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? *
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.
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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A baseball player starts the season with 77 career home runs. Ten games into the
season, he has hit 2 home runs. Assume he continues at this pace. Write an
equation for the number of career home runs he has hit. How many career home
runs would you expect him to have at the end of the season (162 games)?
If there are a total of 162 games, and every then games the player hits 2 home runs, we can divide the total amount of games by 10 then multiply the quotient by 2.
162 / 10 is approximately 16.
16 × 2 = 32
32 + 77 = 109 career home runs
Using the slope intercept relation, the required equation and the number of home runs at season end would be ;
y = 0.2x + 77109Recall :
y = bx + cc = initial number of hime runs = 77b = slope y = total career home runs x = number of games playedSlope, b = 2 home runs per 10 games = 2/10 = 0.2
The expression can be represented thus:
y = 0.2x + 77Number of home runs at the end of the season :
x = 162
y = 0.2(162) + 77
y = 32.4 + 77
y = 109.4
y = 109
Hence, Total number of hime runs would be 109.
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The area of a rectangular painting is 5734cm^2
If the length of the painting is 94cm , what is its width?
Answer: 61cm
Step-by-step explanation:
So to work out this question you do 5734÷94 which would work out the with which is 61
61×94=5734
x-(x(x-y to the power of 3)) ; use x=9 and y=1
Answer:
-4599
Step-by-step explanation:
x-(x(x-y)^3) , x=9, y=1
=9-(9(9-1)^3)
=9-(9(8)^3)
=9-(9*512)
=9-4608
= -4599
If SV is a perpendicular bisector of RT, which statement is true?
Answer:
The correct answer is A
Step-by-step explanation:
Pleasssssse help meeeeee
Answer: [tex]x \geq 3[/tex]
The graph has a closed circle pointing to the right
Please answer real quick
Answer:
use symbolab
Step-by-step explanation:
Express the following number as a decimal:
2 x 10^-6
Answer:
0.000002
Step-by-step explanation:
2* 10^-6
is the same as
2 * 0.000001
which is
0.000002
Answer:
The answer is: 0.000002
Step-by-step explanation:
Have a great day!
Rectangle ABCDABCDA, B, C, D is graphed in the coordinate plane. The following are the vertices of the rectangle: A(-2, 2)A(−2,2)A, left parenthesis, minus, 2, comma, 2, right parenthesis, B(6, 2)B(6,2)B, left parenthesis, 6, comma, 2, right parenthesis, C(6, 3)C(6,3)C, left parenthesis, 6, comma, 3, right parenthesis, and D(-2, 3)D(−2,3)D, left parenthesis, minus, 2, comma, 3, right parenthesis.
What is the area of rectangle ABCDABCDA, B, C, D?
The area of rectangle ABCD with the given vertices is: 8 units².
What is the Area of a Rectangle?Area of rectangle = (length)(width).
Given the following vertices:
A(-2, 2)B(6, 2)C(6, 3)D(-2, 3)Area = (length)(width) = (AB)(BC)
AB = |-2 - 6| = 8 units
BC = |2 - 3} = 1 unit
Area of rectangle = (8)(1) = 8 units².
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Answer: 8
Step-by-step explanation:
-5 -2q = 9
please help me
Answer:
q = -7
Step-by-step explanation:
-5 - 2q = 9
Add 5 to both sides of the equation.
-2q = 14
Divide both sides by -2.
q = -7
ILL MARK BRAINLIST IF YOU GET IT RIGHT .which expression is equivalent to s - t?
Answer:
s(6)×t(6)
hope this helps
Which is the graph of the equation y-1=2/3(x-3)?
Answer:
The second graph ( one with the coordinates (3,1) and (6,3))
Step-by-step explanation:
Answer:
The answer is B.
Step-by-step explanation:
1. What is 10% of 75?
Answer:
7.5
Step-by-step explanation:
i hope this helps!!
A container of coffee is 1/6 full. The container contains 2/3 a pound of coffee. a. Write a division expression that represents the capacity of the container. b.Write a multiplication expression that represents the capacity of the container. c.Find the capacity of the container.
Answer:
(a) [tex]x= \frac 2 3\div \frac 1 6[/tex]
(b) [tex]x= \frac 2 3\times \frac 6 1[/tex]
(c) 4 pounds
Step-by-step explanation:
Let the capacity of the container is [tex]x[/tex].
The container has coffee which is 1/6 of the capacity of the container and the amount of coffee is 2/3 pounds.
So, 1/6 of the capacity of the container has 2/3 pound of coffee, i.e
[tex]\frac 1 6 \times x = \frac 2 3\cdots(i)[/tex]
(a) From the equation (i), the required division expression for the capacity of the box, x, is
[tex]x= \frac 2 3\div \frac 1 6[/tex]
(b) The division expression can be changed to multiplication expression by interchanging the numerator and the denominator of the divisor. So, from part (a), the required multiplication expression for the capacity of the box, x, is
[tex]x= \frac 2 3\times \frac 6 1\cdots(ii)[/tex]
(c) From equation (ii), the capacity of the box is
[tex]x= \frac 2 3\times 6= 4[/tex] pounds.
-5 = -2x + 27 - 3x this has to be 20 characters so ignore this lollllll
Answer:
6 2/5=x
Step-by-step explanation:
CAN SOMEONE HELP ME ?
