(3.1 x 10¹⁵) + (3.7 x 10¹³) in simplified form. Please hurry​

Question:

The recursive function [tex]f(0) = 1[/tex], [tex]f(n) = f(n-1) + 2n[/tex] represents the nth term of a sequence. Determine the explicit function

Answer:

[tex]f(n) = n^2 + n+1[/tex]

Step-by-step explanation:

Given

[tex]f(0) = 1[/tex]

[tex]f(n) = f(n-1) + 2n[/tex]

Required

Write an explicit formula

Let n = 1

[tex]f(1) = f(1-1) + 2*1[/tex]

[tex]f(1) = f(0) + 2[/tex]

[tex]f(1) = 1 + 2 = 3[/tex]

Let n = 2

[tex]f(2) = f(2-1) + 2*2[/tex]

[tex]f(2) = f(1) + 4[/tex]

[tex]f(2) = 3 + 4 = 7[/tex]

Let n =3

[tex]f(3)=f(3-1) + 2 * 3[/tex]

[tex]f(3)=f(2) + 6[/tex]

[tex]f(3)=7+ 6 = 13[/tex]

Let n = 4

[tex]f(4) = f(4 - 1) + 2 * 4[/tex]

[tex]f(4) = f(3) + 8[/tex]

[tex]f(4) = 13+ 8 = 21[/tex]

So, we have:

[tex]f(1) = 3= 1 + 2 * 1=1+0*1*2*1[/tex]

[tex]f(2) = 7= 3 + 2 * 2=1+1*2+2*2[/tex]  

[tex]f(3) = 13= 7 + 2 * 3= 1+2*3+2*3[/tex]

[tex]f(4) = 21 = 13 + 2 * 4= 1+3*4 +2 *4[/tex]

Following the above pattern:

[tex]f(n) = 1 + (n - 1) * n + 2 * n[/tex]

[tex]f(n) = 1 + n(n - 1) + 2n[/tex]

Open bracket

[tex]f(n) = 1 + n^2 - n + 2n[/tex]

[tex]f(n) = 1 + n^2 + n[/tex]

[tex]f(n) = n^2 + n+1[/tex]

Answer:

Step-by-step explanation:

the factors and prime factorization of 7 and 13. The biggest common factor number is the GCF number. So the greatest common factor 7 and 13 is 1.

Volume is measured in cubic units.

The Pyramid is cut in half, so the ratio of the volume would be 1/2^3 units which simplifies to 1/8

The ratio is 1/8

Answer:

Follows are the solution to this question:

Step-by-step explanation:

Given value:

[tex]\to X = 84\\\\\to \mu = 68\\\\\to \sigma= 10\\\\[/tex]

Using formula:

[tex]\bold{Z= \frac{X-\mu}{\sigma}}[/tex]

    [tex]= \frac{84-68}{10}\\\\ = \frac{16}{10}\\\\=1.6[/tex]

Calculating the percent of the sales which is less than or equal to 84 inches:

[tex]\to P(Z \leq 1.6)=0.9452[/tex]

                      [tex]= 0.9452 \times 100\\\\ =94.52\% \approx 95.5\%[/tex]

Calculating the remaining value [tex]100-94.5=5.5\%[/tex] were more than 84 inches.

Answer:

There is no image. Please repost.

Answer:

BD = 22, DC = 11√3

Step-by-step explanation:

In triangle ABC, ∠B = 45°, ∠C = 90°. Hence:

∠A + ∠B + ∠C = 180° (sum of angles in a triangle)

∠A + 45 + 90 = 180

∠A + 135 = 180

∠A = 45°

Using sine rule to find BC:

[tex]\frac{BC}{sinA}=\frac{AB}{sinC} \\\\\frac{BC}{sin45}=\frac{11\sqrt{2} }{sin90} \\\\BC=\frac{11\sqrt{2}*sin45 }{sin90} \\BC=11[/tex]

In triangle BCD, ∠D = 30°, ∠C = 90°. Hence:

∠D + ∠B + ∠C = 180° (sum of angles in a triangle)

∠B + 30 + 90 = 180

∠B + 120 = 180

∠B = 60°

Using sine rule to find BD:

[tex]\frac{BD}{sinC}=\frac{BC}{sinD} \\\\\frac{BD}{sin90} =\frac{11}{sin30} \\\\BD=\frac{11*sin90}{sin30}\\\\BD=22[/tex]

Using sin rule to find DC:

[tex]\frac{DC}{sinB}=\frac{BC}{sinD} \\\\\frac{DC}{sin60} =\frac{11}{sin30} \\\\DC=\frac{11*sin60}{sin30}\\\\DC=11\sqrt{3}[/tex]

Answer:

8.9

Step-by-step explanation:

Answer:

the answer will be 8.9 if im not wrong

Answer:

D) 22

Step-by-step explanation:

Since it gives you two rays just set them equal and solve for X.

6x - 14 = 3x +4

      +14        +14

6x = 3x + 18

-3x   -3x

3x = 18

/3    /3

x = 6

Then plug x into either one of the equations

6(6) - 14

36 - 14

22

Answer:

D. 22

Step-by-step explanation:

Answer:

the measurement of x is 30 degrees

Answer:

it is D hope this helps

Step-by-step explanation:

Answer:

it should be b i think

Step-by-step explanation:

Answer:

It was C

Step-by-step explanation:

I took the test

Answer:

c and d are the correct answers

Answer:

3x^2+7x-20

Step-by-step explanation:

Answer:

expand the brackets

3x^2 + 7x -20

Step-by-step explanation:

(3x-5)(x+4)

= 3x^2 + 12x - 5x + 20

= 3x^2 + 7x + 20

Answer:

Because he has to send one more parcel than the estimation.

