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

the function f(x) is shown in this graph
the function g(x) = -6x -5

Answers

Answer:

C.

Step-by-step explanation:


Is this a function? Explain

Answers

Answer:

Yes

Step-by-step explanation:

The only reason a graph will not be a function is if it doesn't pass the vertical line test. In other words, if you draw a vertical line at any point, it will never pass through more than 1 point.

In that case, that is true, so it must be a function.

Determine the domain, range and whether each table represents a function.​

Answers

The domain is the possible x values- so it is 1,2,3 .
The range is the possible y values- which are 4,6,8 .
Yes it does represent a function because each element of X is related to ONE element of y.

Hope that helped!
Domain = {1,2,3}Range = {4,6,8}This is a function

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

Explanation:

The domain is the set of all possible x values. The range is the set of all possible y values.

Since we don't have any repeated x values, we have a function. Any given input x leads to exactly one y output value. Visually plotting the points leads to the graph passing the vertical line test, which shows the relation is a function.

what is (3,0) reflected on the y-axis

Answers

Reflecting across the y axis, the x value becomes opposite and the y value remains the same.

(3,0) becomes (-3,0)

Answer:

(-3, 0)

Step-by-step explanation:

There is the same amount of units from either side of the y-axis to the points.

HELPPP

Given h(x) = 2x + 2, solve for x when h(x) = 4.

Answers

Answer:

x = 1

Step-by-step explanation:

2x + 2 = 4

2x = 2

x = 1

2x + 2 = 4
2x = 2
x = 1

Point AAA is at {(1, 5)}(1,5)left parenthesis, 1, comma, 5, right parenthesis and point CCC is at {(-5,-7)}(−5,−7)left parenthesis, minus, 5, comma, minus, 7, right parenthesis. Find the coordinates of point BBB on \overline{AC} AC start overline, A, C, end overline such that ACACA, C is 666 times as long as ABABA, B.

Answers

Answer:

(0, 3)

Step-by-step explanation:

If a point O(x, y) divides a line XY in the ratio n:m with [tex]X\ at\ (x_1,y_1)\ Y\ at\ (x_2,y_2)[/tex], the coordinates of O is:

[tex]x=\frac{n}{n+m} (x_2-x_1)+x_1\\\\y=\frac{n}{n+m} (y_2-y_1)+y_1[/tex]

AC is 6 times AB, this means that point B, divides line AC in the ratio 1:5. Given A at (1,5) and C at (-5, -7)

Let us assume B to be at (x, y), hence:

[tex]x=\frac{1}{1+5}(-5-1)+ 1=\frac{1}{6}(-6)+1 =0\\\\y=\frac{1}{1+5}(-7-5)+5=\frac{1}{6} (-12)+5=3[/tex]

Therefore the location of B is (0, 3)

Answer:

(0, 3)

Step-by-step explanation:

someone please help me with this! please write out the steps as well, thank you!

Answers

Answer:

60°

140°

Step-by-step explanation:

From the given figures,

 a. we use the concept of alternate angles.

   Two parallel lines cut by a transversal will have equal alternate angles;

  So;

       6x + 12 = 7x + 4

    collect like terms and solve for x;

     6x - 7x = 4 - 12

         -x = -8

         x = 8

Now, 6x + 12 = 6(8) + 12

                     = 48 + 12

                     = 60°

b. Here we use alternate angles and angles on a line;

     4x is an alternate angle to that angle to the left of 13x + 10

   

And sum of angles on a line = 180

    4x + 13x + 10 = 180

        17x = 170

          x = 10

Now,  13x + 10 = 13(10) + 10 = 140°

describes the end behavior of the graph.

Answers

Answer:  B) [tex]+\infty[/tex]

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

Explanation:

As x goes to positive infinity, we're moving forever to the right.

If we have a point on the curve, then the point will move to the right and it will also move upward forever.

So as [tex]x \to \infty[/tex] we have [tex]y \to \infty[/tex]

Because y = f(x), this is the same as saying [tex]f(x) \to \infty[/tex]

The notation [tex]+\infty[/tex] is the same as [tex]\infty[/tex]

In terms of words, we can say "the curve rises to the right" to describe the end behavior on the right.

Which statement(s) apply to stratified random sampling? Check all that apply.

A) It can provide better estimates than a simple random sample.
B) The researcher needs some knowledge of the population in terms of characteristics relevant to the study.
C) A challenge is that it is necessary to have strata of the same size.
D) Creating strata of similar individuals to sample from reduces variability.
E) It can be difficult to obtain with a very large population.

