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.
So a pentagon is constructed by five identical triangles, that's why you can find the area of one triangle and multiply it with 5:
A_pentagon=A_triangle*5
To find the area of a triangle you must use tangens.
You can watch this for more on that on youtube.
For the length of an arc or a portion of a circle you can find it using:
arc lenght = 2π*r(A/360), where A=angle.
So if you know radians, then 2π is a whole circle. And to calculate for the specific circle you have to use the radius. That's why you multiply with radius, which is the only difference between any two different circles. you then multiply with the part of the circle that you want to find the lenght for, which is A/360 (because there are 360° in a circle)
I hope that helped.
Answer:
answer = 3
Step-by-step explanation:
same slope and different y-intercept would make the two lines parallel. hope this helps <3
Answer:
108 units
Step-by-step explanation:
(6x4x9)divided by 2
