Answer:
34 cm
Step-by-step explanation:
The nth term of a geometric progression Tₙ = arⁿ⁻¹ where a = first term, and r = common ratio.
Given that our first term, T₁ = ar¹⁻¹ = a = 121 cm and our third term T₃ = ar³⁻¹ = ar² = 64 cm
Then, T₃/T₁ = ar²/a = r²
r² = T₃/T₁
r² = 64 cm/121 cm
r = √64/121
r = 8/11
So, the height of our fifth bounce T₅ = ar⁵⁻¹
= ar⁴
= 121 cm × (8/11)⁴
= 121 × 4096/14641
= 4096/121 cm
= 33.9 cm
≅ 34 cm to the nearest cm
Using a geometric sequence, it is found that the height of the fifth bounce is of 33.85 cm.
In a geometric sequence, the quotient between consecutive terms is always the same, and it is called common ratio r.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1r^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
The height of the first bounce is of 121 cm, hence [tex]a_1 = 121[/tex].The height of the third bounce is of 64 cm, hence [tex]a_3 = 64[/tex], and this is used to find r.[tex]a_n = a_1r^{n-1}[/tex]
[tex]64 = 121r^{2}[/tex]
[tex]r^2 = \sqrt{\frac{64}{121}}[/tex]
[tex]r = \frac{8}{11}[/tex]
Hence:
[tex]a_n = 121\left(\frac{8}{11}\right)^{n-1}[/tex]
The height of the fifth bounce is of [tex]a_5[/tex], hence:
[tex]a_5 = 121\left(\frac{8}{11}\right)^{4} = 33.85[/tex]
The height of the fifth bounce is of 33.85 cm.
You can learn more about geometric sequences at https://brainly.com/question/11847927
Find the slope of the line that passes through (4,-5) and (-2,9)
a -2/3
b 5/3
c -7/3
d 2
Answer:
C) -7/3
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(9-(-5))/(-2-4)=(9+5)/-6=14/-6
simplify -14/6 to -7/3
In triangle KLM, the measure of angle M is 90 degrees, the measure of angle K is 75 degrees, and LM is equal to 6.3 feet. Find the length of KL to the nearest tenth of a foot.
Answer:
6.5feet
Step-by-step explanation:
Using the SOH CAH TOA identity
<K = 75 degrees
opposite = LM = 6.3 feet
Hypotenuse = KL
sin theta = opp/hyp
sin 75 = 6.3/x
x = 6.3/sin75
x = 6.3/0.9659
x = 6.5feet
Hence the length of KL to the nearest tenth of a foot is 6.5feet
what is the factored form of -1/2(32x - 40) - (20x - 4)?
Answer:
12(-3x + 2)
Step-by-step explanation:
-1/2 ( 32x - 40) - (20x - 4) = -16x + 20 - 20x + 4 = -36x + 24 = 6(-6x + 4) = 12(-3x + 2)
PLEASE HELP ASAP
What is (-105 + (-35) X(-3 + 5)?
Answer:
-175 I believe
Step-by-step explanation:
Answer:
-280
Step-by-step explanation:
-105+-35= -140
-3+5= 2
-140*2= -280
Hope this helps others
Using properties of logarithms in excersises 13-18, use the properties of logarithms o write the logarithm in terms of log3(5) and log3(7) log3 (21/5)
Answer:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Step-by-step explanation:
Given
[tex]log_3(\frac{21}{5})[/tex]
Required
Express in terms of [tex]log_3(5)[/tex] and [tex]log_3(7)[/tex]
[tex]log_3(\frac{21}{5})[/tex]
Express 21 as 7 * 3
[tex]log_3(\frac{21}{5}) = log_3(\frac{7 * 3}{5})[/tex]
Apply law of logarithm
[tex]log_3(\frac{21}{5}) = log_3(7) + log_3(3) - log_3(5)[/tex]
[tex]log_3(3) = 1[/tex]. So, we have:
[tex]log_3(\frac{21}{5}) = log_3(7) + 1 - log_3(5)[/tex]
Rewrite:
[tex]log_3(\frac{21}{5}) = log_3(7) - log_3(5)+ 1[/tex]
Solve the system of linear equations by elimination. Check your solution. 3x + 2y = 7 -3x + 4y = 5
Answer:
(3x+2y=7-3x+4y)=5
3x+3x+2y-4y-7=5
6x-2y-7=5
6x-2y=5+7
=12
2(3x-y)=12
3x-y=12/2
= 6
46 e 64 sao cemtena e unidade
Answer:
nn
Step-by-step explanation:
pq centena são de 100 dezena são de 10
Ex: 46 (dezena e unidade)
146 (centena, dezena e unidade)
C = -y - a/b
Solve the variable a
Can you please show each step
Which is bigger 8 kg or 850 grams
Which is bigger 1 kg or 1000 grams
Which is bigger 3 liters or 3500 milliliters
Which is bigger 5 liters or 520 milliliters
PLZ ANSWER ALL 3 WILL GIVE 15 PIONTS
PLZ HELP ME PLZ I NEED IT
Answer:
Step-by-step explanation:
The intersection occurs at the point (3,-3) so those are the coordinates.
x^2y+y^2-30x+221=0 find the radius
Answer:
2
Step-by-step explanation
Let's complete the square. We get:
(x^2-30x)+y^2+221=0
(x^2-30x+225)+y^2+221-225=0
(x-15)^2+y^2-4=0
(x-15)^2+y^2=4
By analyzing this, we see that the radius is just :[tex]\sqrt{4}[/tex]=2
SMART PPL HELP HELP PLEAse
Answer:
help with what
Step-by-step explanation:
Answer:
did you mean to post a question?
