A dragon lived in a cave.
The dragon doubled in size every day.
After 20 days the dragon filled the cave.
After how many days did the dragon half-fill the cave?
Answer: After 19 days, the dragon filled half of the cave.
Step-by-step explanation:
The dragon doubled in size every day and after 20 days he filled the cave.
So, one day before, the dragon occupied half of the cave.
20 - 1 = 19 [days]
After 19 days did the dragon half-fill the cave.
The dragon doubles in size every day, and after 20 days, it completely fills the cave.
To find out when the dragon half-filled the cave, we need to determine how many days it took for the dragon to reach half of the cave's capacity.
we know that,
On the 20th day, the dragon filled the entire cave.
and, The dragon doubled in size every day.
so, we have,
On the 19th day, the dragon's size would have been half of what it was on the 20th day.
On the 18th day, the dragon's size would have been half of what it was on the 19th day.
And so on...
We can see that every day before the 20th day, the dragon's size was halved.
So, on the 19th day, the dragon's size was half of the size it was on the 20th day.
Therefore, on the 19th day, the dragon half-filled the cave, and on the 20th day, it filled the entire cave.
Hence, After 19 days did the dragon half-fill the cave.
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please answer fast!!
I am really confused and I don't know what to do.
Answer:
C
Step-by-step explanation:
A farm is to be built in the shape of Quadrilateral ABCD, as shown below. All four sides are equal.
A rhombus ABCD is shown with diagonal AC equal to 18. 3 feet and diagonal BD equal to 13.8 feet
What is the area of the farm? (1 point)
a
73.2 square feet
b
111.2 square feet
c
126.27 square feet
d
168.36 square feet
Answer:
c 126.27 square feet
Step-by-step explanation:
sum of two triangles
18.3 * (13.8/2) * 2 = 126.27
ANSWER THIS QUESTION RIGHT WHAT YOU NEED TO FIND THE ANSWER IS ON THE PHOTO The Figure below shows the graph of the function f(x) In the coordinate plane. Identify the following key features of the graph
Answer:
vertex: (0,3)
Axis of symmetry: x=0
y-intercept: (0,3)
x-intercept: n/a
min
A would be positive since the parabola opens at the top
Step-by-step explanation:
The side lengths of a triangle are 5, 8, and 12. Is this a right triangle?
O A. No, because 52 + 32 + 122.
OB. No, because 5+ 8 + 12.
C. Yes, because 52 + 82 = 122.
O D. Yes, because 52 + 82 < 122
Answer:
A) No...
Step-by-step explanation:
We can check if this triangle is a right triangle by using the Pythagorean Theorem.
a² + b² = c² where a and b are the legs of the right triangle, and c is the hypotenuse (longest side)Using 5 for a, 8 for b, and 12 for c, let's see if this satisfies the equation:
5² + 8² = 12²Simplify.
25 + 64 = 144 89 = 144We can see that 89 ≠ 144, so this leaves us with answer choices A and B. I think you meant to write < for the last + sign.
Seeing as the sum of the two lengths of the triangle is greater than the third side length, this creates a normal triangle. This cannot be the correct answer choice since this only satisfies the requirements for a triangle, but not a right triangle.
This leaves us with answer choice A. 52 + 32 ≠ 122 and 52 + 32 < 122. (I'm not sure why the squares of the side lengths are not used, but this should be the correct answer.)
PLEASE NEED HELP ASAP TYTY I WILL BE GIVING THANKS!
Answer:
B. 112°
Step-by-step explanation:
4x -4 = (3x+4) + (2x-44)
4x -4 = 5x - 40
5x - 4x = -4 + 40
x = 36
∠BCA = 3 * 36 + 4 = 112
What is the constant of proportionality for the table? What does it represent? Reminder: k= y/x
Answer:
The constant of proportionality is 5. It represents the cups of yellow paint needed for 1 cup of blue paint.
if 50% is 10 what is 100%
Answer:
20
Step-by-step explanation:
Valeria is playing with her accordion. The length of the accordion A(t)A(t)A, left parenthesis, t, right parenthesis (in \text{cm}cmstart text, c, m, end text) after she starts playing as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts playing, the accordion is 15\text{ cm}15 cm15, start text, space, c, m, end text long, which is the shortest it gets. 1.51.51, point, 5 seconds later the accordion is at its average length of 21\text{ cm}21 cm21, start text, space, c, m, end text. Find A(t)A(t)A, left parenthesis, t, right parenthesis. \textit{t}tstart text, t, end text should be in radians.
Answer:
−6cos( π/3 t)+21
Step-by-step explanation:
The length of the accordion is −6cos( π/3 t)+21.
How to derive a sinusoidal expression?We must figure out the periodic phenomenon's amplitude, period, and vertical shift in order to create a sinusoidal function that models it. Additionally, we must choose between using a sine or a cosine function and calculate the ensuing phase shift.
