Ask question

Ask question

All categories

3 years ago

12

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? f(n) = 5n − 1 f(n) = 5n + 1 f(n) = 4n + 1 f(n) = 4n − 1

2 answers:

Rama09 [41]3 years ago

8 0

Answer:

(C) f(n) = 4n + 1

Step-by-step explanation:

i just took the test

joja [24]3 years ago

6 0

Answer:

The rule is $\implies f(n)=4n+1$

Step-by-step explanation:

The ordered for Larry's inputs and the corresponding outputs displayed by the calculator are:

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

We use the y-values of the ordered pairs to obtain the rule.

The y-values are:

$5,9,13,17$

The y-values form a sequence. The first term of this sequence is:

$a=5$

The common difference of this sequence is

$d=9-4=5$

The rule is given by:

$f(n)=a+d(n-1)$

We substitute the values to obtain:

$f(n)=5+4(n-1)$

$\implies f(n)=5+4n-4$

The rule is $\implies f(n)=4n+1$

You might be interested in

Find the length of AB

aniked [119]

FIRST QUESTION
Given points are:
A(2, -4) and B(6, 2)
Now, Use the distance formula.
distance formula = $\sqrt{ (x_{2}- x_{1})^{2} + ( y_{2} - y_{1} )^{2} }$

Now, plug the values into the formula, So,
distance = $\sqrt{ (6- 2)^{2} + ( 2 - (-4))^{2} }$

= $\sqrt{ (6- 2)^{2} + ( 2 +4))^{2} }$

= $\sqrt{ (4)^{2} + ( 6))^{2} }$

= $\sqrt{ 16+36}$

= $\sqrt{52}$

= $2 \sqrt{13}$

So, the length of AB is $2 \sqrt{13}$ .

<span>THIRD QUESTION
</span>Two points given are:
A(3, -2) and B(1, 1)
Also given that B is the midpoint of AC.

Let, the co-ordinates of C be C(a, b).
Now, using midpoint formula,
Midpoint = $(\frac{ x_{1}+ x_{2} }{2} , \frac{ y_{1}+ y_{2} }{2} )$

$(1, 1)=(\frac{ 3+ a }{2} , \frac{ -2+b }{2} )$

Now, equaling the ordered pair, we have,

$1=\frac{ 3+ a }{2}$ .............equation (1)

$1=\frac{ -2+b }{2}$ ................equation (2)

Now, taking equation (1)
$1=\frac{ 3+ a }{2}$

$1*2=3+a$

$2-3=a$

$a=-1$

Now, taking equation (2)
$1=\frac{ -2+b }{2}$

$1*2=-2+b$

$2+2=b$

$b=4$

<span>So, the co ordinates of C are (a, b) which is <u>(-1 , 4)

</u></span>
<span>SECOND QUESTION:
</span>Given equations are:
2x + 3y = 14.....................equation (1)
-4x + 2y = 4 .....................equation (2)
Taking equation (2)
-4x + 2y = 4
2y = 4 + 4x
y = (4 + 4x) / 2
y = 2 + 2x .......................equation (3)
Now, Taking equation (1)
2x + 3y = 14
Substituting the value of y from equation (3), we get,
2x + 3(2 + 2x) = 14
2x + 6 + 6x = 14
8x = 14 - 6
x = (14 - 6) / 8
x = 1

Taking equation (3)
y = 2 + 2x
Now, substituting the value of x in equation (3), we get,
y= 2 + 2 (1)
y = 2 + 2
y = 4

So, x=1 and y=4

6 0

3 years ago

The radius of a circle is 4 inches. What is the circle's circumference?

mojhsa [17]

Answer:

8π inches or approximately 25.12 inches

Step-by-step explanation:

What's the circumference of a circle?

❖ The circumference of a circle is the distance around a circle.

How do we find the circumference of a circle?

❖ The formula to find the circumference of a circle is 2πr, where r =

radius. We can solve in terms of pi, or approximate pi to 3.14

<u>Solving</u>

<u></u> $\pi * 4*2$
$\pi *8$
8π inches

<u>or</u>

<u /> $3.14*4*2$
$3.14*8$
25.12 inches

Have a lovely rest of your day/night, and good luck with your assignments! ♡

7 0

2 years ago

Read 2 more answers

Which division fact corresponds to the problem of 8×9 equals 72

kondor19780726 [428]

Basically just do the problem backwards.
72÷9=8
72÷8=9

7 0

3 years ago

Point A is located at (0, 4), and point B is located at (−2, −3). Find the x value for the point that is 1 over 4 the distance f

Serjik [45]

-0.5

Hope this helps, explanation is in image :)

7 0

2 years ago

If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period. a. what wi

Setler79 [48]

Answer:

a. $9,425.10

b. $3,707.60

Step-by-step explanation:

5 0

3 years ago