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

HELPPP 16 POINTS. It was estimated that 325 people would attend game night, but 315 people actually attended.
What is the percent error, to the nearest percent, of the estimate? Enter the answer in the box.

Answers

Answer:

3%

Step-by-step explanation: 315/325 as a percent would be 96.92%. After finding that, we would do 100 - 96.92, yielding 3.08, 3.08 to the nearest percent would result in 3%

Answer:

the answer to the nearest percent is 3%

will you guys help me with anything i need?


(don't listen about the subject for now i just need to know)

Answers

Answer:

Ummm yeah , i'm literally a nice person and a good listener .

Step-by-step explanation:

Can i pls have brainly ? <3

Answer:

yes

Step-by-step explanation:

hjoyybhfddsjjsjajajdhvdbenwkwq

What exponent should you use to represent the power of 10 below?
10,000,000 = 10?

Answers

Answer:

10^6

Step-by-step explanation:

Answer:

[tex]10 {}^{6 } = 10000000[/tex]

It helps you ☺️☺️

Thank you ☺️☺️

How do you write something in slope intercept form?

Answers

Answer:

Slope-intercept form is y=mx+b. You find the slope of the line and you plug that in for m. Then you find the y-intercept, which is where the line crosses the y-axis, and plug that in for b.

Step-by-step explanation:

What is the range of the following numbers?
12, 20,18,25, 6
O A 5
OB. 164
O C. 18
O D. 19
O E. 25

Answers

D. 19 Hope this helps :)

Find the Highest Common Factor (HCF) of 196 and 12

Answers

Answer:

The greatest common factor is 4

Step-by-step explanation:

1.Find the prime factorization of 12

         a) 12 = 2 × 2 × 3

2.Find the prime factorization of 196

         a) 196 = 2 × 2 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

          a)GCF=2x2

Therefore, GCF = 2 × 2

GCF = 4

The greatest common factor of the numbers 196 and 12 is 4.

What is the greatest common factor?

The largest factor of the two numbers which divides both numbers is called as greatest common factor or GCF. The greatest common factor is the largest number which can divide both the numbers.

1. Find the prime factorization of 12

12 = 2 × 2 × 3

2. Find the prime factorization of 196

196 = 2 × 2 × 7 × 7

To find the GCF, multiply all the prime factors common to both numbers:

GCF=2x2

GCF=4

Therefore, the greatest common factor of the numbers 196 and 12 is 4.

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Need help (don’t give me inn correct answer and don’t comment if you don’t know)

Answers

Answer:

I believe that the answer is number 2

Step-by-step explanation:

5x - 2y= 26 y + 4 = x
Plzzz help I got 10 minutes

Answers

the answer is (x,y) = (4/51 - 8/51)

The Value of x and y are (x,y) = (7,3).

What is Algebraic expression ?

Algebraic expressions are numbers expressed using letters or alphabets without specifying their values. Algebra taught us how to express unknown values using letters such as x, y, and z. There can also be a single value that is placed before and multiplied by a variable in an algebraic expression in addition to these letters, which are called variables.

GIven equations are :

5x - 2y= 26.....(1)

y + 4 = x..........(2)

Solve by substitution :

substitute equation 2 in equation 1 and solve for y

5x - 2y= 26

5(y+4) - 2y = 26

5y + 20 -3y = 26

2y = 26 - 20

2y = 6

y = 3

now, the value of x will be :

x = y + 4

x = 3+4

x = 7

Therefore, The Value of x and y are (x,y) = (7,3).

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Chase and sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of gum for 5.70. Sara bought 2 pieces of fudge and 10 pieces of gum for 3.60. Determne If I were to buy 20 pieces of fudge and 20 pieces of bubble gum, it would cost me $

Answers

Let, price of fudge and gum is x and y respectively.

Converting given statements into mathematical equation.

We get :

5x + 3y = 5.70  ....1)

2x + 10y = 3.60 ....2)

Solving equation 1 and 2, we get :

x = $1.05 .

y = $0.15 .

Price of buying 20 pieces of fudge and 20 pieces of bubble gum is :

P = 20( 1.05 ) + 20( 0.15 )

P = $24

Hence, this is the required solution.

-4 5/6 + (3 1/3) =
How dI you do this?

Answers

they should have common denominators so 1/3 turns into 2/6 and - 5/6 + 2/6 is -3/6 simplify that to -1/2 and -4 + 3 is -1 so the answer is -1 1/2

Ellie ordered 3/4 of a pound of cheese from the deli. The deli has cheese slices that weigh 0.05 pounds each. Enter the number of cheese slices Ellie will receive.

Answers

Ellie will receive 15 slices of cheese.

Some please help me!!! please I need it in 20 minutes!!!!

Answers

4. Acute triangle

5. Equilateral triangle

6. Right triangle

7. Acute triangle

8. Right triangle

9. Obtuse triangle

10. Obtuse triangle

11. Acute triangle

12. Acute triangle.

Those are all the answers I know. I'm pretty sure someone might do the rest.