Given
A = 5+1 = 6
Shift = 21
ω =- π/3[because of 4th quadrant]
exp = Asin[-ωt] + shift
=-Acosωt + shift = -6cosπ/3 t + 21
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Solve using Graphing. x-y=-7 2x+9y=19
Answer:
(-4, 3)
General Formulas and Concepts:
Algebra I
Solving systems of equations by graphingStep-by-step explanation:
Where the 2 lines intersect would be the solution set to the systems of equations.
Howard is picking out some movies to rent, and he has narrowed down his selections to 4 children's movies, 7 comedies, 7 mysteries, and 5 horror films. How many different combinations of 9 movies can he rent if he wants all 4 children's movies
Answer:
6188
Step-by-step explanation:
Number of children's movies = 4
Number of comedy movies = 7
Number of mystery movies = 7
Number of horror movies = 5
Total number of movies to be rented = 9 out of which 4 are fixed to be children's movies
To find:
Number of different combinations to rent 9 movies out of which 4 are children's movies
Solution:
Number of movies left to be rented = 9 - 4 = 5
Number of movies left out of which these 5 are to be rented = 7 + 7 + 5 = 17
Now, there are a total of 17 movies out of which 5 are to be selected.
Therefore, we can use:
[tex]_nC_r = \dfrac{n! }{r!(n-r)!}[/tex]
where, [tex]n = 17[/tex]
[tex]r = 5[/tex]
[tex]_{17}C_5 = \dfrac{17! }{5!(12)!}\\\Rightarrow \dfrac{17.16.15.14.13}{5.4.3.2.1} = \bold{6188}[/tex]
What is the answer to this question really need the answer
Answer:
A, B, D
Step-by-step explanation:
2 x 3x =6x - 2 times 9y which equals 18y+ and 2 times 18 equals 36 so 2(3x-9y+18)
Ed use 3 2/3 cups of peanut butter and 2 cups of powdered sugar to make 1 batch of peanut butter fudge. How much more peanut butter will Ed use than powdered sugar to make 3 batches of fudge?
Answer:
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
Step-by-step explanation:
3 2/3 cups of peanut butter (x)
2 cups of powdered sugar(y)
for every one batch you need 2 cups, and for 3 batches you need 6 cups of powdered sugar(2*3=6)
and for every batch you need 32/3 cups of peanut butter and for three batches you need (3 2/3 *3)= 11/3 *3=33/3=11 cups of peanut butter to make the fudge
Ed will use 5 more peanut butter than powdered sugar to make 3 batches of fudge(11-6=5)
Ben wants to buy a new collar for each of his 5 dogs. The collars come in a choice of 9 different colors. Step 1 of 2 : How many selections of collars for the 5 dogs are possible if repetitions of colors are allowed
Answer:
59049 ways
Step-by-step explanation:
Given
[tex]Colors = 9[/tex]
[tex]Dogs = 5[/tex]
Required
Determine number of selection (repetition is allowed)
The number of collars is not given.
So, we'll assume that there are enough collars to go round.
If no repetition is allowed, each of the 5 dogs have 9 colours to select from.
i.e.
[tex]Dog\ 1 = 9[/tex]
[tex]Dog\ 2 = 9[/tex]
[tex]Dog\ 3 = 9[/tex]
[tex]Dog\ 4 = 9[/tex]
[tex]Dog\ 5 = 9[/tex]
So, the number of selection is:
[tex]Selection = 9 * 9 * 9 * 9 * 9[/tex]
[tex]Selection = 59049[/tex]
4. A rectangle has a diagonal of 8 cm. The diagonal creates a 60° angle at the base of the rectangle.
[2]
a. Draw a picture of the rectangle
[4]
b. Write an EXACT expression for the base and the height of the rectangle.
[2]
C. Use your expressions to find the EXACT area of the rectangle.
9514 1404 393
Answer:
a) see attachment
b) base: 4, height: 4√3
c) area: 16√3
Step-by-step explanation:
a) The figure is drawn in the attachment
__
b) The side lengths of a 30-60-90 right triangle have the ratio ...
1 : √3 : 2
Multiplying these by 4 gives the side lengths of each triangle created by the diagonal. The base (short leg) is 4 units; the height (long leg) is 4√3 units.
__
c) The area is the product of base and height:
A = bh
A = 4(4√3) = 16√3 . . . . square units
A=
B=
Blank 1:
Blank2:
Answer:
a=3,b=1
Step-by-step explanation:
In a parallelogram opposite sides are equal/congruent.
Using this, we know that 3a-4=a+2 and b+1=2b
1st equation:
3a-4=a+2
-a -a
2a-4=2
+4 +4
2a=6
a=3
2nd equation:
b+1=2b
-b -b
b=1
a=3, b=1
Is the following table proportional or non-proportional?
Answer:
proportional
Step-by-step explanation:
y= -7x
Interest calculated only on the principle is
If each of the numbers in the following data set were multiplied by 17, what
would be the median of the data set?
