1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
anygoal [31]
2 years ago
14

hello i really need help with this problem ive been stuck on it for 20 minutes so far i am willing to give 20 points if someone

can help me or give me the answer thank u!

Mathematics
1 answer:
Rasek [7]2 years ago
5 0

Answer:

-9/20 with the given information i believe this is the answer

You might be interested in
Prove for any positive integer n, n^3 +11n is a multiple of 6
suter [353]

There are probably other ways to approach this, but I'll focus on a proof by induction.

The base case is that n = 1. Plugging this into the expression gets us

n^3+11n = 1^3+11(1) = 1+11 = 12

which is a multiple of 6. So that takes care of the base case.

----------------------------------

Now for the inductive step, which is often a tricky thing to grasp if you're not used to it. I recommend keeping at practice to get better familiar with these types of proofs.

The idea is this: assume that k^3+11k is a multiple of 6 for some integer k > 1

Based on that assumption, we need to prove that (k+1)^3+11(k+1) is also a multiple of 6. Note how I've replaced every k with k+1. This is the next value up after k.

If we can show that the (k+1)th case works, based on the assumption, then we've effectively wrapped up the inductive proof. Think of it like a chain of dominoes. One knocks over the other to take care of every case (aka every positive integer n)

-----------------------------------

Let's do a bit of algebra to say

(k+1)^3+11(k+1)

(k^3+3k^2+3k+1) + 11(k+1)

k^3+3k^2+3k+1+11k+11

(k^3+11k) + (3k^2+3k+12)

(k^3+11k) + 3(k^2+k+4)

At this point, we have the k^3+11k as the first group while we have 3(k^2+k+4) as the second group. We already know that k^3+11k is a multiple of 6, so we don't need to worry about it. We just need to show that 3(k^2+k+4) is also a multiple of 6. This means we need to show k^2+k+4 is a multiple of 2, i.e. it's even.

------------------------------------

If k is even, then k = 2m for some integer m

That means k^2+k+4 = (2m)^2+(2m)+4 = 4m^2+2m+4 = 2(m^2+m+2)

We can see that if k is even, then k^2+k+4 is also even.

If k is odd, then k = 2m+1 and

k^2+k+4 = (2m+1)^2+(2m+1)+4 = 4m^2+4m+1+2m+1+4 = 2(2m^2+3m+3)

That shows k^2+k+4 is even when k is odd.

-------------------------------------

In short, the last section shows that k^2+k+4 is always even for any integer

That then points to 3(k^2+k+4) being a multiple of 6

Which then further points to (k^3+11k) + 3(k^2+k+4) being a multiple of 6

It's a lot of work, but we've shown that (k+1)^3+11(k+1) is a multiple of 6 based on the assumption that k^3+11k is a multiple of 6.

This concludes the inductive step and overall the proof is done by this point.

6 0
3 years ago
Read 2 more answers
Carlos is going for a walk. He walks for
seraphim [82]
I pretty sure the answer is 3.2 hours. I'm not completely sure though....
3 0
3 years ago
Will give brainliest:)<br><br>-2x-¼(12x-8)​
katrin2010 [14]

answer

Answer:

here you go

Step-by-step explanation:

-5x+2

8 0
3 years ago
Which decimal is equivalent to 2.5%​
Vesna [10]

Answer:

0.025

Explanation:

Divide the percentage by 100 to convert it to decmals.

for example 20%=

20

100

=.2

30%=

30

100

=

.3

2.5%=

2.5

100

=

.025

8 0
3 years ago
Read 2 more answers
Please help Linear equations
svlad2 [7]

Answer:

2 and 4

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • Be a detective and solve this case: There are 53 bicycles in a room, and a man is dead on the floor next to them. Why was the ma
    9·1 answer
  • find the y value for the point that splits segment GH in half of point G is located at (-3,5) and point H is located at (0,-2)
    9·2 answers
  • Please help me on number 3
    5·1 answer
  • What is the slope of the line through (1, -1)and (5,-7)<br> Choose 1 answer:
    11·2 answers
  • Please help!!!!!!!!!!!!!!!!!!
    6·1 answer
  • In the question for exponential functions y=a•b^x how does the a term relate to a key feature of the graph
    13·1 answer
  • Vertical, Complementary and Linear Pair Angles help me please
    6·1 answer
  • Which pair of triangles is congruent by asa?​
    10·2 answers
  • The dimensions of four rectangles are given below. Which has an area different from the area of each of the other three?
    11·1 answer
  • 2 lines are not parallel, how many solutions are there
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!