Using a geometric sequence, it is found that:
The rule for the height of the nth bounce is:[tex]a_n = 52(0.65)^{n-1}[/tex]
The height of the fifth bounce is of 9.28 cm.In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
In this problem:
Bounces to 65% of the height from which it was dropped, thus the common ratio is of [tex]q = 0.65[/tex].Dropped from 80 cm, thus, the height of the first bounce is [tex]a_1 = 80(0.65) = 52[/tex].Thus, the rule for the height of the nth bounce is:
[tex]a_n = 52(0.65)^{n-1}[/tex]
The height of the fifth bounce is [tex]a_5[/tex], thus:
[tex]a_5 = 52(0.65)^{5-1} = 9.28[/tex]
The height of the fifth bounce is of 9.28 cm.
A similar problem is given at https://brainly.com/question/11847927
21
15
10
What’s the next number to this pattern
Answer:
here's one possibility
Step-by-step explanation:
21 - 6 = 15
15 - 5 = 10
10 - 4 = 6
6 - 3 = 3
3 - 2 = 1
1 - 1 = 0
Im stuck need explanation and answer
Answer:
[tex]1. \: \: \: x + 5 = 10 \\ 2. \: \: \: \: \: \: \: \: {x}^{2} = 25 \\ 3. \: \: \: \: \: \: \: \: \: 3x = 15[/tex]
please help me, i will mark the brainliest pls!
9514 1404 393
Answer:
yes5 × (6 - 3) = (5 × 6) - (5 × 3)Step-by-step explanation:
The distributive property tells you the factor outside parentheses multiplies each of the terms inside parentheses.
The difference 6 -3 inside parentheses has two terms, and there is a factor of 5 outside those parentheses. The setup for the distributive property is there, so the distributive property can be used.
__
The outside factor multiplies each inside term. The sign can be left with the inside term, or can be placed between the products.
5 × (6 - 3) = (5×6) - (5×3)
__
or
5 × (6 - 3) = (5×6) +(5×(-3))
1200 loan 6 months at 7% monthly payment is 204.10
Answer:This would be 1
Because 1 plus 1 equals 2
Step-by-step explanation:
That was fun
Aurora had 35 jellybeans. She ate 8 and divided the rest equally among 3 of her friends. How many jellybeans did each friend get?
What is the value of j in the equation?
3j + 8 = 35
8
9
17
27
Answer:
9
Step-by-step explanation:
3j + 8 = 35
3j = 35 - 8
3j = 27
3j ÷ 3 = 27 ÷ 3
= 9
Answer:
9
Step-by-step explanation:
the total is 35 she ate 8 so that's subtract then divide the answer u get for 35-8 and divide that by 3
35-8=27
27÷3=9
The ratio of corresponding sides of the first triangle to the second triangle below is
equal to in lowest terms.
n
The value of n is
The solution is
Answer:
4
Step-by-step explanation:
irst note that 6/8=6/8=9/12, which shows that these are similar triangles. Any of these fractions is the ratio of corresponding sides. Reduce it and find the denominator
Two triangles are known to be similar if the ratio of the similar sides and angles are equal. The value of n, if the two triangles are similar is 3.75
What are similar triangles?Two triangles are known to be similar if the ratio of the similar sides and angles are equal.
From the given triangles, we have the following
Scale factor = 3/n
Determine the ratio of the sides
Ratio = 12/15 = 3/n
Cross multiply
12n = 15 * 3
12n = 45
n = 3.75
Hence the value of n, if the two triangles are similar is 3.75
Learn more on similar triangles here: https://brainly.com/question/2644832
750 m - 150cm
A. 600cm
B.1000cm
C.7650cm
D.74,850
Answer:
D
Step-by-step explanation:
First, convert 750 meters to centimeters:
75,000cm
Next, take away 150cm from 75,000cm:
74,850cm
The answer is D.
