Find the value of x and y.

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:

[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

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Answer:

  m∠SVW = 80°

Step-by-step explanation:

3. The sum of same-side interior angles SVW (4x°) and VWT (5x°) is 180°. This can be used to solve for x and to find the angle values.

  4x + 5x = 180

  9x = 180 . . . . . . . . collect terms

  x = 20 . . . . . . . . . . divide by 9

m∠SVW = 4x° = 4(20)°

m∠SVW = 80°

_____

4. Then m∠VWT = 180° -80° = 100° = 5x°.

__

5. Consecutive interior angles are supplementary. ("Same-side" and "consecutive" are used interchangeably in this context.)

Answer: $3.69

Step-by-step explanation:

Laura bought 4 1/3 bushels of apples.

Firs convert this to an improper fraction for easier calculation:

= 13/3 bushels of apples.

If cost $16 altogether, individually they must cost:

= Cost / Quantity purchased

= 16 ÷ 13/3

= 16 * 3/13

= $3.69

Note: You can divide by a fraction by multiplying the inverse of that fraction.

Answer:

First is 144

Second is 16

Third is 9

Step-by-step explanation:

Answer:

[tex]4.4*10^9[/tex]

Step-by-step explanation:

[tex]8.8(10^6)(5(10^2))\\=8800000*500\\=8.8*1000000*5*100\\=(8.8*5)*(1000000*100)\\=44*100000000\\=4400000000\\4400000000=4.4*10^9[/tex]

Answer:

Step-by-step explanation:

If the sumof two numbers is 4 and the sum of their squarea minus three times their product is 76, find the two numbers

Let us represent:.

First number = x

Second number = y

If the sum of two numbers is 4

= x + y = 4

x = 4 - y

The sum of their squares minus three times their product is 76

x² + y² - 3xy = 76

We substitute 4- y for x

(4 - y)² + y² - 3(4 - y)y = 76

(4 - y)(4 - y) + y² - (12 - 3y)y = 76

16 - 4y - 4y - y² + y² - 12y - 3y² = 76

16 -20y - 3y² = 76

3y² + 20y - 16 + 76 = 0

3y² + 20y + 60 = 0

Answer:

It was easy

Step-by-step explanation:

11 x 2 = 22

3 x 2 = 6

22 x 6 = 132

The time Jazzy has before going to bed is  [tex]\frac{5}{6}[/tex] hour

The first step to take in determining the answer is to add the hours she spent on various activities she did after dinner

Sum of activities done after dinner = hours spent on homework + hours spent on the telephone

[tex]1\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex]

[tex]1\frac{3 + 4}{6}[/tex]

= [tex]1\frac{7}{6}[/tex]

=[tex]2\frac{1}{6}[/tex]  hours

Th second step is to subtract the total hours Jazzy spent on activities from the hours Jazzy has before going to bed after dinner

Time left before she goes to bed = time she has to go to bed after dinner - total hours spent before going to bed

3 - [tex]2\frac{1}{6}[/tex]  hours = [tex]\frac{5}{6}[/tex] hour

A similar question was solved here: https://brainly.com/question/18157047?referrer=searchResults

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x - y = 5 → (1)

4x + y = - 10 → (2)

Rearrange (1) expressing y in terms of x

(a)

y = x - 5 → (3)

Substitute y = x - 5 into (2)

4x + x - 5 = - 10

5x - 5 = - 10 ( add 5 to both sides )

5x = - 5 ( divide both sides by 5 )

x = - 1

Substitute x = - 1 into (3) for corresponding value of y

y = - 1 - 5 = - 6

(b)

As a check

Substitute x = - 1, y = - 6 into the left side of the 2 equations and if equal to the right side then they are the solution

(1 ) x - y = - 1 - (- 6) = - 1 + 6 = 5 ← True

(2) 4x + y = 4(- 1) + (- 6) = - 4 - 6 = - 10 ← True

Thus solution is (- 1, - 6 )

Answer:

B

Step-by-step explanation:

Answer:

2x-y=0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The answer for the second part of the question would be.

C)The result suggests that there's a positive correlation between taking 10-minutes breaks during the say and developing cancer in public workers.

The correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

The correlation of two pairs of data values tells about the degree of movement(along or opposite) that can occur in one of the data values when another data value is increased or decreased respectively.