28, 58, 20, 14, 18, 71, 36
A. 986
B. 1207
C. 476
D. 612
Answer:
B
Step-by-step explanation:
Find the value of x
Answer:
x=20°
Step-by-step explanation:
The triangle is equilateral. (All sides are the same).
Each angle in an equilateral triangle is 60.
3x=60
x=20°
the size of a rectangular computer screen is determined by the length of its diagonal. tom buys a 52cm screen that is 33 cm high. how Long is the base of the screen?
Answer:
40.20cm approx
Step-by-step explanation:
Step one
given data
We are told that the dimension of a computer screen
diagonal= 52 cm
height= 33cm
Length = ?
Required
The length of the base of the screen
Step two
Let us use Pythagoras theorem to find the length of the base
Hyp^2= Opp^2+ Adj^2
52^2= 33^2+ L^2
2704= 1089+L^2
L^2= 2704-1089
L^2= 1615
L=√1615
L= 40.20cm approx
The length is 40.20cm approx.
Is this correct? If not plz get answers 25points!!!
That is correct.
Sqrt 5 x sqrt20
Apply the radical rule to get sqrt( 5 x 20)
Simplify to get sqrt(100)
Sqrt(100) = 10
20 POINTS FOR THE FIRST PERSON TO ANSWER
Matt has a bag of candy form a party. The bag contains 8 chocolate bars, 5 pieces of gum,
8 lollipops, and 4 jawbreakers. Which statement is true?
A. The probability of randomly selecting a piece of gum is less than the probability of randomly
selecting a lollipop.
B. The probability of randomly selecting a chocolate bar is equal to the probability of randomly
selecting a jawbreaker.
C. The probability of randomly selecting a lollipop is greater than the probability of randomly
selecting a chocolate bar.
D The probability of randomly selecting a piece of qum is
Answer: its A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
the probability of selecting a piece of gum is less because there's less gum in the bag then there are lollipops
Geometry question plz help
Answer:
I think A
Step-by-step explanation:
look at Michael expression. Why do you add 6+4 first
Answer:
probably cuz its in parentheses but there's no picture
Step-by-step explanation:
what is 12+6x>99 help plz asaaap
Answer:
[tex] \frac{29}{2} [/tex]
Hey please help me answer this and explain your answer :)
Will give brainlst.
Answer:
B for banana
Step-by-step explanation:
50. If angles are complementary, what’s value of x?
Answer:
x = 14
Step-by-step explanation:
For complementary angles, the sum of two angles is equal to 90 degrees.
We have,
[tex]m\angle ABC = 4x-10\\\\m\angle DBC = x+30[/tex]
ATQ,
[tex]4x-10+x+30=90[/tex]
Taking like terms together,
4x+x =90-30+10
5x = 70
x = 14
So, the value of x is 14.
Scrat the squirrel has a few nuts. When he put them in groups of 5 nuts, two nuts were left, and
when he laid them out in groups of 3 nuts, there were no nuts left. How many nuts among the
options provided below could belong to Scrat?
Answer:
The options are not shown, so i will solve this in a general way.
Let's suppose that there are N nuts
If we divide the N nuts into groups of 5, there will be a remainder of 2 nuts.
If we divide the N nuts into groups of 3, there is no remainder.
This means taht N is a multiple of 3. then we can write:
N = 3*k
where k is a random integer.
Now, we know that when we divide N by 5, there is a remainder of 2 nuts, this means that N is equal to a multiple of 5 plus 2, then we can write:
N = 5*j + 2
where j is a random integer.
Now we only need to find a pair of k and j (both positive integers) such that:
3*k = 5*j + 2
We can rewrite this as:
k = (5/3)*j + (2/3)
Now we could just input different values of j, and see if k is also an integer:
j = 2
k = (5/3)*2 + 2/3 = 10/3 + 2/3 = 12/3 = 4
Then the pair j = 2, k = 4 is a possible solution.
N = 3*k = 3*4 = 12
N = 5*j + 2 = 5*2 + 2 = 12
From this we can conclude that N = 12, so Scrat has 12 nuts.
Now with the equation
k = (5/3)*j + (2/3)
We can find other possible combinations of j and k, that will give different values for N.
for example, if j = 5:
k = (5/3)*5 + 2/3 = 25/3 + 2/3 = 27/3 = 9
Then the pair j = 5, k = 9 is also a possible solution:
N = 3*k = 3*9 = 27
N = 5*j + 2 = 5*5 + 2 = 27
In this case, Scrat has 27 nuts.
Ashley ran from home to school in 10 minutes. what has her average speed, if the distance between her house and her school is 1.5 miles?
Answer:
0.15 miles per minute
Step-by-step explanation:
Average speed is in distance over time, so you could write:
1.5 miles / 10 minutes
Now, simplify:
.15 miles per minute
(hope this helps :-D)
Answer:
.15 miles per minute
Step-by-step explanation:
