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Reproduce the proof. When n = 1, we have

n³ + 2n = 1³ + 2 = 3

which is clearly divisible by 3.

Assume n³ + 2n is divisible by 3. Then for the next natural number n + 1, we have

(n + 1)³ + 2 (n + 1) = n³ + 3n² + 3n + 1 + 2n + 2

= n³ + 2n + 3 (n² + n + 1)

The first two terms n³ + 2n are divisible by 3 according to our assumption, and 3 (n² + n + 1) is clearly a multiple of, and therefore divisible by, 3 as well.

So the claim that 3 divides n³ + 2n is true for all natural numbers n.

Answer:

275mm = 27.5cm

1,000L = 1 kL

Hope this helps :)

275mm= 27.5cm and 1000L= 1KL

Step-by-step explanation:

For 257mm to get to 27.5cm, you have to divide the length value by 10 and so it becomes 27.5. Also for 1000L to become to 1KL you have to divide the volume value by 1000.

Answer:

x = 11

Step-by-step explanation:

∠ EAB = ∠ AED = 4x ( alternate angles )

∠ AEB and ∠  GEB are adjacent angles on a straight line and sum to 180° , so

∠ AEB + 125° = 180° ( subtract 125° from both sides )

∠ AEB = 55°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ EBC is an exterior angle of the triangle , then

∠ EBC = ∠ AEB + ∠EAB , that is

9x = 55 + 4x ( subtract 4x from both sides )

5x = 55 ( divide both sides by 5 )

x = 11

Answer:n = 20

Step-by-step explanatio

0.4 * n = 8

n = 8 / 0.4

n = 20

The equation represents 0.4n = 8 and the solution will be n = 20.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given,

Product of 0.4 and n is 8.

0.4n = 8

n = 8/0.4

n = 80/4 = 20

Hence "The answer will be n = 20 because the equation says that 0.4n = 8".

For more about the number system,

https://brainly.com/question/22046046

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Step-by-step explanation:

[tex]\displaystyle \rm -2z+3-z=-4z+2 \\\\ -3z+3=-4z+2 \\\\ 4z-3z=-3+2 \\\\ \underline{z=-1 \ \ \ \ } \\\\[/tex]

[tex]\large{\rm{\underline{\underline{Answer:}}}}[/tex]

Given to solve: -2z+3-z = -4z+2

⇛ -3z + 3 = -4z + 2

⇛ -3z + 4z = 2 - 3

⇛ z = -1

Required value of z is -1. The steps we followed are: We shifted z to a single side and other numbers to other side. Then we equated to get the result.

(-9,6) and (-3,2) help pls

Answer : -12.8

Answer:

3.9X10^-4

Step-by-step explanation:

The value is increasing so your exponent increases

Answer:

6 full days

Step-by-step explanation:

550-40=510

510/85=6

Answer:

you could rent the car for 6 full days.

Step-by-step explanation:

first you would do 85x5=425 and you know that gets you close so then you would do 85x6=510+40=550

Answer:

The leading coefficient of the function shown is negative and the function shown has a maximum vertex point.

Step-by-step explanation:

The leading coefficient is the term with the highest degree in a polynomial.

For example in 4x² + 3x + 1 the leading coefficient would be 4x² as 4x² is the term with the highest degree.

The leading coefficient tells us whether the equation, when graphed, will rise or fall.

If the leading coefficient is negative then the equation will fall when graphed, in contrast if the leading coefficient is positive the equation will rise when graphed.

Looking at the graph, it appears that the equation is falling, meaning that the leading coefficient must be negative.

If the equation falls then it has a maximum point, if it rises then it has a minimum point.

Because the equation shown falls it will have a maximum point.