Pre college need help
Answer:
-4/3
Step-by-step explanation:
3y= -4x -9
y = -4/3x-3
By slope intercept form, m= -4/3
Pls help with this question in geometry and pls show steps thank you
Answer:
9 cm
Step-by-step explanation:
In a 30°-60°-90° triangle, the ratio of the shortest to the longest sides is 1 : 2.
That means DB = 1/2BC = 3 cm. It also means AB = 2BC = 12 cm.
Then the length of AD is ...
AD +DB = AB
AD = AB -DB = 12 cm -3 cm
AD = 9 cm
1/3 plus 1/5 plus 1/2
Answer:
=31/30 hope it was very helpful
Step-by-step explanation:
1/3+1/5+1/2
=8/15+1/2
=31/30
Answer:
=31/30 hope it was very helpful
1/3+1/5+1/2
=8/15+1/2
=31/30
Step-by-step explanation:
PLSSSSSSSSSSSSSSSSSSSSSSSSSS HELPPPPPPPPP
Answer:
h - 3/5 = 13/45
h = 13/45 + 3/5
h= 8/9
pls help
do this I will give 100 points
1. a) 55% b) 34% c) 32% d) 47% e) 90%
2. a) 3/5 b) 7/2 c) 6/5
I gtg now but I’ll answer the rest for you later
19=
\,\,-37+8x
−37+8x
Answer:
43
Step-by-step explanation:
The point (3,-4) is on the terminal side of an angle 0. What is cos O?
A.-3/5
B.3/5
C.3/4
D.-3/4
E.3
9514 1404 393
Answer:
B. 3/5
Step-by-step explanation:
The distance from the origin to the point is given by the distance formula:
d = √((x -0)² +(y -0)²) = √(3² +(-4)²) = √25 = 5
The cosine of the angle is the ratio of x-coordinate to that distance:
cos(θ) = 3/5
ANSWER FAST PLEASE ITS DUE RN
The relationship between avocados(x) and their pricely)
is proportional. The ordered pair (5,8) is graphed.
What is the price of 1 avocado?
What does (10,16) represent?
Answer:
5 is the number of avocados and 8 is the dollars spent
So, one avocado is 1.60
It represents 10 avocados for 16 dollars
Step-by-step explanation:
Can u help me with this please
Answer:
Point (1,5) does not lie on the line.
Step-by-step explanation:
x + y = 4
x + 0 = 4 (the crosses the x-axis at 4
0 + y = 4 ( the line crosses the y-axis at 4
A bag contains 12 counters numbered from 1 to 12. If a counter is picked at random, find
the probability that is: even, a cube number, prime or odd?
Answer:
Step-by-step explanation:
even (2, 4, 6, 8, 10, 12) = 6/12 = 1/2
cube (1, 8) = 2/12 = 1/6 (although all numbers are a cube of something, just not a whole, or even rational, number)
prime (1, 2, 3, 5, 7, 11) = 6/12 = 1/2
odd (1, 3, 5, 7, 9, 11) = 6/12 = 1/2
Please help missed this lesson
Answer:
m∠ABD = 24°, m∠CBD = 24°, m∠ABC = 48°
Step-by-step explanation:
3x+6=7x-18
3x-7x=-18-6
-4x=-24
x=24÷4
=6
Hence, ∠ABD = (3x+6)°
= [3(6)+6]°
= (18+6)°
= 24°
Hence, ∠CBD = 24°
Hence, ∠ABC = 24°×2
= 48°
A. Only Sequence A
B. Only Sequence B
C. Both
D. Neither
Answer:
THE CORRECT ANSWER IS LETTER B.
Step-by-step explanation:
I HOPE IT'S HELP
HAVE A NICE DAY & NIGHT
Are the graphs of 3x-6y=12 and y=1/2x-2 parallel, perpendicular, or neither
Answer:
It will be parallel
Step-by-step explanation:
3x-6y=12
-6y= -3y+12
y= 1/2y+12
simplify(4-x) (7+x)
(4-x) ( 7+ ×)
28 +4x -7x -x²
28 -3x - x²
What is 19 less than 2 times a number is 7 more than half of the number written as a equation?
