Pattern A starts at 20 and has the rule "subtract 2".

Answer:

a) [tex]f(n) = n^{2}[/tex]

[tex]f(1) = 1[/tex], [tex]f(2) = 4[/tex], [tex]f(3) = 9[/tex], [tex]f(4) = 16[/tex], [tex]f(5) = 25[/tex]

b) [tex]f(n) = n^{3}[/tex]

[tex]f(1) = 1[/tex], [tex]f(2) = 8[/tex], [tex]f(3) = 27[/tex], [tex]f(4) = 64[/tex], [tex]f(5) = 125[/tex]

c) [tex]f(n) = n^{2}+n^{3}[/tex]

[tex]f(1) = 2[/tex], [tex]f(2) = 12[/tex], [tex]f(3) = 36[/tex], [tex]f(4) = 80[/tex], [tex]f(5) = 150[/tex]

Step-by-step explanation:

This formulas uses only natural numbers, which means that [tex]n \ge 1[/tex]. Then, we evaluate each function at 1, 2, 3, 4 and 5:

a) [tex]f(n) = n^{2}[/tex]

[tex]f(1) = 1[/tex], [tex]f(2) = 4[/tex], [tex]f(3) = 9[/tex], [tex]f(4) = 16[/tex], [tex]f(5) = 25[/tex]

b) [tex]f(n) = n^{3}[/tex]

[tex]f(1) = 1[/tex], [tex]f(2) = 8[/tex], [tex]f(3) = 27[/tex], [tex]f(4) = 64[/tex], [tex]f(5) = 125[/tex]

c) [tex]f(n) = n^{2}+n^{3}[/tex]

In which each element is the sum of respective results found in a) and b).

[tex]f(1) = 2[/tex], [tex]f(2) = 12[/tex], [tex]f(3) = 36[/tex], [tex]f(4) = 80[/tex], [tex]f(5) = 150[/tex]

Answer:

sorry but can u give me full question

Step-by-step explanation:

like picture

Answer:

Step-by-step explanation:

investment

Answer:

B. 12 pounds

Step-by-step explanation:

All of them are off but if I had to choose an answer between those three I would choose B.

If you round 1112 to 1000 and 56 to 60, and do 1000 divided by 60 you get 16.6

Out of all the answers 12 pounds is closest to 16.

This is how I would answer it. Hope this helps!

Answer:

Nate made a mistake. The LCM is actually 24.

Step-by-step explanation:

So, Jess found the GCF of 8 and 12 is 4. Let's make sure first.

Method 1: List the factors of 8 and 12.

8: 1, 2, 4, 8

12: 1, 2, 3, 4, 6, 12

Method 2: Or find the prime factorization of 8 and 12

8: 2 * 2 * 2

12: 2 * 2 * 3

Both 8 and 12 share 2 2's.

Multiply 2 by 2 to get 4 as the GCF

4 is the greatest factor 8 and 12 share, so Jess is correct.

Nate found the LCM of 8 and 12 is 48. Let's make sure that's correct.

Method 1: List the multiples of 8 and 12.

8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144

24 is the smallest number 8 and 12 have in common.

Method 2: Union of Primes

8: 2 * 2 * 2

12 : 2 * 2 * 3

Create a union of these primes.

Union: 2 * 2 * 2 * 3

4 * 2 * 3

8 * 3

24 = LCM

The LCM of 8 and 12 is 24, not 48, so Nate is incorrect. Thus, Nate made the mistake.

Answer:

$37.50

Step-by-step explanation:

1 money = 12.50

Before spending anything he had 2 money more than this (3 overall)

Therefore we are multiplying-

12.50 x 3 = 37.50

The answer is $37.50

Answer:

2062 employees

Step-by-step explanation:

Basically, you have an exponential function going on here. If you start with 900 employees and add 5 percent to the amount of employees (multiply by 1.005) seventeen times, you will get the equation [tex]E=900*1.05^{17}[/tex]. If we round down (because there can not be a fraction of an employee), there will be 2062 employees after 17 years.

I did the first question as reference. Pretty simple once you get it!

Answer:

27

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

you have to do the inverse so first you need to do 33/3=11 then because it says -7 you add 7 to 11 which is 18.

i hope this helps

The value of 'x' in the given linear equation is 4.

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, 'x' is a variable, 'A' is a coefficient and 'B' is constant."

Given liner equation is:

3(x - 7) = 33

⇒ 3x - 21 = 33

⇒ 3x = 33 - 21

⇒ 3x = 12

⇒ x = 4

Therefore, the value of 'x' is 4.