Answer:

B and C

Step-by-step explanation:

I hope you find this helpful

Answer: 2

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

If u // v, then

19x - 3 = 130   {Corresponding angles are congruent}

19x = 130 + 3

19x = 133

x = 133/19

x = 7

Answer:

The three dollar

Step-by-step explanation:

for the three dollar one its 25% off and the 5 dollar one is 20% off

Answer:

it takes me 14 minutes to go to class

Answer:

a. [tex]\boxed{y=-3x+16}[/tex]

b.[tex]\boxed{y=\frac{1}{3}x+1}[/tex]

Step-by-step explanation:

a.[tex]y-10=-3(x-2)[/tex]

[tex]\rightarrow y=-3x+6+10\\\rightarrow \boxed{y=-3x+16}[/tex]

b. [tex]y-2=\frac{1}{3}(x-3)\\\rightarrow y=\frac{1}{3}x-1+2\\\rightarrow \boxed{y=\frac{1}{3}x+1}[/tex]

Answer:When x=16 , y=36 . Explanation: If y varies directly as x , then if y increases, x increases, and if y decreases, x decreases.

Step-by-step explanation: because

Answer:

tence there will be 6,00 insects abter 8 weeks.

Step-by-step explanation:

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

30+20%=36

Answer:

-48, -96

Step-by-step explanation:

Pattern: The terms double as they go on.

Answer:

Tn=ar^(n-1)

a=first term

r=common ratio

Tn= term n

a= -6

r= -12÷-6 = 2

T4= -6(2)^(4-1) =48

T5= -6(2)^(5-1) =96

Answer:

x = 7

Step-by-step explanation:

The sum of exterior angles in a polygon is 360°.

( 11x - 5 )° + ( 4x + 29 )° + ( 6x + 13 )° + ( 9x - 15 )° + 67° + 61° = 360°

30x + 22 + 128 = 360

30x = 210

x = 7

Answer:

He will have $1092 in 4 years.

Step-by-step explanation:

700 x 0.14 = 98

98 x 4 = 392

700 + 392 = 1092

Answer: The filled out chart is shown below.

===========================================================

Explanation:

For each row, we divide the number of locations over the population count. Treat the population values in millions. Something like 35.2 million means 35,200,000 which is the same as writing 35.2*10^6 when using scientific notation. I prefer to stick to scientific notation.

In the first row, they computed 1460/(35.2*10^6) = 0.0000415 = 4.15*10^(-5); the last entry of 4.15 for this row represents having 4.15 stores for 100,000 people. In other words, we chop off the 10^(-5) portion in 4.15*10^(-5). This is because the 10^(-5) portion represents "1 out of 100,000".

The other remaining rows are handled the same way. I'll show the steps for the second row

Like the previous row, each value is approximate.

Check out the table below. The stuff in gray represents the new entries that were previously blank.

Answer:

Slope of the parrelel line: -2/3x

Slope of the perpendicular line: 3/2x

Step-by-step explanation:

Lets first put this into slope intercept form:

y = mx + b

9y = -6x - 1

y = -2/3x = 1/9

So our slope is -2/3x

If we have a line parrelel to this, it means it has the exact same slope, but a different b value.

So the slope of this parellel line would also be -2/3x

Next we need to find the slope of the perpendicular line.

This is the exact opposite of our slope.

To find this, lets first understand our slope.

Our slope is the change in y over the change in x:

Δy/Δx

A perpendicular line is going to be the flipped, and negative of this.

You can think of a perpendicular line being:

-Δx/Δy

Since our slope is -2/3x

Our perpendicular line would be 3/2x

So our answer for the second question is 3/2x

Useful things to remember:

Hope this helps!

Answer:

7375

24

Step-by-step explanation:

c=5500+125(15)

c=7375

8500=5500+125n

A is the scale or vertical stretch

H is what makes it move right or left.

K is what makes it move up or down.

a = 1

h = -2

k = -7

y = (1) (x-(-2))² + (-7)

y= (x + 2)² -7

(Also, you will learn b in the equation. The equation would be a(b(x-h))² + k. B would be about horizontal compression.)