Answer:
2x - 19 = 1/2x + 7
Step-by-step explanation:
Your charges will be $75.00 per month throughout the 2 years, so at the end of that time you will have paid?
Answer:
$1800
Step-by-step explanation:
twelve months in a year 12*2=24
75*24=1800
Answer:
$1800
Step-by-step explanation:
2 years is 24 months
75*24=1800
2x+7=10 solve x simplify your answer
Answer:
1.5 or 1 1/2
Step-by-step explanation:
2x+7=10 (subtract 7 from both sides)
2x=10-7
2x=3 (divide both sides by 2)
X=3/2
Simplify
X= 1.5 or 1 1/2
Suppose one card is drawn at random from a standard deck.
Answer each part. Write your answers as fractions.
(a) What is the probability that the card drawn is a seven?
(6) What is the probability that the card drawn is a diamond?
(c) What is the probability that the card drawn is a seven or a diamond?
Answer:
a) 4 cards out of 52 will be seven, therefore 4/52 = 1/13
b) 13 cards out of 52 will be diamonds, therefore 13/52 = 1/4
c) 13 diamonds, and 3 seven (1 seven already diamond), therefore 16/52 = 4/13
Step-by-step explanation:
Writing Two-Step Equations
1. SHOPPING Toni and Tricia spend the PHILANTI
day at the mall. At the end of the day,
the follo
the two added up their purchases
and
Three bu
found that they spent a total of $107.50.
The char
Toni spent $10.00 more than Tricia.
made by
Write an equation that can be used to
find how much each girl spent.
4+4 +10)=107.50
An angle measures 60° less than the measure of its complementary angle. What is the measure of each angle?
Answer:
30
Step-by-step explanation:
2p² - 3 = 15 What is the FIRST step
Answer:
2p×2p)-3+3=15-3 im not sure tho
Step-by-step explanation:
Answer:
(2p×2p)-3+3=15-3 that's what I think
Please help!!
Determine whether the inverse of F(x) is a function.
Answer:
f⁻¹(x) is not a function
Step-by-step explanation:
A function can only have one output value per input value. Multiple input values can have the same output value (horizontally), but multiple output values cannot have the same input value (vertically).
For example:
[tex]f(x)=x^2\\f(-2)=-2^2=4\\f(2)=2^2=4[/tex]
This function has 2 inputs with the same output. That is valid.
However, if you take the inverse of that function:
[tex]f^{-1}(x)=\sqrt{x}\\f^{-1}(2)=\sqrt{2}=1.414\\f^{-1}(-2)=\sqrt{-2}=\sqrt{2}i[/tex]
f⁻¹(-2) is an imaginary number. It doesn't exist, and so the inverse of f(x) is still a function because there is no vertical overlap. This is shown more clearly in the attached image.
The graph of the inverse of a function is just mirrored over y = x. This is also shown in the attached image. Any horizontal overlap the function may have becomes vertical overlap, and if those values still exist, the function cannot be a function.
In the function in your question, f(x) has some horizontal overlap around x = 0 and x = 8. If this was mirrored over y = x, the function at x = 8 would have 2 outputs, y = 0 and y = 8. As a result, it cannot be a function.
Let me know if I need to explain any part of that more clearly.
How are the graphs of the reciprocal functions related to their corresponding original functions? What happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? Describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions.
Answer:
Graphs of reciprocal functions reflect against their original functions. For example, y=arcsinx reflects against y=sinx. To graph trigonomoetric functions, simply use a graphing calculator, like Desmos. It's easy. go to Desmos and type y=sinx. It will make a graph for you. Then on a line below the function, type y=arcsinx. You will notice how the inverse of sine reflects against sine. I would teach a visual person by not saying as much and just writing out the equations and using Desmos. To an auditory person, I'd explain as I do the math. I don't know what some of these words mean, but if someone wants a physical example, I'd give them a realistic world problem. I'd ask them to stand up and imagine they are this many feet away from an object that is this many feet tall. We will set up a realistic equation together.
Step-by-step explanation:
