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Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? She showed that an explicit formula could be created. She showed that a recursive formula could be created. She showed that f(n) ÷ f(n - 1) was a constant ratio. She showed that f(n) - f(n - 1) was a constant difference.


Answer:

D

Step-by-step explanation:

She showed that f(n) - f(n - 1) was a constant difference.

The definition of an arithmetic sequence is the difference between consecutive terms is constant, aka common difference.



Related Questions

Posted in Mathematics

The binomials shown below will be multiplied to produce a quadratic trinomial. (x + p)(x + q) Which part of the trinomial will equal the sum of p and q? A. The constant term B. The coefficient of the x-term C. The degree D. The coefficient of the x2-term

I believe the correct answer from the choices listed above is option B. The part of the trinomial will equal the sum of p and q would be the coefficient term. We do it as follows:

(x + p)(x + q) 
x^2 + px + 1x +pq
x^2 + (p+q)x + pq

Hope this answers the question. Have a nice day.

Posted in Mathematics

If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial. true or false

The Factor theorem states that  for any polynomial f(x) if f(c)=0 then x-c is a factor of the polynomial f(x).

If any polynomial f(x) is divided by x-a and remainder is 0 that means f(a)= 0 .In other words we can say x-a is a factor of the polynomial f(x).So the statement :If a polynomial is divided by (x-a) and the remainder equals zero then (x -a) is a factor of the polynomial is True.

Posted in Mathematics

For f(x)=2x+1 and g(x)=x^2-7, find (f-g)(x)

I hope this helps you



(f-g)(x)=2x+1-(x^2-7)



(f-g)(x)=2x+1-x^2+7


(f-g)(x)= -x^2+2x+8

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A quadratic equation is shown below: 9x2 - 36x + 36 = 0 Part A: Describe the solution(s) to the equation by just determining the discriminant. Show your work. (3 points) Part B: Solve 2x2 - 9x + 7 = 0 using an appropriate method. Show the steps of your work and explain why you chose the method used.(4 points)

For part A:
9x² - 36x + 36 = 0 
9(x² - 4x + 4) = 0 
9(x-2)(x-2) = 0 
Radicand = Discriminant = 36² - 4(9)(36) = 0 
there is 1 real zero that repeats itself)

zero is x=2. 

Use factoring. Factors of 7 are 1 and 7 
2x²-9x+7 = 0

(2x-7)(x-1) = 0 
2x-7 = 0              (x-1)=0 
2x = 7x=1 
x = 7/2 
Your solutions are x = 1 and x = 7/2 

I hope my answers helped you

Posted in Mathematics

Anastasia uses the equation p = 0.7(rh + b) to estimate the amount of take-home pay, p, for h hours worked at a rate of r dollars per hour and any bonus received, b. What is an equivalent equation solved for h? h = (– b)÷ r h = – b ÷ r h = ÷ r – b h = ÷ r

For the answer to the question above, first we must enlist the given

p = take home pay
r = rate of dollars per hour
h = number of hours worked
b = bonus

So now we can find h and let us start with the formula.

p = 0.7(rh + b)

p = 0.7*r*h + 0.7b

p - 0.7b = 0.7rh

So the answer for this problem is

h = (p-0.7b)/0.7r 

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The sum of two positive integers, a and b, is at least 30. The difference of the two integers is at least 10. If b is the greater integer, which system of inequalities could represent the values of a and b? A. a + b ≥ 30 b ≥ a + 10 B.a + b ≥ 30 b ≤ a – 10 c. a + b ≤ 30 b ≥ a + 10 D. a + b ≤ 30 b ≤ a – 10

I believe the correct answer from the choices listed above is option A.  If b is the greater integer, then the system of inequalities that could represent the values of a and b would be a + b ≥ 30 and b ≥ a + 10. Hope this answers the question. Have a nice day.

Posted in Mathematics

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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Posted in Mathematics

What 2-dimensional shape can be rotated about the y-axis to create a cylinder which has a smaller diameter than height?

Based on the given description above, the two dimensional shape that can be rotated about the y-axis to create a cylinder which has a smaller diameter than the height would be a rectangle. Hope this is the answer that you are looking for. 

Posted in Mathematics

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.

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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.
                   

Posted in Mathematics

If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets _____ interest rates to find willing buyers.

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions.
If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2% sellers of interest-bearing financial assets greater than interest rates to find willing buyers.

Posted in Mathematics

The sum of the angle measures of any triangle is 180 degrees. Suppose that one angle in a triangle has a degree measure of 7x+3 and another has a degree measure of 3x-6 . Write an expression for the degree measure of the third angle in the triangle.

The sum of the angle measures of any triangle is 180 degrees. It should be that a + b + c = 180. For this problem, we are given the two angles which we assume to be a and b so,

180 = 
7x+3 + 3x-6 + c
c = 180 - (
7x+3 + 3x-6) 
c = 180 - (10x - 3)
c = 177 - 10x

Hope this answers the question. Have a nice day.

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Which of the following statements is true of a reflection? -It is an isometry. -It slides a plane. -The transformation is done over a line of reflection. -It flips a plane about a fixed line. I-t changes the size of the figure being reflected.

I think the correct answers from the choices listed above are the first and the fourth option. The statements that are true about a reflection would be that it  is an isometry and the it flips a plane about a fixed line. reflection over a line k (notation rk) is a transformation in which each point of the original figure (pre-image) has an image that is the same distance from line k.

Posted in Mathematics

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

Which of the binomial is a factor of this trinomial x2-7x-44?

I hope this helps you



x^2-7x-44

x -11



x +4



(x-11)(x+4)

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The y-coordinate of the y-intercept is the _____ term in the equation of the line.

For the answer to the missing term in the question above, the question is as simple as its answer. The right answer is constant.
I hope my answer helped you. Feel free to ask more questions. Have a nice day!

Posted in Mathematics

The soccer team voted on what they wanted to eat. there are 20 members on the team. six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. which ratio represents the number of votes for hot dogs to chicken

Since there are 20 members in the soccer team. Then six members voted to eat pizza and 10 member voted to eat chicken and the rest is hotdog

Member voted for hotdog = 20 – 10 – 6 = 4

Ratio for hotdog to chicken is 10 : 4 or 5:2

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Posted in Mathematics

How to solve this problem 14-6= 10-6=?

I really don't think you wrote the question properly. Or maybe you did, but this question doesn't make any sense! :/

Posted in Mathematics

Algebraic terms are separated by ______. Choose all that apply. 1)= 2)+ 3)x 4)÷ 5)-

Answer

1)=

2)+

5)-

Explanation

When letter or numbers are separated by multiplication or division can be combined to make one term.

In an algebra equation, terms are separated by an addition sign, subtraction sign or an equal sign. For example,

3a + 7b = 21.

This equation have 3 terms.

Posted in Mathematics

What is the ratio of the area of the inner square to the area of the outer square? (a−b)²+b²/a² a²−b²/a² (a−b)²/(a+b)² (ab)²/(a+b)²

The answer is
(a−b)²+b²/a²


proof

if A is the area of the
inner squared, so A= c², and c²= (a−b)²+b²

so the side of the outer must be a-b +b=a, its area is a²

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The discriminant of a quadratic equation is negative. One solution is 3+4i . What is the other solution? A.4-3i B.3-4i C.4+3i D.-3+4i

The way you stated the problem, there is an infinity of possibilities for the other solution. 

► For instance, the quadratic equation: 
   x² – (6 + 4i)x + (9 + 12i) = 0 
has for discriminant: 
   Δ = (6 + 4i)² – 4(9 + 12i) = 36 – 16 + 48i – 36 – 48i = -16 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 4i) + 4i]/2 = 3 + 4i 
   x₂ = [(6 + 4i) – 4i]/2 = 3 
And the other solution here is 3. 

► If you are not convinced, the quadratic equation: 
   x² – (6 + 5i)x + (5 + 15i) = 0 
has for discriminant: 
   Δ = (6 + 5i)² – 4(5 + 15i) = 36 – 25 + 60i – 20 – 60i = -9 
which is indeed negative. 
Its solutions will then be: 
   x₁ = [(6 + 5i) + 3i]/2 = 3 + 4i 
   x₂ = [(6 + 5i) – 3i]/2 = 3 + i 
And the other solution here is 3+i. 

► In fact, every quadratic equation of the form: 
   x² – [6 + (4 + α)i]x + (3 + 4i)(3 + αi) = 0 
where α is any real, has for discriminant: 
   Δ = [6 + (4 + α)i]² – 4(3 + 4i)(3 + αi) 
      = 36 – (4 + α)² + 12(4 + α)i – 36 + 16α – 12(4 + α)i 
      = 16α – (4 + α)² 
      = 16α – 16 – 8α – α² 
      = -16 + 8α – α² 
      = -(α – 4)² 
WILL be negative. 
Their solutions will then be: 
   x₁ = [ [6 + (4 + α)i] – (α – 4)i ]/2 = 3 + 4i 
   x₂ = [ [6 + (4 + α)i] + (α – 4)i ]/2 = 3 + αi 
And the other solution will then be is 3+αi. 

Since α can take any real value, you'll obtain an infinity of solutions of the form 3+αi. 

► So conclusively: 
If the discriminant of a quadratic is negative AND one of the solutions is 3+4i, the only thing we can say about the other solution is that its real part must be 3. 

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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2 ratios equivalent to 8\3


Some equivalent fractions of 8/3 are:
8/3 = 16/6 = 24/9 = 32/12 = 40/15 = 48/18 = 56/21 = 64/24 = 72/27 = 80/30 = 88/33 = 96/36 = 104/39 = 112/42 = 120/45 = 128/48 = 136/51 = 144/54 = 152/57 = 160/60

Posted in Mathematics

The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls?

Answer:25 %

Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%

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