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3 years ago

Which Expression Can Be Used To Determine the nth term in the pattern below 20,25,30,35,40

Mathematics

1 answer:

maw [93]3 years ago

8 0

Answer:

see explanation

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

$a_{n}$ = a + (n - 1)d

where a is the first term and d the common difference

d = 25 - 20 = 30 - 25 = 5 and a = 20, hence

$a_{n}$ = 20 + 5(n - 1) = 20 + 5n - 5 = 5n + 15 ← n th term formula

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I will give 5 points

ikadub [295]

Use the sum of cubes factoring rule

$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

to transform the left hand side into the right hand side.

$\frac { \sin^{3} \theta + \cos^{3} \theta } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\\frac { (\sin \theta + \cos \theta)(\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta) } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\$

$\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta = 1 - \sin \theta \cdot \cos \theta\\\\(\sin^2 \theta + \cos^2\theta)- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta\\\\1- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta \ \ \checkmark\\\\$

Throughout the entire process, the right hand side stayed the same.

On the last step, I used the pythagorean identity.

8 0

2 years ago

(b) Scott added 8 fish to his pond each day for 64 days. What was the total change in the number

serious [3.7K]

Answer:

512

Step-by-step explanation:

8 fish per day x 64 days

512 fish

8 0

3 years ago

Show work please!!! Solve the equation by completing the square. If necessary, round to the nearest hundredth.

weeeeeb [17]

Answer:

1. B 2. C

Step-by-step explanation:

1. x^2-18x+(18/2)^2=19+(18/2)^2

(x-18/2)^2=100

(x-9)^2=100

x1= -1 x2= 19

2. x^2=81

x=+-9

x1=-9 x2=9

5 0

3 years ago

What is -2 × 1 1/4=

RoseWind [281]

Answer: -11/2

Step-by-step explanation:

Just set it up so it looks like this:

-2/1 x 11/4 and multiply across the top, which would be -22 and then the across the bottom, which would equal 4. So it’s -22/4. BUT you can simplify it down to -11/2 by dividing both sides of the fraction by 2. So then answer is -11/2

Hope that makes sense! :)

5 0

3 years ago

If I told you that Mexico's population was 100,000,000 and that their population growth rate was 3.5%, then what would their pop

Stels [109]

Answer:

The population one year from now would be 103,500,000

Step-by-step explanation:

The current population is 100,000,000

Growth rate of 3.5%.

So the population one year from now is 3.5% of the current population(100,000,000) added to the current population(100,000,000).

3.5% of 100,000,000 is 0.035*100,000,000 = 3,500,000.

Added to 100,000,000

100,000,000 + 3,500,000 = 103,500,000

The population one year from now would be 103,500,000

7 0

3 years ago