The health ministry only distributes forms to workers every five years to collect information on office jobs and worker health concerns. They are just monitoring the workers, and the survey allows them to assess and establish a link between office employment and worker health concerns. Therefore, it is an observational study.

The conclusion that can be concluded from this study is that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

Hence, the correct option is A, The result suggests that there’s a positive correlation between taking 10-minute breaks during the day and developing cancer in public workers.

Learn more about Correlation:

https://brainly.com/question/6563788

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Answer:

2.4 miles per hour

Step-by-step explanation:

1/5 of a mile is 0.2 miles. If 0.2 miles is 5 minutes, then 0.04 miles is 1 minute, as you divide 0.2 by 5. 0.04 miles per minute=2.4 miles per hour as you times 0.04 by 60.

Answer:

i think you need to include a picture  

Step-by-step explanation:

Answer:

3 1/2 hours

Step-by-step explanation:

Multiply 4/8 by 7 and you get 28/8 whihc reduces to 3 4/8 and 4/8 can be simplified to 1/2

Answer:

Step-by-step explanation:

Hi! So I am not sure if when you mention for the week if she is talking about the school week(5Days) or a regular week (7 days). So we'll do both.

We know that 4/8 hour can be simplified to 1/2 hour. We also know that 1 hour is 60 minutes ... so 1/2 hour is 30 minutes. This means she reads 30 minutes per day.

School Week: 5 Days

30 minutes x 5 Days = 150 minutes or 2 hours and 30 minutes (2 1/2 hours) (20/8 of an hour)

Regular Week: 7 Days

30 minutes x 7 days= 210 minutes or 3 hours and 30 minutes (3 1/2 hour) (28/8 of an hour)

Please mark me the brainliest or not ! I hope this answers your question

Answer: There are a total of 66 conversations.

Step-by-step explanation:

Ok, we have 12 members.

let's call them:

member 1, member 2, member 3, etc...

Let's assume that member 1 starts talking to the others, then he talks to:

member 2, member 3, member 4, etc.

So member 1 talks to the other 11 members.

We have already 11 conversations.

Now let's count the conversations of member 2.

He talks to member 1, member 3, etc.

But the conversation between member 1 and member 2 was already counted, so we do not count it this time, then here we have other 10 conversations.

now for member 3. He talks with member 1, member 2, member 4, member 5, etc...

But conversations between member 1 and member 3, and member 2 and member 3 are already counted, so here we have 9 new conversations.

We already can see the pattern here.

For each new member that we count, the number of conversations is one less than for the previous member.

The total number of conversations will be:

11 + 10 + 9 + 8+ 7 + 6+5 + 4 + 3+ 2+ 1 = 66

-2, 2 and for the other 4,5

Answer:

(-2,2) ; (4,5)

Step-by-step explanation:

Answer:

The answer is -37x - 48

Answer:

x<=2

Step-by-step explanation:

-5x+19>=9

-5x>=9-19

-5x>=-10

5x>=10

x>=10/5

x>=2

x<=2

Answer:

v = -35

Step-by-step explanation:

-4 -31= -35 which leaves V. so v=-35

Answer:

I think that  the is -27

Step-by-step explanation: 32 - (-27) = -4

Answer:

61

Step-by-step explanation:

As we can see the triangles are congruent so

< F = < C ( being corresponding angles of congruent triangle)

< C = 29

Now

<A +<B + <C = 180° { being sum of angles of triangle }

5x + 1 + 90 + 29 = 180°

5x = 180° - 120°

5x = 60°

x = 12°

<A = 5 * 12° + 1 = 61°

Hope it will help :)

Answer:

26mm

Step-by-step explanation:

w+10 + w+ 20 = 144/3

3w+30 = 48

3w = 18

w=6

longest side is 6+20 = 26

Answer:

F ( -1,4)

E (-1,2)

G (-4,5)

Step-by-step explanation:

Answer:

on what

.....................

Answer:

Positive infinite to negative infinite

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

The question is incomplete, here is the complete question

Michael split 3/4

pounds of candy among 8 people.

What is the unit rate in pounds per person?

Write your answer in simplest form

SOLUTION:

Micheal splits 3/4 candy among 8 people

Therefore the unit rate per pounds per person can be calculated as follows

= 3/4 ÷ 8

= 3/4 × 1/8

= 3/24

= 1/8

Hence the unit per pound per person is 1/8

Answer:

5-2x

Step-by-step explanation: