1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rjkz [21]
3 years ago
6

Larry is using an online calculator to calculate the outputs f(n) for different inputs n. The ordered pairs below show Larry's i

nputs and the corresponding outputs displayed by the calculator:
(1, 5), (2, 9), (3, 13), (4, 17)

Which of the following functions best represents the rule that the calculator uses to display the outputs?

a
f(n) = 5n − 1

b
f(n) = 5n + 1

c
f(n) = 4n + 1

d
f(n) = 4n − 1
Mathematics
1 answer:
FrozenT [24]3 years ago
5 0

Answer:

Option c:

f(n)=4n+1

Step-by-step explanation:

The functional relationship between two variables can be easily found if it's represented as a line.

Larry's online calculator collects these points

(1, 5), (2, 9), (3, 13), (4, 17)

We can see there is a linear relation because every time the first component increases by 1, the second increases by 4.

The equation of a line is given by

f(n)=m.n+b

Where m is the slope of the line and can be computed as

\displaystyle m=\frac{d-b}{c-a}

Where (a,b), (c,d) are two known points of the line. Let's use the first two points (1, 5), (2, 9)

\displaystyle m=\frac{9-5}{2-1}=4

We now know that

f(n)=4n+b

To compute the value of b, we use one of the points again, for example (1,5):

5=4(1)+b => b=1

The relation is

f(n)=4n+1

We can test our results by using other points like (3,13)

f(3)=4(3)+1=13

And also

f(4)=4(4)+1=17

All points belong to the same function or rule

f(n)=4n+1

You might be interested in
SOME ONE HELP ME PLZ FAST it's already late
ololo11 [35]

Answer:

4

Step-by-step explanation:

6 0
3 years ago
this formula, i represents the _____ of the loan. a. annual interest rate b. interest rate per period c. initial amount d. incid
Phantasy [73]

Answer:

b. interest rate per period

Step-by-step explanation:

We know that

Annual interest rate is APR or (r)

Po is initial amount

n is number of periods

t is time in years

A is the amount after t years

so,

i is the interest rate per period

Hence ,

answer is

i is the interest rate per period


3 0
3 years ago
8^(x+4)=2^x..........
Ludmilka [50]

Answer:

Step-by-step explanation:

x = 0

6 0
3 years ago
1. Rewrite the expression. Use an exponent, rather than repeated multiplication. (–4)(–4)
ikadub [295]
You can rewrite the multiplication using properties of the exponents.
 We have that if the base is the same, the exponents are added.
 For this case, we have:
 Base = (- 4)
 Exponent = 1
 Applying properties of exponents:
 (-4) (- 4) = ((- 4) ^ 1) ((- 4) ^ 1) = (- 4) ^ (1 + 1) = (- 4) ^ 2
 answer:
 the expression is the same as (-4) ^ 2
7 0
3 years ago
use the information provided to write the standard form equation of each hyperbola vertices:(4,14), (4,-10) foci: (4,15), (4,-11
Evgen [1.6K]
So... if you notice the picture below, based on the given vertices, is a hyperbola with a vertical traverse axis

meaning for the equation, the fraction with the "y" variable is the positive fraction, thus \bf \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1

so... what' the point h,k for the center?  well, just take a peek at the graph, the center is half-way between both vertices, that's h,k

what's the "a" component or the traverse axis... well, is the distance from one vertex to the center, notice the picture, notice how many units from either vertex to the center, that's "a"

now.. what's "b"?  well, "b" comes from the conjugate axis, or the other runnning over the x-axis   hmm the smaller one in this case.... well, we dunno what "b" is

however, we know the distance from either focus, to the center of the hyperbola, and that distance "c", is  \bf c=\sqrt{a^2+b^2}

notice the picture, notice the distance from either focus to the center, that's the distance "c", thus  \bf c=\sqrt{a^2+b^2}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b

that'd be "b"

bearing in mind that   \bf \cfrac{(y-{{ k}})^2}{{{ a}}^2}-\cfrac{(x-{{ h}})^2}{{{ b}}^2}=1
\qquad 
\begin{cases}
center= ({{ h}},{{ k}})\\\\ b=\sqrt{c^2-a^2}
\end{cases}

8 0
3 years ago
Other questions:
  • Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than π/100 square
    13·1 answer
  • Suppose you purchase sunglasses that are regularly priced at $87.20. They are on sale for 30% off, and you have a coupon for 10%
    5·1 answer
  • Which of the following lines is not parallel to the graph of y=4x+7. y-4x=9 4x-y=8 . 4y-x=8 8x-2y=8
    9·1 answer
  • Z+(z-6)-2=-10 how do you solve this
    13·1 answer
  • Jim has 2 gems. He got 2 more on Monday and 5 more on Tuesday. How many does he have now?
    12·2 answers
  • 1. Give at least two examples of how you have used digital money.
    15·2 answers
  • A museum opened at 8:00 am. In the first hour, 350 people purchased admission tickets. In the second hour, 20% more people purch
    9·2 answers
  • Expression tha have the same vaule
    14·1 answer
  • John drew rhombus RSTV. He drew both diagonals that intersect at point M. in johns figure, which would be the measure of RMS
    11·1 answer
  • Problem #2
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!