Lerna's Hydra is a mythological character that appears in some stories such as the 12 Tasks of Hercules. The Hydra was a one-headed monster but when it is cut off, 2 more heads grow in its place. If a hero tried to conquer it by cutting off all of its heads every day, how many heads would the Hydra have on the third day? And at the end of 10 days of trying to kill it? *

Answers

Answer 1

Answer:

Step-by-step explanation:

Initially the monster is one-headed, when it is cut off, 2 more heads grow in its place, when the two heads are cut off, 4 will grow in its place. This will go on an on and the amount of heads that grows each day will form a geometric sequance as shown;

1, 2, 4...

The nth term of an arithmetic sequence is expresses as;

[tex]T_n = ar^{n-1}[/tex] where;

a is the first term

r is the common ratio

n is the number of terms

To get the number of heads that the Hydra have on the third day, we will have to find the fourth term of the sequence since the first cutting was done the next day (second day).

from the sequence above;

a = 1

r = 2/1 = 4/2 = 2

T4 = 1(2)^{4-1}

T4 = 2^3

T4 = 8

Hence the hydra will have 8 heads on the third day.

To know the number of heads at the end of 10 days, we will find the 11th term of the progression

T11 = 1(2)^{11-1}

T4 = 2^10

T4 = 1024

He will have 1024 heads after 10 days of trying to kill the monster.

Answer 2

The number of heads that would the Hydra have on the third day is 8

And, at the end of 10 days of trying to kill it is 1024.

The calculation is as follows:

a = 1

r = 2 by 1 = 2  

T4

= 8

So the hydra will have 8 heads on the third day.

Now  

To know the number of heads at the end of 10 days, we will determine the 11th term of the progression

= 1024

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Related Questions

Select ALL the statements that are true about 22/7.
A.It is a rational number.
B.It is an irrational number.
C.When written as a decimal, it repeats.
D.It is an approximate value of Pi.
E.It is a terminating decimal.

Answers

Answer:

It is an approximate value of pi

−3(k+7)>−57 please help and solve

Answers

Answer:

k>12

Step-by-step explanation:

distribute -3 into the parenthesis

-3k-21>-57

add 21 on both sides

-3k>-36

divide both sides by -3

k>12

HOPE THIS HELPS!!!

Answer:

k < 12

Hope this helps!

y=3x y=18 solve for x

Answers

Answer:

6=x

Step-by-step explanation:

y= 18; y= 3x

18=3x

18/3 = 3x/3

6=x

Hope this helps!

X=6 because if you are trying to get the answer to 18 then you would do 18=3x and 18 decided by 3 is 6. And 6*3=18

Select the correct answer.
Jenny is tracking the monthly sales totals for her boutique. The given piecewise function represents the boutique's monthly sales, in dollars,
where x represents the number of months since Jenny began tracking the data.
(4,000(1.1)
0 < I<3
f(0) = 1001 + 5,024 , 3 - 2 + 5x + 5,630, 6 3
What were the boutique's monthly sales when Jenny first began tracking the data?
A.
$4,000
B.
$5,324
C.
$5,616
D.
$4,400
MacBOOK

Answers

Answer:

what is your question here can you be more specific?

Step-by-step explanation:

Answer:

Please mark me as Brainliest :)

Step-by-step explanation:

Please hurry it is urgent . Make sure to do 5 and 6

Answers

Answer:

5) 36

6) 113

Step-by-step explanation:

5)

As a reminder, complementary angles add up to 90; therefore, we can set up an equation:

(5x+4)+(3x+6)=90

8x+10=90

8x=80

x=10

Now that we know x, we can plug x as 10 into the original expression for angle A:

3(10)+6

=30+6

=36

6)

As a reminder, supplementary angles add up to 180; therefore, we can set up an equation:

(5x+8)+(3x+4)=180

8x+12=180

8x=168

x=21

Now that we know x, we can plug x as 21 into the original expression for angle D:

5(21)+8

=105+8

=113

Can someone tell me them least to greatest please!!!!!

Answers

Answer:

11/3 , 17 , 20 hope this helps

ax+bx=c solve for x

Answers

Answer:

x= c/a+b

Step-by-step explanation:

How many subscribers will there be in week 9 if the initial number of subscribers is 10?

Answers

Answer:

if the number of substribers has a constant rate of change than the number of subscribers in 9 weeks should be around 90

56 men can do a work in 42 days then how many men will do the same work in 14 days ​

Answers

Given : 56 men can do a work in 42 days .

To Find : In how many men will do the same work in 14 days .

Solution : We will use Unitary method here to solve the above problem . This is a case of inversely proportional that is when one will increase the other will decreases . Here if the number of men will increase then the number of days will decrease and vice - versa .

If in 42 days 56 men can do the work ,

Then in 1 day 42 × 56 men can do the work .

Then in 14 days , [tex]\sf \dfrac{42\times\cancel{56}}{\cancel{14}}[/tex] will do the work = 168 .

Hence 168 men will do the work in 14 days .

