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3 years ago

Solve the inequality −x/2<4

Mathematics

1 answer:

FinnZ [79.3K]3 years ago

5 0

Isolate the x. First, multiply 2 to both sides

-x/2(2) < 4(2)

-x < 4(2)

-x < 8

Isolate the x. Divide - 1 to both sides (because you are dividing a negative number, flip the sign).

-x/ -1 < 8/-1

x > -8 is your answer

hope this helps

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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:

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

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

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

$S_{n}=910.22\ ft$

8 0

2 years ago

Please answer this, thanks.

elena55 [62]

First, put it into point-slope form.

Find the slope:

m=(y2-y1)/(x2-x1)
m=(-6-(-2)/(2-1)
m=(-6+2)/1
m=-4/1
m=-4

Now, put it into point-slope:

y-y1=m(x-x1)

y-2=-4(x-(-6)
y-2=-4(x+6)
y-2=-4x-24

Slope intercept form: y= mx+b

Add 2 to the other side.

y=-4x-22 <== the answer

I hope this helps!
~kaikers

4 0

2 years ago

Read 2 more answers

What is the value of the underlined digit 65?

PIT_PIT [208]

It is obviously 65,duh, what is the value of 65

3 0

3 years ago

The price of a technology stock was $9.71 yesterday today the price rose to $9.84 find the percentage increase round your answer

VARVARA [1.3K]

Answer:

1.34%

Step-by-step explanation:

In order to find the percentage increase between these two prices, we must first find the difference in price. We calculate this by subtracting the final price by the initial price like so...

$9.84 - 9.71 = 0.13

Now we divide the difference by the initial price to find what percentage of the initial price this difference is, since this percentage difference was added to the initial price to get the new and final price point.

0.13 / 9.71 = 0.013388 ... multiply by 100 to get percent value

0.013388 * 100 = 1.3388% or 1.34% rounded.

4 0

3 years ago

A dependent system of equations is a system with<br> the same line

Naddik [55]

I don’t understand your question

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3 years ago