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2 months ago

Guest #6877546

2 months ago

Steps to inductive

1. show it's true for n=1

2. replace n with k

3. replace k with k+1 and show it is true statement

4. state that it's true

1. show it's true for n=1

1(1+1)=[1(1+1)(1+2)]/3

1(2)=[(2)(3)]/3

2=6/3

2=2

true

2. assume it's true for n=k

1*2+2*3+3*4+...+k(k+1)=[k(k+1)(k+2)]/3

3. show it's true for replaceing k with k+1

1*2+2*3+3*4+...+k(k+1)+(k+1)((k+1)+1)=[(k+1)((k+1)+1)((k+1)+2)]/3

remember from before that 1*2+2*3+3*4+...+k(k+1)=[k(k+1)(k+2)]/3

[k(k+1)(k+2)]/3+(k+1)(k+2)=[(k+1)(k+2)(k+3)]/3

use algebra to show this is true (get it to k=k or something like that)

here's the fun part

deal with left side to get to like right side

[k(k+1)(k+2)]/3+(k+1)(k+2)

make over 3, so muliptlu 2nd thing by 3/3

[k(k+1)(k+2)]/3+((k+1)(k+2)3)/3

[k(k+1)(k+2)+3(k+1)(k+3)]/3

we can undistribute the (k+1)(k+2) part

[(k+1)(k+2)(k+3)]/3

now remember the right side?

[(k+1)(k+2)(k+3)]/3=[(k+1)(k+2)(k+3)]/3

tada

true

4. state it

therefor 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 is true for all real numbers

1. show it's true for n=1

2. replace n with k

3. replace k with k+1 and show it is true statement

4. state that it's true

1. show it's true for n=1

1(1+1)=[1(1+1)(1+2)]/3

1(2)=[(2)(3)]/3

2=6/3

2=2

true

2. assume it's true for n=k

1*2+2*3+3*4+...+k(k+1)=[k(k+1)(k+2)]/3

3. show it's true for replaceing k with k+1

1*2+2*3+3*4+...+k(k+1)+(k+1)((k+1)+1)=[(k+1)((k+1)+1)((k+1)+2)]/3

remember from before that 1*2+2*3+3*4+...+k(k+1)=[k(k+1)(k+2)]/3

[k(k+1)(k+2)]/3+(k+1)(k+2)=[(k+1)(k+2)(k+3)]/3

use algebra to show this is true (get it to k=k or something like that)

here's the fun part

deal with left side to get to like right side

[k(k+1)(k+2)]/3+(k+1)(k+2)

make over 3, so muliptlu 2nd thing by 3/3

[k(k+1)(k+2)]/3+((k+1)(k+2)3)/3

[k(k+1)(k+2)+3(k+1)(k+3)]/3

we can undistribute the (k+1)(k+2) part

[(k+1)(k+2)(k+3)]/3

now remember the right side?

[(k+1)(k+2)(k+3)]/3=[(k+1)(k+2)(k+3)]/3

tada

true

4. state it

therefor 1 ∙ 2 + 2 ∙ 3 + 3 ∙ 4 + . . . + n(n + 1) = [n(n + 1)(n + 2)]/3 is true for all real numbers

Question

Which expression is equivalent to the given expression? 8(3/4a)−8
1. 3/4a
2. 6a
3. 8(3/4a - 1)
4. 3/4a -1

Solution 1

**Answer:**

**Step-by-step explanation:**

8 (3/4a) - 8

The above expression can be written as:

Since 8 is a common factor here which is multiple of 3/4a as well as 1 therefore taking 8 as a common factor from whole equation,

Therefore option (3) is the correct answer.

Solution 2

The answer is 3 cause we can factor 8 from the whole equasion .

that means to take 8 out of every given data so

since we have 8 multiple 3/4a we can have an 8 and we also have -8 so we can divide it to 8 and take 8 out of it which leads us to 8(3/4a-1)

that means to take 8 out of every given data so

since we have 8 multiple 3/4a we can have an 8 and we also have -8 so we can divide it to 8 and take 8 out of it which leads us to 8(3/4a-1)

Question

When a nonzero rational and an irrational number are multiplied, is the product rational or irrational?

Solution 1

The sum of a rational number and an irrational number is irrational.

Question

Harvey is 3 times as old as Jane. The sum of their ages is 48 years. Find the age of each. Jane is a0 years old. Harvey is a1 years old.

Solution 1

Let jane = j

Harvey = 3*j = 3j

Sum = 48 years

j + 3j = 48

4j = 48

j = 48/4

j = 12

Jane, j =**12 years old**

Harvey, 3j = 3*12 =**36 years old**

Hope this helped.

Harvey = 3*j = 3j

Sum = 48 years

j + 3j = 48

4j = 48

j = 48/4

j = 12

Jane, j =

Harvey, 3j = 3*12 =

Solution 2

Harvey is 36, jane is 12

Question

When calculating the effective rate of a loan, which statement or statements must be true if n is greater than 1? I. The length of the loan is greater than a single year.
II. The effective rate will exceed the nominal rate.
III. The interest will be compounded monthly.

Solution 1

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.

When calculating the effective rate of a loan, the statement or statements must be true if n is greater than 1 is The length of the loan is greater than a single year.

When calculating the effective rate of a loan, the statement or statements must be true if n is greater than 1 is The length of the loan is greater than a single year.

Solution 2

**Answer: A**

**Step-by-step explanation:**

its a

Question

All equilateral triangles are also isosceles triangles.
TRUE OR FALSE?

Solution 1

false kljfoidjfdiojfoidjfoijfoidjfodijfoidjf

Solution 2

**Answer:**

I think it's true but not 100% sure :)

**Step-by-step explanation:**

Question

Which expression is equivalent to the given expression? −(2n−6)
1. −2(n−3)
2. −2(n−6)
3. 2n−62
4. 2n + 6

Solution 1

−(2n−6)

= -2n + 6

= -2(n - 3)

answer is 1. −2(n−3)

= -2n + 6

= -2(n - 3)

answer is 1. −2(n−3)

Question

Audrey is buying a new car for $32,998.00. She plans to make a down payment of $4,200.00. If she's to make monthly payments of $525 for the next five years, what APR has she paid?

Solution 1

**Answer:**

3.7%

**Step-by-step explanation:**

Given:

Cost = $32,998

Down payment = $4,200

Remaining amount = $32,998 - $4,200 = $28,798

Monthly payment = $525

Duration = 5 years

Present value = Monthly payment ×

here, k = 12 when compounded monthly

r is the rate of interest

thus,

$28,798 = $525 ×

or

54.85 =

or

r = **3.7%**

Solution 2

For the next five years Audrey paid 3.7% i belive

Question

Simplify. 9y+11z+7y−4z

Solution 1

16y+7z its easy, combine like terms

Solution 2

9y+11z+7y−4z

=16y + 7z

....................

=16y + 7z

....................

Question

If a = 14 and b = 14, then a = b. What algebraic property is illustrated above?
A. identity property of multiplication
B. symmetric property
C. addition property of equality
D. transitive property

Solution 1

B symmetrical property. its pretty easy symmetrical means same so they are the same. think logically :)

Solution 2

**Answer:**

its actually D. transitive property

**Step-by-step explanation:**

Question

Which expression is equivalent to 3x+10−x+123x+10−x+12 ? 1 . 4x + 22
2. 24x
3. 2x + 22
4. 26x

Solution 1

I think its 2 I'm not 100% though

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