Answer:
sure ill help
Step-by-step explanation:
Answer:
a+b=f
Step-by-step explanation:
180-f= c
180-(a+b)= c
SO
a+b= f
help!!!! due now ( right answer's only)
Answer:
Minimum, Vertex(1,-7) and sorry what do you mean by aos? i dont get that please type in the comments I'll answer that too. Hope you understand the rest
Step-by-step explanation:
The vertex of a parabola means the stationary point/turning point which is denoted by the following:
[tex]x=\frac{-b}{2a} \\[/tex]
and for y we just simply put the value of x that we get into the equation so lets get started
The equation [tex]y=x^2-2x-6[/tex] is a quadratic equation
and if we compare it by the standard form [tex]y=ax^2+bx+c[/tex] we get the following values
a=1 , b=-2 , c=-6
and now for the vertex
[tex]x=\frac{-b}{2a}[/tex]
[tex]x=\frac{-(-2)}{2(1)} \\x=\frac{2}{2} \\x=1[/tex]
and now for y
[tex]y=x^2-2x-6\\y=(1)^2-2(1)-6\\y=1-2-6\\y=-7[/tex]
so the vertex is (1,-7)
and the graph is minimum not maximum because the value of a is greater than 0 if the value of a>0 then the graph is minimum and if the value of a<0 meaning a is negative the graph is maximum and here in the equation a=1 which means a>0 then our graph is minimum.
Answer:
hey we were talking in the comment section with someone else 16 min ago and that chat maxed out so he made another one and wants you to come back. Just letting you know.
Step-by-step explanation:
Find the product
(7+2u) (7-2u)
Options:
a) 49+4u
b) 49-4u(square root sign)
c) 4u(square root sign) - 49
Answer:
b
Step-by-step explanation:
if you mean squared and not square root, then it would be b because if you factor it back out, you will get the original expression back because of the subtraction of perfect squares.
Answer:
b) [tex]\boxed{\bold{(7+2u)(7-2u)=49-4u^2}}[/tex]Step-by-step explanation:
[tex](7+2u) (7-2u)=(7)(7)+(7)(-2u)+(2u)(7)+(2u)(-2u)=\\\\=49-14u+14u-4u^2=\ \underline{49-4u^2}[/tex]
PLEASE ANSWER FAST.
The question is in the picture.
(question 24)
Answer:
As the values of x increase both function decrease in value.
Step-by-step explanation:
Find two consecutive integers whose sum is eleven less than three times the smaller integer.
Answer:
If you call the smaller integer "x" and the greater integer "y", then:
x+y=3x-11 The sum of the two is 11 less than 3 times the smaller
y=x+1 Because they are consecutive, the greater must be 1 more than the smaller
Then you can solve for x:
x+(x+1)=3x-11 Substitute x+1 for y
2x+1=3x-11 Combine like terms
2x+12=3x Add 11 to both sides
12=x Subtract 2x from both sides
The smaller integer is 12, thus the greater integer is 1 more or 13.
Check:
12+13=3(12)-11
25=36-11
25=25 Yes, so the integers are 12 and 13
Step-by-step explanation:
thats pretty much it
2. Lauren is thinking about spending all of her allowance money to buy a new bike. If she has $224
and she can only afford of the price of the bike, how much does the bike cost?
Answer:
Ffyguggjbkbkhigu
Step-by-step explanation:
Hjvjgjgugugugugugigkhkhkhkhkhkhkh
i know it’s a lot to ask for but what are the answers for all of these you get 100 points and you get marked brainliest
how to find the sequence
X. Y
0. 0
1. 1.5
2. 4
3. 7.5
4. 12
Answer:
they add one half to each number
What is 3/5 as a percent?
Answer:
3/5 as a percent is 60% hope that helps
1. Factor the expression completely 20x^4+80x^3-5x^2-20x
Answer:
5x(x+4)(2x+1)(2x−1)
Step-by-step explanation:
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Total Interest = $
What is Tarah's new total balance?
New Balance Total = $
Answer:
Total interest = $28.72
New balance = $ 387.72
Explanation: Tarah has $359 in the bank. To find the amount of interest, multiply 359 by .08.
She gets $28.72 interest annually.
In one year, she will make $387.72. (Add the total interest to her original balance)
Plz mark brainliest:)
A 24-roll package of toilet paper is $14.88. If the price per roll stays the same, what would be the price of a ten-roll package?
Answer:
Step-by-step explanation:
put these fractions to least to greatest 8/9 6/9 5/9 7/9 please help
Fifty eighth graders attend a
charter school. If 1/10 are
home with the flu and 2/3 of
the remaining students are
on a field trip, how many are
in school?
Answer:
15
Step-by-step explanation:
1/10 of 50 is 5, so remove that.
2/3 of 45 is 30, so remove that too.
therefore, 15 kids are in school
hope this helps!! <3
Suppose a person starts the day by drinking 3 cups of coffee containing 130 mg of caffeine EACH.
Let C = mg of caffeine remaining in the body and let t = hours since the 390 mg of caffeine was consumed. Write a function C(t) that expresses the amount of caffeine remaining in the body as a function of time.
Answer:
C = t * 3
Step-by-step explanation: