is 33 square inches.
Step-by-step explanation:
I took the iready diagnostic :)
Answer:
z < 8
Step-by-step explanation:
Add 3 to both sides
8 > z OR z < 8
