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Paha777 [63]
3 years ago
11

The first term of an arithmetic sequence is 4. The common difference is 8. What is the 25th term of sequence

Mathematics
1 answer:
lukranit [14]3 years ago
3 0

Answer:

196

Step-by-step explanation:

T25=4+(25-1)8

=4+192

T25=196

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#2 <br> #3 <br> Need help for my discrete math class
miss Akunina [59]

For (2), start with the base case. When n = 2, we have

(n + 1)! = (2 + 1)! = 3! = 6

2ⁿ = 2² = 4

6 > 4, so the case of n = 2 is true.

Now assume the inequality holds for n = k, so that

(k + 1)! > 2ᵏ

Under this hypothesis, we want to show the inequality holds for n = k + 1. By definition of factorial, we have

((k + 1) + 1)! = (k + 2)! = (k + 2) (k + 1)!

Then by our hypothesis,

(k + 2) (k + 1)! > (k + 2) 2ᵏ = k•2ᵏ + 2ᵏ⁺¹

and k•2ᵏ ≥ 2•2² = 8, so

k•2ᵏ + 2ᵏ⁺¹ ≥ 8 + 2ᵏ⁺¹ > 2ᵏ⁺¹

which proves the claim.

Unfortunately, I can't help you with (3). Sorry!

3 0
3 years ago
One number is 6 less than 3 times another number and their sum is 62
Elodia [21]
Let one of those numbers be x.

Now,
according to question,
The other number must be,

3x-6

Now,


as said in the question,

x+3x-6 =62
4x -6 =62
4x = 68
x = 17.


Now,
we got one of those numbers which was x = 17,

and the other number should be 3(17)-6 = 51-6 = 45.
8 0
3 years ago
Does any one know the answer?
nekit [7.7K]

Answer: option C

find f(x) - g(x)

f(x)= -9x^2 - 7x + 12

g(x) = 3x^2 - 4x -15

To find f(x) - g(x) we plug in the functions and subtract

-9x^2 - 7x + 12- ( 3x^2 - 4x -15)

Remove the parenthesis and change the sign of each term

-9x^2 - 7x + 12 - 3x^2 + 4x +15

Combine like terms

-12x^2 - 3x + 27

So option C is correct

5 0
3 years ago
Use what you've learned in this unit to model the population of Western
nekit [7.7K]

The population function of the Western Lowland Gorillas can either represent population growth or population decay

<h3>How to model the population</h3>

The question is incomplete, as the resources to model the population of the Western Lowland Gorillas are not given.

However, the following is a general guide to solve the question.

An exponential function is represented as:

y = a(1 \pm r)^x

Where:

  • (a) represent the initial value i.e. the initial population of the Western Lowland Gorillas
  • (r) represents the rate at which the population increases or decreases.
  • (x) represents the number of years since 2022
  • (y) represents the population in x years

Given that the population of the Western Lowland Gorillas decreases, then the rate of the function would be 1 -r (i.e. an exponential decay)

Take for instance:

y = 2000 * 0.98^x

By comparison.

a = 2000 and 1 - r = 0.98

The above function can be used to model the population of the Western Lowland Gorillas

Read more about exponential functions at:

brainly.com/question/26829092

5 0
3 years ago
Factor -7^3+21x^2+3x-9 by grouping. what is the resulting expression​
OverLord2011 [107]

Simplify 7^3 to 343

-343 + 21x^2 + 3x - 9

Collect like terms

(-343 - 9) + 21x^2 + 3x

Simplify

<u>= -352 + 21x^2 + 3x</u>

8 0
3 years ago
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