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yulyashka [42]
3 years ago
5

Help is needed thanks

Mathematics
1 answer:
scoundrel [369]3 years ago
4 0

Answer:

6

Step-by-step explanation:

All it is asking is what value should you plug in for x to make the equation true.

Lets solve it:

x - 11 = -5

Solve by adding 11 to both sides to isolate the x:

x = 6

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What is the value of 5 in 756 write and draw to explain how you know?
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In the attached diagram you can see Place Value Chart that is used to help understand the value of each digit based on the place or position.

For the number 756:

  • 7 has a value of 7 hundreds, or 700;
  • 5 has a value of 5 tens, or 50;
  • 6 has a value of 6 ones, or 6.

Answer: 5 has a value of 5 tens, or 50

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If x2=4(5-1) what is the value of x
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X2=4(5-1)
x2=4(4)
x2=16
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4. a) A ping pong ball has a 75% rebound ratio. When you drop it from a height of k feet, it bounces and bounces endlessly. If t
Klio2033 [76]

First part of question:

Find the general term that represents the situation in terms of k.

The general term for geometric series is:

a_{n}=a_{1}r^{n-1}

a_{1} = the first term of the series

r = the geometric ratio

a_{1} would represent the height at which the ball is first dropped. Therefore:

a_{1} = k

We also know that the ball has a rebound ratio of 75%, meaning that the ball only bounces 75% of its original height every time it bounces. This appears to be our geometric ratio. Therefore:

r=\frac{3}{4}

Our general term would be:

a_{n}=a_{1}r^{n-1}

a_{n}=k(\frac{3}{4}) ^{n-1}

Second part of question:

If the ball dropped from a height of 235ft, determine the highest height achieved by the ball after six bounces.

k represents the initial height:

k = 235\ ft

n represents the number of times the ball bounces:

n = 6

Plugging this back into our general term of the geometric series:

a_{n}=k(\frac{3}{4}) ^{n-1}

a_{n}=235(\frac{3}{4}) ^{6-1}

a_{n}=235(\frac{3}{4}) ^{5}

a_{n}=55.8\ ft

a_{n} represents the highest height of the ball after 6 bounces.

Third part of question:

If the ball dropped from a height of 235ft, find the total distance traveled by the ball when it strikes the ground for the 12th time. ​

This would be easier to solve if we have a general term for the <em>sum </em>of a geometric series, which is:

S_{n}=\frac{a_{1}(1-r^{n})}{1-r}

We already know these variables:

a_{1}= k = 235\ ft

r=\frac{3}{4}

n = 12

Therefore:

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{1-\frac{3}{4} }

S_{n}=\frac{(235)(1-\frac{3}{4} ^{12})}{\frac{1}{4} }

S_{n}=(4)(235)(1-\frac{3}{4} ^{12})

S_{n}=910.22\ ft

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