[tex]\Large\boxed{\red{\bf Answer = 168 \:men}}[/tex]

Work out the volume of this sphere. Radius is 4cm
Give your answer rounded to 1 DP.

Answers

Answer:

268.08257

Step-by-step explanation:

v=4/3πr^3=4/3•π•4/3=268.08257

10x+y when x = 7 and y = 5

Answers

Answer: 75

Step-by-step explanation:

Plug in 7 for x and 5 for y

10(7)+5

70+5

75

What is 25 percent of 530?

Answers

It’s gonna be 132.5


:)))))))

Which illustration shows the correct construction of an angle bisector?

Answers

 Option (3) will be the correct construction of the angle bisector.

   Steps to construct an angle bisector are as followed,

Step - 1

Put the compass at the vertex of the angle.

Step - 2

Draw an arc cutting both the arcs at two distinct points.

Step - 3

Draw two arcs from these points intersecting at a point.

Step - 4

Join the vertex and the point of intersection formed in step - 3 which will be the angle bisector.

     Therefore, Option (3) will be the correct option.

Learn more,

https://brainly.com/question/8607612

Given that R = 3x + 9y
Find x when y = 6 and R=7
Give your answer as an improper fraction in its simplest form.​

Answers

Answer:

Step-by-step explanation:

R = 3x + 9y

They told us that R = 7, y = 6

So you can rewrite the equation as:

R = 3x + 9y

7 = 3x + 9(6)

7 = 3x + 54

Subtract 54 from both sides.

7 - 54 = 3x

-47 = 3x

To find x, you need to divide both sides by 3

3x = -47

x = -47/3

PLEASE HELP!
Solve x2 + 5x = −6.

x = 5 and x = 1
x = −5 and x = −1
x = 3 and x = 2
x = −3 and x = −2

Answers

X^2 + 5x = -6

Add 6 to both sides:

X^2 + 5x + 6 = 0

Using the quadratic equation x = -b +/-sqrt(b^2 -4ac )/2a replace the letters with their values and solve for x.

A = 1, b = 5 , c = 6

Solving for x you get -2 and -3

The answer would be x = -3 and x = -2

A certain star is 5.2 x 10^2 light years from the Earth. One light year is about 5.9 x 10^12 miles. How
far from the earth (in miles) is the star?

Answers

the correct answer is 5.89999999948*10^12

please answer i need help

Answers

Answer:

h < 2

Step-by-step explanation:

Given

5(2h + 8) < 60 ( divide both sides by 5 )

2h + 8 < 12 ( subtract 8 from both sides )

2h < 4 ( divide both sides by 2 )

h < 2

Answer:

h<2

Step-by-step explanation:

5(2h+8)<60

2h+8<12

2h<4

h<2

how do i to find the slope

Answers

Answer:

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points .

Step-by-step explanation:

Answer:

The equation to find slope is y=mx+b. Find two points in the line that are clear. subtract x1 and x2 and y1 and y2. Plug in the x and y values of one into the equation. b is equal to y when x is 0

Step-by-step explanation:

Solve for the value of x that makes likes r and s parallel.

Answers

Answer:

x = 65

Step-by-step explanation:

If Alternate exterior angles are congruent, r and s will be parallel

3x - 63 = 2x + 2

3x - 2x  - 63 = 2

         x - 63 = 2

            x  = 2 + 63

            x = 65

Describe the Squeeze Theorem as simply as possible.​

Answers

Hey there,

The squeeze theorem shows if [tex]f(x)\leq g(x)\leq h(x)[/tex] for all real numbers [tex](-\infty,~\infty)[/tex] then f(x) = h(x) but g(x) has to equal that as well.

Let's say we have [ [tex]\lim_{n \to \infty} (\frac{cos~x}{x})[/tex] ]

~Apply the theorem

Note that [ [tex]-1 \leq cos~x \leq 1[/tex] ] and [ [tex]\lim_{n \to \infty} (-\frac{1}{x})\leq \lim_{n \to \infty} (\frac{cos~x}{x})\leq \lim_{n \to \infty} (\frac{1}{x})[/tex] ]

~Apply the infinity property to every side but the middle

[tex]\lim_{n \to \infty} (-\frac{1}{x}) = 0[/tex]

[tex]\lim_{n \to \infty} (\frac{1}{x}) = 0[/tex]

So... [tex]\lim_{n \to \infty} (\frac{cos~x}{x})=0[/tex]

Best of Luck!

Triangle XYZ is reflected across the y-axis to create triangle PQR (not shown).
What is the measure, in degrees, of angle R

Answers

Answer:

The measure of ∠R = 60°

Step-by-step explanation:

The given parameters are;

Triangle XYZ is reflected across the y-axis to create triangle PQR

The measure of ∠Y = 30°

Triangle XYZ = A right triangle

The measure of ∠X = 90°

Where we have;

The image of the preimage of vertex X = P

The image of the preimage of vertex Y = Q

The image of the preimage of vertex Z = R

Therefore, given that a reflection is a rigid transformation, we have;

The measure of ∠X = The measure of ∠P

The measure of ∠Y = The measure of ∠Q

The measure of ∠Z = The measure of ∠R

Given that the measure of ∠Y = 30° and the measure of ∠X = 90°

∠X +∠Y + ∠Z = 180° (angle summation of a triangle property

∴ The measure of ∠Z = 180° - (∠X + ∠Y)  = 180° - (90° + 30°) = 60°

Therefore;

The measure of ∠Z = 60° = The measure of ∠R

The measure of ∠R = 60°.

