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What is the explicit formula for the sequence? 6, 5, 4, 3, 2, . . .


I think that the right answer for this question is  6

Related Questions

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4. Which of the following sets of numbers is a Pythagorean triple? A. 4, 5, 6 B. 8, 15, 17 C. 5, 12, 14 D. 8, 24, 25 Suppose a triangle has side lengths 6, 7, and 10. Which of the following best describes this triangle? A. obtuse B. acute C. right D. Cannot be determined.

Here are the answers to the given questions above:
4. When we say pythagorean triple, this would consists of three positive integers a, b, and c, such that a2 + b2 = c2. So for the given numbers above, the set that is considered a pythagorean triple would be B.  8, 15, 17.
5. The correct answer for this question would be option D. It cannot be determined whether the triangle is obtuse, acute or right if the given values are the side lengths. It should be angles. Hope this answer helps.

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1. Which set of ordered pairs in the form of (x,y) does not represent a function of x? (1 Point) A. (1, 1.5), (2, -1.5), (3, 1.5), (4, 1.5) B. (0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5) C. (1, 1.5), (-1, 1.5), (2, 2.5), (-2, 2.5) D. (1, 1.5), (-1, -1.5), (2, 2.5), (-2, 2.5)

Based on the given set of ordered pairs above, the set of ordered pairs in the form of (x,y) that does not represent a function of x would be option B. Why is this so? if you notice, the number 1 in the x is being repeated so this means this is not a function. Hope this answer helps.

Posted in Mathematics

Which test point holds true for y − 2x ≤ 1? (0, 2) (-2, 4) (1, 4) (5, 0)

So in order to find the correct answer, we can just easily plug in the values to check which ordered pair matches the given inequality above. So based on my solutions, the correct answer would be the last pair. 
 y − 2x ≤ 1
0 - 2(5)
 ≤ 1
0-10  ≤ 1
-10  ≤ 1
Hope this answer helps.

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Given f(x)=17-x^2, what is the average rate of change in f(x) over the interval [1, 5]?

For the answer to the question above, I'll show my to solution to the answer below.
average rate of change is 
(f(5) - f(1))/(5 - 1) = 

(17 - 5^2 - (17 - 1^2))/4 = 

(17 - 25 - 17 + 1)/4 = 
So the answer for this problem is
-6
I hope my answer helped you. Feel free to ask for more questions.

Posted in Mathematics

What is the solution to the system of equations? y = 1.5x – 4 y = –x a. (–1.6, 1.6) b. (–1.5, 1.5) c. (1.5, –1.5) d. (1.6, –1.6)

I believe the correct answer from the choices listed above is option D. The solution to the system of equations given above would be (1.6, –1.6). We can use the substitution method to solve this. We do as follows:

-x = 1.5x – 4
4 = 2.5x
x = 1.6
y = -x = -1.6

Posted in Mathematics

A certain forest covers an area of 2,000 square kilometers. Suppose that each year this area decreases by 6%. What is the function that best represents the area of the forest each year and how much area remains after 12 years? Round your answer to the nearest square kilometer. Hint: Use the formula, f(x) = P(1 + r)x

For the answer to the question above, I think the formula you is wrong. The x must be in exponential form. It must look like this

f(x) = P(1 + r)^x
Now we can solve.

Given:
P = 2000
r = -0.06

f(x)  =  2000 (1 - 0.06)^x
       =  2000 (0.94)^x


         
2000 (0.94)¹² = 

2000 (0.476)  = 
The answer is 
951.8 square kilometers.
                   

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Which ordered pair is a solution of the equation 2x − y = 9 (-4,1) (-2,5) (5,1) (6,-3)

In order to confirm if which ordered pair is a solution of the given equation above, we can just simply plug in the values.
So based on my solution, the correct answer would be the third option: (5,1) 
So let us try to plug in the values.
2(5) - 1 = 9
10 -1 = 9
9 = 9
So this is the correct one. Hope this answers your question.

Posted in Mathematics

The following data values represent a population. What is the variance of the values? 8, 10, 14, 12 A.22 B.11 C.5 D.10

 Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set. We do as follows:

Mean = 8+10+14+12 / 4 = 11

Variance = (8-11)^2 + 
(10-11)^2 + (12-11)^2 + (14-11)^2 / 4
Variance = 5 <-------OPTION C

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Posted in Mathematics

What interval includes all possible values of x, where –3(6 – 2x) ≥ 4x + 12? (–∞, –3] [–3, ∞) (–∞, 15] [15, ∞)

The solution to the problem is as follows:

solve for x :

−3(6−2x)≥4x+12

−18+6x≥4x+12

2x≥30

x≥15

So the answer is D ) 15 to +infinity


I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

Let P be a point between points S and T on 2004-01-01-02-00_files/i0120000.jpg. If ST = 21, SP = 3b – 11, and PT = b + 4, solve for b. A. –7 B. 7 C. 14 D. 32

The best and most correct answer among the choices provided by your question is the third choice or letter C.