Step-by-step explanation:
What is the area of a square with side length:
3cm
Answer:
Since every square has the same length in sizes...
3 x 3 = 9cm
Answer: 9cm
−12 = −0.6k solve for k
Answer:
-20
Step-by-step explanation:
Step-by-step explanation:
-12=-0.6k
divide both sides by -0.6
k=20
lmk if this is right
Which of the following descriptions is TRUE regarding linear and exponential functions?
There is no difference between a linear function and an exponential function.
Linear functions cross the y-axis above exponential functions.
Linear functions slope down, while exponential functions slope up.
Linear functions have a constant slope, while exponential functions start flat and get steeper.
Answer: Linear functions have a constant slope, while exponential functions start flat and get steeper
Step-by-step explanation: I just took the quiz so I know it’s right. I hope this helps :)
Answer:
Answer: Linear functions have a constant slope, while exponential functions start flat and get steeper
Step-by-step explanation:
I took the test
why do the angles in a triangle add up to 180 degrees?
Answer:
Angles in a triangle add up to 180 degrees because triangles are have the measure and sizes of quadrilaterals, which have an angle measure of 360 degrees. If you divide 360 degrees by 2, you will get 180 degrees.
Step-by-step explanation:
Hope that helps!
Answer:
Let N equal the number of angles in the polygon
Use the formula:
(N x 180)-360 = the sum of all the angles in the polygon
A triangle has 3 angles so:
(3 x 180)-360=180 degrees
(this formula works for any polygon, regardless of the number of it's angles)
You rent a canoe for $4.50 per hour. Your cost before the tax is added is $18. Write an equation to find the number of hours H that you retend the canoe
Answer:
total cost = cost/hour x hours
$18.00 = ($4.50)(X hours)
X=4 hours
Step-by-step explanation:
total cost = cost/hour x hours
$18.00 / 4.50=4 hours
Simplify the following
(1 1/2) ^-2
Answer:
1/2.25 or 4/9
Step-by-step explanation:
Factorise fully
X^2 - 25
Answer:
(x+5)(x-5)
Step-by-step explanation:
x^2-25 = x^2 - 5^2 = (x+5)(x-5)
rule: a^2 - b^2 = (a+b)(a-b)
how many solutions 9x +2y =9 / -3x + y=2
Answer choices-
1 solution
No solution
Infinite solutions
the solution to the system is (1,3)
the solution to the system is (3,1)
the solution to the system is (1/3,3)
Answer:
Maybe the sum was a simultaneous equation....if so, this is the solution.
and the answer comes (1/3, 3)
Hope it helps! :)
you buy some bags of tomatoes for $6.75. If each bag costs $2.25, how many bags do you buy?
Answer:
you would of bought three bags of tomatoes
Will give Brainly! Please help!
Answer:
The answer is option c.
Hope this helps!
please help me if you can
Answer:
[tex]x=35[/tex]
Step-by-step explanation:
M is the midpoint of AB. If A ( 4,0) and M (2, 1.5), then find the coordinates of B
Answer:
Step-by-step explanation:
(4 + x)/2 = 2
4 + x = 4
x = 0
(x + 0)/2 = 1.5
x + 0 = 3
x = 3
(0, 3)
answer is C
Please help me with this
Answer:
1) equation is set up to determine when the cost of printing at home is the same as the cost of printing at the office
2) p = 500 means that, at printing 500 pages, the costs of home versus office printing are the same
Step-by-step explanation:
Answer:
1) No, it does not represent the story.
2) It represents the number of pages.
Step-By-Step Explanation:
1) It has nothing to do with the story.
2) It says: Let p represent the number of pages
Mare has a monthly cell phone plan that has a fixed charge of $12 per month plus
$0.30 per text message. Marie wants to spend no more than $40 per month on her
call phone. Which inequality represents the number of text messages, X, that Marie
Please hurry
You need to multiply the cost per text message by the number of messages (x) add that to the fixed charge.
The total of those need to be less than or equal to the amount she wants to spend.
The equation would be written as:
0.30x + 12 <= 40
PLEASE HELP ASAP!
Triangle CAT has vertices C (2,3), A(-2,6) and T(-1,-4). A translation maps the point A to A' (-1,4). What are the coordinates of C' under this translation?
A. (1, -3)
B. (3, 1)
C. (1, 8)
D. (-8, 1)
you add 1 and subtracted 2
so 2 + 1 = 3
3 - 2 = 1
answer: b. (3, 1)
În desen este reprezentat trapezul
ABCD și O punctul de intersecție a di-
agonalelor AC și BD. Completați case-
ta, astfel încât să obțineți o propoziţie
adevărată:
Dacă aria triunghiului DOA este egală
cu 20 cm², atunci aria triunghiului COB
este egală cu
Answer:
ab hyppotenusejabqianahqiwnna. jajabanqk
What kind of solution does the equation have? - 13 = 5(1 + 4m) - 2m
Answer: = − 1
Step-by-step explanation:
8 x ÷ 4 = 100 What is the value of x in the equation?
5
A. 5
B. 25
C. 50
D. 200
Answer:
Hi there. I had put a comment replying to your question as I didn't see any place that I could answer. If you still need it, then the answer was
C. 50
Step-by-step explanation:
8 * 50 = 400
400 / 4 = 100
In any way possible, I hope this helps you! Have a great day!
