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
============================================
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.
============================================
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:
143
Step-by-step explanation:
lets make a fraction:
so
91 oil changes/7days
lets take "x" as the unknown # of oil changes:
so
x/11
91/7=x/11
we can cross multiply:
91*11=7*x
1001=7x
143=x
so 143 oil changes in 11 days
Hope this helps!
Answer:
The pattern is:
Step-by-step explanation:
they are the first letters of each month in the year -
J - January
F- Febuary
M - March
A - April
M - May
Continuing...
J - June
J - July
A - August
S - September
O - October
N - November
D - December
Answer:
A. 6
Step-by-step explanation:
Since, cake is of right triangled shape, so measure of its one angle would be 90° and the sum of the measures of the remaining two angles will also be equal 90°.
Therefore,
5x +10x = 90
15x = 90
x = 90/15
x = 6
Answer:
The radius is: 
Step-by-step explanation:
The equation of a circle in center-radius form is:
Where the center is at the point (h, k) and the radius is "r".
So, given the equation of the circle:
You can identify that:
Then, solving for "r", you get that the radius of this circle is:
