Answer:
D. 12
Step-by-step explanation:
Based on the Angle Bisector theorem, the opposite sides of ∆ABC are divided into proportional segments alongside the two other sides of the triangle, as BD bisects the <ABC. This implies that:
AB/AD = CB/CD
Substitute
AB/8 = 6/4
Cross multiply
AB*4 = 6*8
AB*4 = 48
AB = 48/4
AB = 12
Answer:
No, the sequence neither has a common difference or a common ratio. The sequence is the list of perfect squares.
Step-by-step explanation:
You are right that is neither.
For it to be arithmetic you must have a common difference. That is, a chosen term minus it's previous term has to be the same number no matter the pair.
Let's look at that:
4-1=3
9-4=4
16-9=7
25-16=9
36-25=11
These are definitely not the same difference so there is no common difference which means the sequence is not arithmetic. We could have stopped at the first two since those differences weren't even the same.
For it to be geometric you must have a common ratio. That is, a chosen term divided by it's previous term must be the same number no matter the pair.
Let's look at that:
4/1=4
9/4=2.25
16/9=1.777777777777777(repeating)
25/16=1.5625
36/25=1.44
These are definitely not the same ratio so there is no common ratio which means the sequence is not geometric. We didn't have to find all of the ratios. We could have stopped at first two and said yep not geometric because the first two weren't even the same.
The list you have here is actually the sequence of perfect squares.
The ratio of the robot's height to its arm length is 24 to 12 or 2 to 1. So if its height is 6 meters, then its arm length is 3 meters.
In order to have infinitely many solutions with linear equations/functions, the two equations have to be the same;
In accordance, we can say:
(2p + 7q)x = 4x [1]
(p + 8q)y = 5y [2]
2q - p + 1 = 2 [3]
All we have to do is choose two equations and solve them simultaneously (The simplest ones for what I'm doing and hence the ones I'm going to use are [3] and [2]):
Rearrange in terms of p:
p + 8q = 5 [2]
p = 5 - 8q [2]
p + 2 = 2q + 1 [3]
p = 2q - 1 [3]
Now equate rearranged [2] and [3] and solve for q:
5 - 8q = 2q - 1
10q = 6
q = 6/10 = 3/5 = 0.6
Now, substitute q-value into rearranges equations [2] or [3] to get p:
p = 2(3/5) - 1
p = 6/5 - 1
p = 1/5 = 0.2
Answer:
One possible equation is 2m+16 = 40
There are other possible equations to set up as well.
That equation solves to m = 12 which means both plans cost the same when you go 12 MB over the limit (using 27 MB total).
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Explanation:
The unlimited plan costs $40 a month no matter how much data you use.
The second plan costs $16 a month, and there are no extra fees as long as you don't go over the limit of 15 MB. If you do exceed this limit, then you're charged an extra $2 per MB. That means an extra 2m dollars is tacked onto the 16 mentioned earlier, where m is the amount of MB you've gone over the limit. Overall, the expression 2m+16 represents the cost of the second plan. If you don't go over the limit, then you'll use m = 0 for the second plan.
Set that expression equal to 40 to set up the equation. Solving the equation leads to...
2m+16 = 40
2m = 40-16
2m = 24
m = 24/2
m = 12
If you exceed the limit by 12 MB, then both plans cost the same at $40 per month.
Note: Going 12 MB over the limit means you've used 15+12 = 27 MB.