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
Kitty [74]
3 years ago
12

42 = -7 ( Z - 3 ) Z =?

Mathematics
1 answer:
ipn [44]3 years ago
6 0

Answer:

-3

Step-by-step explanation:

You might be interested in
Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.
frutty [35]
<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

2^n\leq 2^{n+1}-2^{n-1}-1

where n is a positive integer.

  • Let us take n=1

then we have:

2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2

Hence, the result is true for n=1.

  • Let us assume that the result is true for n=k

i.e.

2^k\leq 2^{k+1}-2^{k-1}-1

  • Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u>  2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Let us take n=k+1

Hence, we have:

2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)

( Since, the result was true for n=k )

Hence, we have:

2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2

Also, we know that:

-2

(

Since, for n=k+1 being a positive integer we have:

2^{(k+1)+1}-2^{(k+1)-1}>0  )

Hence, we have finally,

2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

2^n\leq 2^{n+1}-2^{n-1}-1  where n is a positive integer.

6 0
3 years ago
3. The following is raw data in respect to expenses incurred by a family on education from
dalvyx [7]
I don’t really understand what you have said. But I need help on my homework.
3 0
3 years ago
The _____ in the hundreds place has a value ____ times as great as the _____ in the _____ place. 440
solong [7]

Answer:

The 4 in the hundreds place has a value 10 times as great as the 4 in the tens place.

Step-by-step explanation:

440 = 400 + 40 + 0

the hundreds place is worth 400 here

it is worth 10x the tens place (40 here)

5 0
3 years ago
A train traveled 1360 miles in 16 hours. What was the average speed of the train in miles per hour?
notsponge [240]

Answer:

85 miles per hour

Step-by-step explanation:

5 0
2 years ago
What is 99.96 rounded to the nearest tenth​
nirvana33 [79]

Answer:

It is 100. You round the 6 to the 9 which makes the 9 round the 99 which makes it 100.

3 0
3 years ago
Other questions:
  • I have no clue how to answer this or where to start
    14·2 answers
  • Which of the following is a result of shifting a circle with equation (x + 3)² + (y - 2)² = 36 left 3 units?
    15·2 answers
  • For a certain year, the combined revenues for Pepsi cola and coca-cola were 57 billion. If the revenue for Pepsi co was 13 billi
    14·2 answers
  • 41,464,700+?=50,000,000
    15·2 answers
  • Which of the expressions are equivalent to the one below? (14+4)/6
    7·2 answers
  • Find the equation of the line that passes through (3,1) and is parallel to
    14·1 answer
  • A shooting star forms a right triangle with the Earth and the Sun, as shown below:
    13·1 answer
  • I need help fast thank you!!
    5·2 answers
  • The bill at a restaurant is $28.48, not including tax. A family wants to leave an 18% tip. How much money
    11·1 answer
  • The set of ordered pairs represents a functuon. Write a rule represents the function. (0,0),(1,6),(2,24),(3,54),(4,96)
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!