Answers

Answer:

The correct options are;

A) It can provide better estimates than s simple random sample

B) The researcher needs some knowledge of the population in terms of characteristics relevant to the study

E) Creating strata of similar individuals reduces variability

Step-by-step explanation:

In order to reduce the variance in the population being studied the stratified sampling technique is used which consists of separating the given sample from the population into different strata based on known characteristics and finding out the result of the experiment in each strata. Each strata posses a common or shared attribute such as educational level or total level of income.

The statements that apply to stratified random sampling are;

A) It can provide better estimates than a simple random sample.

B) The researcher needs some knowledge of the population in terms of characteristics relevant to the study.

D) Creating strata of similar individuals to sample from reduces variability.

E) It can be difficult to obtain with a very large population.

Stratified random sampling is a method of sampling from a population that involves dividing the entire population into homogeneous groups that called strata.

The way it is done is that a random sample from each stratum is usually taken in a number that proportional to the size of the stratum if we compare it to the population size.

From the definitions above, the options that apply are, A, B, D and E.

Read more about stratified random sampling at; https://brainly.com/question/1954758

Find the area of the rectangle contained within the following four lines

x =1, x = -2 , y= -3, y=2



How do you do this please help with this question pleaseeeeeee if you give good explanation I will make you brain list thing. This is a linear relation ship question. PLEASE HELP WITH THIS QUESTION

Answers

Answer:

should be 15 hope I helped you out.

Step-by-step explanation:

Answer:

15 sq unit

Step-by-step explanation:

Easiest way to understand this question is to plot the lines on the graph which will give you a rectangle with four sides at given points.

the length of the said rectangle will be l = 1 + (-2)

and the breath b = 2 + (-3)

Area= lxb = 15 sq.unit

The distance required to stop a car varies
directly as the square of its speed. If 250
feet are required to stop a car traveling 60
miles per hour, how many feet are required to
stop a car traveling 96 miles per hour?

Answers

Answer:

400

Step-by-step explanation:

How do you solve 26 = 18v Equation

Answers

Answer:

v = 1.444

Step-by-step explanation:

v = 26/18

v = 1.444

Answer:

26 = 18v

=> 26 / 18 = v (By the law of transposition)

=> 13/9 = v

=> 1.44444 repeating = v (After solving)

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

A blouse that is size x in country A is size​ s(x) in country​ B, where ​s(x)x. A blouse that is size x in the country B is size​ t(x) in country​ C, where ​t(x)x. Find a function​ f(x) that will convert blouse sizes in country A to blouse sizes in country C.

Answers

Answer:

f(x) = [k(x): x = s(x) = t(x)]

Step-by-step explanation:

To make the question clearer, rewrite;

A blouse that is size x in country A is size s(x) in country B.

s(x) = x

A blouse that is size x in country B is size t(x) in country C.

t(x) = x

Find a function f(x) that will convert blouse sizes in country A to blouse sizes in country C.

f(x) = [k(x): x = s(x) = t(x)]

Interpretation:

f of x is equal to k of x such that x is equal to s of x which is also equal to t of x.

Where the other blouse sizes are represented by k(x) or as a function of the given size x.

Help mehh please
Alaina has $28 in her account. She wants to purchase a pair of shoes that costs $45. If Alaina makes the purchase, which integer will represent the amount of money in Alaina’s account?
–73
–27
–23
–17

Answers

Answer:

The real answer is -17, do the math.

Step-by-step explanation:

28 - 45= -17

28 + 17 = 45

45 - 28 = 17

· Yolanda deposited $3,547 into an account that earns 4.5%
simple annual interest. Calculate the interest Yolanda will earn
after 6 years. How much will Yolanda have in her account after 6
years?

Answers

Answer:

$4,504.69

Step-by-step explanation:

Select ALL graphs that do NOT represent a function.

Answers

Answer:

3 and 5

Step-by-step explanation:

If you do the vertical line test those ones do not pass. The vertical line test is the test you do to see if it is a function. You draw a vertical line and if that line crosses the graphed line only once it is a function.

just had a brain spat. help?

Answers

Answer:

6

Step-by-step explanation:

First you multiply both sides by 3. Than you simplfiy. Next you add 24 to both sides. Simplify. Finally you divide both sides by 12 & simplify. Which should give you 6.

(Answer = 6)

Answer:6

Step-by-step explanation:

the mean number of goals scored is 2.5.
the mean number of away goals scored is 1.8.

How many home and away games have been played in total?

Answers

Answer:

2 games.

Step-by-step explanation:

2.5 + 1.8 = 4

4 divided by 2 = 2

Total 32 games home and away games have been played.

What is the mean?

The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.

