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:
16+2=18
18-3=15
2*3=6
Step-by-step explanation:
You have to divide 46 by 5. The anwser would be $9.20 for 1 toy .
When you write a check for an amount you don't have in the bank.
Answer:
68°
Step-by-step explanation:
Here,
- Two supplementary angles are (2x – 8)° and (3x - 2)°.
As we know that the sum of two supplementary angles are 180°. So,
→ (2x – 8)° + (3x – 2)° = 180°
→ 2x° – 8° + 3x° – 2° = 180°
→ 5x° – 10° = 180°
→ 5x° = 180° + 10°
→ 5x° = 190°
→ x = 190° ÷ 5°
→ <u>x</u><u> </u><u>=</u><u> </u><u>3</u><u>8</u><u>°</u>
Supplementary angles are,
→ 2(38°) – 8
→ (76 – 8)°
→ 68°
→ 3(38°) – 2
→ (114 – 2)°
→ 112°
Therefore, the measure of the smaller angle is 68°.
