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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:

5/8

Step-by-step explanation:

1/4+3/8=5/8

Answer:

wait what do you want to know?

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

Answer:

x= -1

Step-by-step explanation:

4 (2x + 3) = 6x + 10

8x+12=6x+10

8x+12-12=6x+10-12

8x=6x-2

8x-6x=6x-2-6x

2x=-2

x= -1

Answer:

p = 6

Step-by-step explanation:

3p - 4 = 14 / +4

3p = 18 / ÷ 3

p = 6

Answer:

3 friends played golf.

Step-by-step explanation:

Answer:

b i am pretty sure

Step-by-step explanation:

Direction, displacement, and distance are the measurements are necessary for determining both the speed and velocity of a moving object

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

The measurements which are necessary for determining both the speed and velocity of a moving object.

Speed=Distance/Time

To calculate speed we need to know the distance and time.

Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference

Velocity=Displacement / Time

Hence  Direction, displacement, and distance are the measurements are necessary for determining both the speed and velocity of a moving object

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

Hey there!

The answer is $48.44

We can solve this by first finding how much the discount is.

0.25 x 59.80

14.95

The amount of the discount is 14.95, so we then take the discount off.

59.80 - 14.95

44.85

Then, we find the amount of tax.

.08 x 44.85

3.588 (round to nearest cent = 3.59)

Then, add the price of the tax onto the price of the jeans.

3.59 + 44.85

48.44

Hope this helps! Good luck!

Answer:

Y=4

Step-by-step explanation:

The line is horizontal, which means that variable would be 4. The line starts at 4, which mean the equivalent of the variable is 4.

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:

4 quizzes are taken per week

Step-by-step explanation:

12/3=4

20/5=4

Answer:

sorry but can u give me full question

Step-by-step explanation:

like picture

Answer:

She would need to play AT LEAST 15 games

Step-by-step explanation:

If she wants to score 90 points or above in a season she would have to play at least 15 games because, 90 divided by 6 (How many points she scores) equals 15.

Answer:

This is what I got

Step-by-step explanation:

1. Is decreasing so therefore is negative

2. Is undefined, Changed but is neither negative or positive

3. Is zero because it just stays the same

4. Is increasing therefore is positive

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:

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:

The x is the domain and the y is the range. It's still a function

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

It b.

Step-by-step explanation:

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

Answer:

It can be simplified to: -4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

combine like terms 8n-8n-6+2

8n-8n=0 so

-6+2=-4

Answer:

c) 100

Step-by-step explanation:

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.

Answer:

The answer is B

The numbers -2.23   [tex]-2\frac{2}{5}[/tex], and -0.95 are numbers that are less than -0.94 option (B) is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have a number list:

-15/16, 0.24, -2.23, 97%, [tex]-2\frac{2}{5}[/tex], -0.95

We can write these numbers such as:

-0.9375, 0.24, -2.23, 0.97, -2.4, -0.95

Now comparing the each number with -0.94

-0.9375 > -0.94

0.24 > -0.94

-2.23 < -0.94

0.97 > -0.94

[tex]-2\frac{2}{5}[/tex] or -2.4 < -0.94

-0.95 < -0.94

Thus, the numbers -2.23   [tex]-2\frac{2}{5}[/tex], and -0.95 are numbers that are less than -0.94 option (B) is correct.

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Answer:

27

Step-by-step explanation:

Answer:

$55.50 for three shirts

Step-by-step explanation:

The computation is shown below:

For this question we calculate the average for both the options

For the first option, the average is

= $55.50 ÷ 3 shirts

= $18.50 per shirt

For the second option, the average is

= $79.99 ÷ 5 shirts

= $15.998 per shirt

As per the above calculation, the first option is to be best deal as the amount per shirt is high so the same is to be selected