From the bar chart :

We can obtain the total number of goals scored :

Home goals (quarter 1 to quarter 4) :

= (9 + 6 + 8 + 7)

= 30

Away goals (quarter 1 to quarter 4) :

= (2 + 7 + 4 + 5)

= 18

Using the relation :

Mean goals scored = total goals scored / number of games played

Home games :

Mean goals = 2.5

Number of home games played = total goals scored / mean goals

= 30 / 2.5

= 22

Away games :

Mean goals = 1.8

Number of away games played = 18 / 1.8

= 10

Therefore, number of home and away games played in total = 22 + 10 = 32 games

To learn more about the mean;

brainly.com/question/13451489

#SPJ2

Order these in descending order (greatest to least). 1 is the greatest. 2 is the middle. 3 is the least.

Answers

Answer:

3/20 then 0.015 then 0.15%

Step-by-step explanation:

3/20 then 0.015 then 0.15%

3/20 is 0.15

0.15% is .0015

0.015 is 0.015

HELP PLS (picture below)

Answers

The answer is C
5.26x10^3 = 5,260

C

Because it will equal 5,260 but all the other are bigger

I need help pls , Solve: 5a + 4 = 19

Answers

5a+4=19 this is the equation to solve for a 5a=19-4

5a=15

a=15÷3

a=3

Cinco menos tres cuartos x ?

Answers

Answer:

4.25

Step-by-step explanation:

5-3/4=4.25

sry if im wrong hope this helps

brainliest? please?

In the diagram below

Answers

Answer:

m∠A = 39°

Step-by-step explanation:

From the figure attached,

BE ≅ BC

m∠C = 32°

m∠BFD = 103°

In ΔBCE,

m∠E = m∠C = 32°  [Since, BE ≅ BC]

m∠E + ∠C + m∠EBC = 180°

32° + 32° + m∠EBC = 180°

m∠EBC = 116°

m∠EBC + m∠EBA = 180° [Linear pair of angles]

116° + m∠EBA = 180°

m∠EBA = 64°

Similarly, m∠AFB + m∠DFB = 180° [Linear pair of angles]

m∠AFB + 103° = 180°

m∠AFB = 77°

Now in ΔAFB,

m∠A + m∠AFB + m∠FBA = 180° [Sum of internal angles of a triangle = 180°]

m∠A + 77° + 64° = 180°

m∠A = 39°

-6x =48

need help urgently

Answers

Answer:

x = -8

Step-by-step explanation:

Divide each side by -6 to cancel out the -6 next to x. It should now look like this: x = -8

I hope this helps!

[tex]equation \: given[/tex]

[tex]→-6x =48[/tex]

[tex]step \: by \: step \: explanation:[/tex]

[tex] \implies{- 6x = 48}[/tex]

[tex]\implies \: x = \frac{48}{ - 6 } [/tex]

[tex] \blue{\implies \: x = - 8}[/tex]

two in 1 more points​

Answers

Answer:

Your photo wont show up

Step-by-step explanation:

Answer:

Hello

1.  B. 2.35 * 10^11

2. A. 3 * 10^-2

Carlos has saved $19.80. Shaq saved 5/6 of the amount that Carlos saved. Deontae saved 4 times as much as shaq. What is the total saved amount of all threw

Answers

102.30this is your answer to your question

و please tell me what the slope is​

Answers

Answer: slope = 6

Step-by-step explanation:

Slope is rise over run.

Find two perfect points and see how many up/down you go and how many left/right you go.

On this one, you go up 6, right 1.

6/1 is 6.

Hope this helps!

Answer:

6

Step-by-step explanation:

m=y2-y1/x2-x1

take two points from the graph (0, -1) and (1, 5)

5-(-1)=6

1-0=1

6/1=6

hope this helps :3

In the expression 3x2y + 4x – 5x2y, are the terms 3x2y and –5x2y like terms? Explain by providing support for your answer.

Answers

Answer:

yes

Step-by-step explanation:

These are like terms because they  have the same variables and powers. The coefficients do not need to match for it to be considered a like term.

Answer:

Sample Response: Yes, they are like terms because like terms have the same variables raised to the same powers. Both terms contain an x and y variable with the x variable squared.

Step-by-step explanation:

Write the slope intercept form of an equation for the line containing (0,-3) with slope -1.

Answers

Answer:

y=-x-3

Step-by-step explanation:

Formula (point slope): y-y1=m(x-x1)

y-(-3)=-1(x-0)

(distribute the -1)

y+3=-1x+0

(combine like terms)

y=-1x-3

Which expression is equivalent to Start root80 ?
O ^4start root2end root•√5
0 start root2^4•start root5
0 start root2end root•start root2end root•start root5end root
0 start root2^2end root•start root2^2end root•start root5^2end root

Answers

Answer:

I believe your answer is C

Hope this helps!

Answer:

It's B

Step-by-step explanation:

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