If ST = 21, SP = 3b – 11, and PT = b + 4, the value of b would be 14.


I hope my answer has come to your help. God bless and have a nice day ahead!

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Posted in Mathematics

Each set of ordered pairs represents a function. Write a rule that represents the function. 1. (0,0),(1,4),(2,16),(3,36),(4,64) 2. (0,0),(1,0.5),(2,2),(3,4.5),(4,8)

My answer to the question is as follows:

First one looks like you are squaring the number, then multiplying the result by 4, i.e.

y=4x2

second one is similar, but instead of squaring and multiplying by 4, you are squaring and then dividing by 2

I hope my answer has come to your help. God bless and have a nice day ahead!

Posted in Mathematics

You can buy an 8 pack of paper towels for $7.92 or 12 pack for $11.64, which is a better buy?

Divide $7.92 by 8 and then divide $11.64 by 12 and see which has the lowest answer.

The first option has a price of $0.99 for one paper towel, and the second option has a price of $0.97 for one paper towel.

The second option is the better buy.

Posted in Mathematics

If the purchase price for a house is $445,500, what is the monthly payment if you put 5% down for a 30 year loan with a fixed rate of 6.25%?

Answer:

The monthly payment is $2603.17

Step-by-step explanation:

The purchase price is = $445500

5% is down payment = 0.05\times445500=22275

Loan amount is = 445500-22275=423225

The EMI formula is = \frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }

p = 423225

r = 6.25/12/100=0.0052

n = 30*12 = 360

Putting the values in the formula we get:

\frac{423225*0.0052*(1.0052)^{360} }{(1.0052)^{360}-1 }

= $2603.17

The monthly payment is $2603.17 approx

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What is the equation in point slope form of the line that passes through the point (–2, 4)(–2, 4) and has a slope of 5?

Point-slope formula: y-y1=m(x-x1) 
Now we'll plug in the numbers they give us into the formula:

y-4= 0(x+2).

Posted in Mathematics

What is 22,274 divided by 37

The answer is 61.459 repeating

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The public library has fewer than 4,000 books. Let b represent the number of books in the library. Which inequality describes the number of books? b < 4,000 b > 4,000 b ≤ 4,000 b ≥ 4,000

Answer:  The correct option is (A) b < 4000.

Step-by-step explanation:  Given that the public library has fewer than 4,000 books.

We are to select the inequality that describes the number of books in the library.

The number of books in the library is represented by b.

According to the given information, the inequality hat describes the number of books in the library is given by

b<4000.

Thus, (A) is the correct option.

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Which rule represents the translation of hexagon DEFGHI to hexagon D'E'F'G'H'I'? (x, y)→(x - 8, y - 7) (x, y)→(x - 7, x - 8) (x, y)→(x - 4, x - 5) (x, y)→(x - 5, y - 4)

Correct answer is A.

Each vertex of the hexagon is translated 8 units left and 7 units down. So, the x-coordinate is 8 units smaller (x - 8), and the y-coordinate is 7 units smaller (y - 7).

Therefore (x, y) → (x - 8, y -7)

Posted in Mathematics

Which of the following ordered pairs corresponds to an arrow on a mapping diagram that starts at 4 and ends at 1? Map Diagram: Input 1 2 3 4 5 Output 1 2 3 4 5 The arrow points from 4 under input to 1 under output. Answer Choices are: A. (1, 1) B. (1, 4) C. (4, 1) D. (4, 4)

Input options represent first number in ordered pair and output options represent second number in ordered pair.

We can see that arrow starts from 4 and is pointing to 1 which means:
first number is 4 and second is 1

Ordered pair is:
(4,1)

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Which answer describes the type of sequence? −99, −88, −66, −55, ... A. arithmetic B. neither arithmetic nor geometric C. geometric

Here, Geometric ratio, r = -88/-99 or -66/-88 which is 8/9 or 6/8. As they are not equal, it is not a geometric.

Now, Arithmetic difference, d = -88-(-99) or -66-(-88) which is 11 or 22. As they are not equal, it is not a Arithmetic.

So, it's neither an Arithmetic nor a Geometric.

Option B is your answer!

Hope this helps!

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What is the common ratio for the geometric sequence? 54, 36, 24, 16...

Geometric ration, r = 36/54 or 24/36 which is equal to 2/3

So, your final answer is 2/3

Hope this helps!

Posted in Mathematics

What is the common difference d of the sequence? 9, −8, −25, −42, −59, ... d =

Common difference, d = -8-9 or -25-(-8) which is equal to -17

So, your final answer is -17

Hope this helps!

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