−184 is the product of 23 and p.

Answers

I believe the correct answer would be -203

Answer:

p= -8

Step-by-step explanation:

23 x p= -184

-184 divided by 23= -8

23 x -8= -184

Usually, when Elena makes bird food, she mixes 9 cups of seeds with 6 tablespoons of maple syrup. However, today she is short on ingredients. Think of a recipe that would yield a smaller batch of bird food but still taste the same.
Group of answer choices

3 cups of seeds and 5 tablespoons of syrup

2 cups of seeds and 3 tablespoons of syrup

5 cups of seeds and 2 tablespoons of syrup

3 cups of seeds and 2 tablespoons of syrup

MATH
6TH GRADE
GIVING AWAY FREE BRAINLIEST

Answers

Answer:

3 cups of seeds and 2 tablespoons of syrup

Step-by-step explanation:

Compare the ratios to the original one (9:6) see what is equal. In order, they are:

3:5

2:3

5:2

3:2

Look!

3:2 is equal to 9:6 because:

9 ÷ 3 = 3

and

6 ÷ 3 = 2

Hope this helped!

Answer:

thanks for the free points britt

Step-by-step explanation:

people wont solve my question i need it ASAP

Answers

Answer:

A pig has 10,000 kg mass more than a mass

Step-by-step explanation:

[tex]\frac{2*10^{2}}{2*10^{10}}=\frac{10^{2}}{10^{-2}}\\\\=10^{2}*10^{2}\\\\=10^{2+2}\\\\=10^{4}\\\\=10000[/tex]

which one does not belong ?

and what is the answer correct ?​

Answers

Answer:

5/4

5/4 = 1 1/4

It does not belong here

Step-by-step explanation:

Answer:

5/4 because the top is bigger than the bottom

help me plz thank you

Answers

Answer:

4^5,6^7,8^6,7^4

Step-by-step explanation:

add the power to the other and then put the base

Can someone please give me a free disney plus account

Answers

Answer:

Uh- I cant ;w;

Step-by-step explanation:

Answer:

yes I can if you still want one

Step-by-step explanation:

HELP PLEASE & I WANT EVERY STEP THIS MY GRADE NOT YA'LLS

Brian rides his bike 0.27 of a mile per min. If it takes him 27 mins to ride his bike to his friends house, how far away does his friend live ?

Answers

Answer:

7.29 miles

Step-by-step explanation:

In 1 minute, Brian rides his bike for 0.27 of a mile.

in 27 mins the distance is going to be more than the other ( i.e 0.27 miles)

We use the proportion then get a solution

1 min = 0.27 miles

27 mins = (27 mins÷ 1 min) × 0.27

= 27 × 0.27 miles

= 7.29 miles

Step-by-step explanation:

Given parameters:

  Speed of the Brain's bike  = 0.27mile/min

Time = 27min

Unknown:

distance between Brain's house and where his friend lives =?

Solution:

Speed is a physical quantity.

   It is mathematically expressed as'

     Speed  = [tex]\frac{distance}{time}[/tex]

   Distance  = speed x time

  Input the parameters;

    Distance  = 0.27mile/min x 27min  = 7.29miles

PLSSS HELPPP ASAPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!

An underground mine elevator descends 12% of the total depth every minute. The total depth of the elevator is 75 meters below the ground. How many meters below the ground is the elevator after 2 minutes?

1. −18 meters
2. −9 meters
3. −4.5 meters
4. −22.5 meters

Answers

Answer:

I believe its 1. -18 meters

Step-by-step explanation:

first find how many meters the elevator is descending per minute. to do this:

what is 12% of 75?

(75×.12) = 9

the elevator is descending 9 meters per minute.

9×2=18

The equation a = StartFraction one-half EndFraction left-parenthesis b 1 plus b 1 right-parenthesis.(b1 + b2)h can be used to determine the area, a, of a trapezoid with height, h, and base lengths, b1 and b2. Which are equivalent equations? Check all that apply.

Answers

Answer:

It's a &d

Step-by-step explanation:

The required Area of trapezoid(a) = 1/2(b1+b2)h.

What is quadrilateral?

Quadrilateral is four sided shape as given in the picture in question.

Question seems to be incomplete. So the correct option resembles with
Area of trapezoid a = 1/2(b1+b2)h

Thus, the required area of trapezoid
a
= 1/2(b1+b2)h

Learn more about quadrilateral here:
https://brainly.com/question/13805601

#SPJ2


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