Step-by-step explanation:

Step-by-step explanation:

2x + 6 > 84

2x > 78

x > 39

is the answer

Answer:

shirt = $20

sweater = $35

Step-by-step explanation:

This question would be solved using simultaneous equation

Let the price of sweater be represented by a

Let the price of shirt be represented by b

The following equations can be derived from the question

2a + 4b = 150   equation 1

4a + 3b = 200   equation 2

Multiply equation 1 by 2

4a + 8b = 300    equation 3

Subtract equation 2 from 3

5b = 100

divide both sides of the equation by 5

b = 20

substitute for b in equation 1

2a + 4(20) = 150

2a + 80 = 150

collect like terms

2a = 150 - 80

2a = 70

divide both sides by 2

a = 35

Price of sweater = $35

Price of shirt = $20

Answer:

What the other guy said

Step-by-step explanation:

Answer:

Step-by-step explanation:

Here, we want to solve the given quadratic equation using the quadratic formula

We need to rewrite the equation in the standard form;

-4x^2 + 3x + 5 = 0

we have the value a as -4

value b as 3

C = 5

we then substitute these values into the quadratic formula as seen in the attachment

Answer:

$165

Step-by-step explanation:

Dinner bill = $132

Sales tax = 10% of dinner bill

Tip left = 15% of dinner bill

Amount of sales tax :

10% of $132

0.1 * $132 = $13.2

Amount of tip left :

15% * $132

0.15 * $132 = $19.8

Total bill :

Dinner cost + sales tax + tip

$132 + $13.2 + $19.8

= $165

Answer:

hypotenuse =

[tex] \sqrt{a {}^{2} } + b {}^{2} [/tex]

=

[tex] \sqrt{} 24 {}^{2} + 10 {}^{2} [/tex]

= 26mi

Answer:

SAS

Step-by-step explanation:

Bro it's right

Answer: B: b=1/2

Step-by-step explanation: 1/4+2/4=3/4

2/4=1/2 so B or b=1/2

plz mark me brainliest

How to Mark Brainliest:

look at the bottom right of an answer there should be a crown if not look if there are 2 players if yes reload the page if no wait for someone else to answer then reload. tap the crown to mark brainliest.

Answer:

4(x+7)=38

4x+28=38

4x=38-28

4x=10

(divide by 4)

x=2whole number 2/4

=2whole number 1/2

or x=2.5

Answer:

37.3

Step-by-step explanation:

Answer:

37.29

Step-by-step explanation:

Answer:

c)0.65

Step-by-step explanation:

Answer:

0.65

Step-by-step explanation:

1.2 + 0.65 = 1.85

1.85 + 0.65 = 2.5

2.5 + 0.65 = 3.15

And so on...

Question:

The cost of a car rental is ​$42 per day plus 20 cents per mile. you are on a daily budget of ​$98. write and solve an inequality to find the greatest distance you can drive each day while staying within your budget. use pencil and paper. find 2 other​ two-step inequalities with the same solutions.

Answer:

(a) The greatest distance is 280 miles

(b) [tex]30 + 0.10 m \le 58[/tex] and [tex]5 m-400 \le 1000[/tex]

Step-by-step explanation:

Given

[tex]d = \$42[/tex] ---->daily rate

[tex]m = 20\ cents[/tex] -- amount per mile

[tex]m = \$0.20[/tex] --- in dollars

[tex]Budget = \$98[/tex]

Solving (a): Inequality for the scenario

Because you are on a budget, it means that the spending can not exceed $98 (i.e. less than or equal to $98).

So, the inequality is:

[tex]42 * days + 0.20 * miles \le Budget[/tex]

Represent days with d, miles with m and substitute 98 for Budget

[tex]42d + 0.20m \le 98[/tex]

Because it is daily, then d = 1

[tex]42 * 1+ 0.20 * m \le 98[/tex]

[tex]42+ 0.20m \le 98[/tex]

Collect like terms

[tex]0.20m \le 98 - 42[/tex]

[tex]0.20m \le 56[/tex]

[tex]m \le \frac{56}{0.20}[/tex]

[tex]m \le 280[/tex]

The greatest distance is 280 miles

Solving (b): Two other inequalities with the same solution as: [tex]m \le 280[/tex]

To do this, all you need to do is to perform the same operation on both sides of the inequality.

[tex]m \le 280[/tex]

Multiply both sides by 0.10

[tex]0.10 * m \le 280 * 0.10[/tex]

[tex]0.10 m \le 28[/tex]

Add 30 to both sides

[tex]30 + 0.10 m \le 28+30[/tex]

[tex]30 + 0.10 m \le 58[/tex] --- equation (1)

Another possible equation is as follows:

[tex]m \le 280[/tex]

Multiply both sides by 5

[tex]5 * m \le 280 * 5[/tex]

[tex]5 m \le 1400[/tex]

Subtract 400 from both sides

[tex]5 m-400 \le 1400-400[/tex]

[tex]5 m-400 \le 1000[/tex] --- equation (2)

Answer:

181 1/4 square feet

Step-by-step explanation:

The square feet of carpet is needed to cover the floor would b equal to the area of the floor

area of a rectangle = length x breadth

12 1/2‘ x 14 1/2 = 181 1/4 square feet