Learn more about linear equation here: https://brainly.com/question/2279899?

#SPJ2

Answer:

b

Step-by-step explanation:

Answer:

The answer is B :)

Step-by-step explanation:

Answer:

x = -4 and y = 12

Step-by-step explanation:

Since you have y = -x + 8 you can substitute this into the first equation where y was so you have 3x + 4(-x + 8) = 36.

That way, there is only one variable and it is easier to solve.

3x + 4(-x + 8) = 36

3x -4x + 32 = 36

-x +32 = 36

-x = 4

x = -4

Plugging this into the equation y = -x +8,

y = -(-4) + 8

y = 4 + 8

y = 12

Answer:

c) 100

Step-by-step explanation:

Answer:

How might an author's point of view be related to his or her purpose?

Step-by-step explanation:

Answer:

I can't see it

Step-by-step explanation:

you should zoom in a little bit please

Answer:

a

Step-by-step explanation:

Answer:

It b.

Step-by-step explanation:

You can use demos for this (graphing calculator. :)

Answer:

D is the answer

Step-by-step explanation:

Answer:

a) The building is 150 m tall

b) h(t)=-5(t+6)(t-5)

c) The stone hits the ground at 5 seconds.

Step-by-step explanation:

Function Models

The path of a stone thrown down from a tall building is modeled by the function:

[tex]h(t)=150-5t-5t^2[/tex]

Where h is the height in meters and t is the time in seconds after the stone is thrown.

a) To find the height of the building, we set t=0 because it's the moment when the stone is thrown and has the same height as the building:

[tex]h(0)=150-5*0-5*0^2[/tex]

[tex]h(0)=150[/tex]

The building is 150 m tall

b) The function is

[tex]h(t)=150-5t-5t^2[/tex]

Factoring out -5:

[tex]h(t)=-5(-30+t+t^2)[/tex]

Rearranging:

[tex]h(t)=-5(t^2+t-30)[/tex]

To factor the polynomial in parentheses, we must find two numbers whose product is -30 and sum is 1. We can also use the quadratic formula to find the roots and factor later.

These numbers are 6 and -5, thus the function is:

[tex]h(t)=-5(t+6)(t-5)[/tex]

c) The stone hits the ground when h=0:

[tex]-5(t+6)(t-5)=0[/tex]

The equation has two solutions:

t = -6

t = 5

The only feasible solution is t = 5, thus the stone hits the ground at 5 seconds.

Answer:

15 - 5x

Step-by-step explanation:

10 - 5(x - 1)

Multiply 5 by x and 1 using the distributive property.

10 - 5x + 5

Add like units. 10 + 5 = 15

15 - 5x is your final answer.

Answer:

60% Hope this helped! :)

Step-by-step explanation:

Answer:

Help me with my Physics lol

Answer: x=30

Step-by-step explanation:

Multiply both sides of the equation by 2 to cancel out the divide by 2.

x=15×2=30

Answer:

x=30

Step-by-step explanation:

2*x/2=15*2

x=30

Answer

6/x = 8.7

Step-by-step explanation:

let x = a number that we will find out

6/x = 8.7 (determinethe defined range)

6/8 = 8.7, x = 0 (multiply both sides)

6 = 8.7x (swap sides)

8.7 x = 6 (divide both sides)

x = 20/29

check

x = 20/29, x = 0

OR x = 0.689655

Answer:

x = 7

y = 2

Step-by-step explanation:

x² - y² = 45    

(x+y) (x-y) = 45

x + y = 9   (known)

9 x  (x-y) = 45

x - y = 5

y = x-5  

x + (x - 5) = 9  (substitute)

2x = 14

x = 7

y = 2

Answer:

p = 6

Step-by-step explanation:

3p - 4 = 14 / +4

3p = 18 / ÷ 3

p = 6

Answer:

B.

Step-by-step explanation:

perpendicular lines are the reciprocal and opposite of the slopes. the opposite and reciprocal of -4/5 is 5/4. B is the only one with that slope.

Answer:

2

Step-by-step explanation:

Answer:

8. yes, ASA

9. yes, SAS

10. yes, AAS

11. no

12. no

13. yes, SSS

Step-by-step explanation:

Answer:

1:3 I think

Step-by-step explanation:

3/3=1

9/3=3

Answer:

3/9 = 1/3

Step-by-step explanation:

simplifying