4) Scalene Triangle
5) Equilateral Triangle
6) Isosceles Triangle
7) x= 93
8) x= 91
9)x=115
10)x= 115
11) x= 58
12)x= 75
13) x= 23
14) x= 51
15) x= 40

Can I get the brainliest !!
Thank you

2b^3+5=2(3)^3+5 when b=3

Answers

Answer:

59

Step-by-step explanation:

I got it right on I-Ready

The required simplified value of the given expression is 21.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here, given expression,
= 2b³+5

Now put b = 3
= 2(2)³ + 5
= 2(8) + 5    [since 2³ = 8]

= 16 + 5
= 21

Thus, the required simplified value of the given expression is 21.

Learn more about simplification here:

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What percent is equivalent to 14/25?

Answers

Answer:

56%

Step-by-step explanation:

Answer:

56%

Step-by-step explanation:

[tex]\frac{14}{25} = \frac{56}{100}[/tex]   15/100 = 56%

I hope this helps!

Layla read 1 book in 4 months. What was her rate of reading, in books per month? Give your answer as a whole number or a FRACTION in simplest form.

Answers

Answer:

1/4 books per month.

Step-by-step explanation:

1 book in 4 months means you have to do 1 divided by 4 which equals .25. After converting to a fraction you get 1/4.

If f(x) = -3x + 8
find f(0) = ?

Answers

I believe the answer is 8
Pls mark brainliest if correct
I think the answer would be 8 :)

look at the photo: please help

Answers

Answer:

3.66666666667

Step-by-step explanation:

I calculated it

Answer:

2 1/3

Step-by-step explanation:

4 + (-1 2/3) = 2 1/3

I need help with this please

Answers

Answer:

b

Step-by-step explanation:

Answer:

The answer is B. since the m on the bottom is negative you are taking it away. You basically just combine your variables to make the equation.

Step-by-step explanation:

Solve the simultaneous equations.
You must show all your working.
2x+1/2y =13 ---its 1 devided by 2
3x +2y = 17​

Answers

Answer:

I hope it solve the problem

A train is traveling at 50 miles per hour. What is the train?

Answers

Answer:

The speed of the train = 50 mph = 50*1.61 = 80.5 km/hr = 80.5*1000/3600 = 22.36 m/s. The speed of a train is 54 km/h excluding its halting time.

Hope this helps! :)

Use rounding to estimate the sum.

Estimate the sum.
78.9+71.2

Answers

Answer:

150

Step-by-step explanation:

add 79+ 71 because you rounded to get that number then add :)

150

When estimating you just round off the numbers so, 78.9 becomes 79 and 71.2 becomes 71 so, 79 + 71 = 150.

The points F, G, H and I all lie on the same line segment, in that order, such that the
ratio of FG : GH: HI is equal to 3 : 2: 4. If FI = 18, find FH.

Answers

Answer:

10

   

Step-by-step explanation:

    Given line:

              F       G       H        I

         

 FI  = 18

Unknown:

FH = ?

Solution:

To find the line FH, we use the ratio given;

               FG : GH: HI

               3    :   2  : 4 ; Total  = 3 + 2 + 4 = 9

  Since FI is 18;

FH  = [tex]\frac{3 + 2}{9}[/tex]  x 18 = [tex]\frac{5}{9} x 18[/tex]  = 10

FH  = 10

   

PLEASE HELP AND QUICK!!!

Answers

Answer:

A

Step-by-step explanation:

dude trust me

Simplify the expression (x^2+3x-28)/(x^2+10x+ 21). Show your work.
NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors.

Answers

Answer:

(x-3) (x-7)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +21  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 21 = 21  

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   -10 .

     -21    +    -1    =    -22  

     -7    +    -3    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -3  

                    x2 - 7x - 3x - 21

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x-3)  •  (x-7)

            Which is the desired factorization

A prism has 10 vertices.How many edges does it have?

Answers

15 edges, and 10 vertices.

Answer:

do you men triangular prism is 6 edges

PLEASE ANSWER!! Quadrilateral PQRS is shown on the coordinate plane.

Answers

Answer:

i have no idea

dont spam "please answer" its not cool

Pls answer for brainliest!

Answers

Answer:

h<2

Step-by-step explanation:

5×2h+5×8<60

10h+40<60

10h<60-40

10h<20

10. 10

h<2

Answer:

Step-by-step explanation:

5(2h + 8) < 60

10h + 40 < 60

10h < 30

h < 3

find the midpoint of the line segment joining the points. (6, -5), (6, 3)

Answers

Answer:

The mid point is (6,-1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

3-5/2

6-6/2

-2/2=-1

0/2= 0

(-1,0)

Solve: 3(g − 2) = 8

Answers

Answer:

g=4⅔

Step-by-step explanation:

3(g - 2)=8

3g -6 = 8

3g= 8+6

3g= 14

[tex] \frac{3g}{3} = \frac{14}{3} [/tex]

g=4⅔

hope this helps

Step-by-step explanation:

3(g - 2) = 8

3(g - 2) = 8

+ 2 +2

3g = 8

3÷3= 0 8÷3 = 4.6

so your answer will be g= 4.6 (5 if you round it up) or if you need it in fraction form it will be 4 and 2/3

HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!
please..

Answers

Answer:

53 1/5

Step-by-step explanation:

Make 5 7/10 and 9 1/3 into a fraction which is 57/10 and 28/3

Then multiply the numerators together and the denominators which gives you 1596/30

Simplify by dividing it by 6 getting 266/5

Change to a mixed number 53 1/5

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