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3 years ago

4(4x+3)=19x+9-3x+3 what are the steps

1 answer:

4 0

Ok so:

4(4x+3) = 19x + 9 - 3x +3
parenthesis first:
4 x 4x = 16x then 4 x 3 = 12

16x + 12 = 19x + 9 - 3x + 3
combine :) :
19x - 3x = 16x then 9 + 3 = 12

16x + 12 = 16x +12
-12 -12
16x = 16x
They are the same equations lol they equal 0.

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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

3 years ago

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tiny-mole [99]

the answer is x=100°

...........

4 0

3 years ago

Read 2 more answers

the elves were working when the head elf came in and there was only 2 weeks left until christmas. what percentage of the month w

valentina_108 [34]

Answer:

45 %

Step-by-step explanation:

Time left until Christmas = 2 weeks

= 2 * 7 days [since 1 week = 7 days]

= 14 days

Number of days in December = 31

Percentage of the month left before Christmas = $\frac{Time left until Christmas}{Number of days in December} * 100$

= $\frac{14}{31} * 100$

= 0.45 * 100

= 45 %

4 0

3 years ago

The product of two rational numbers:

Daniel [21]

Answer:

"The product of two rational numbers is rational."

So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication. Thus, multiplying two rational numbers produces another rational number.

Step-by-step explanation:

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3 years ago

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Lakshmi has 11 more20-rupee notes than 10-rupee notes. If she has Rs 550 in total, how many notes of each kind does she have?

olganol [36]

Answer:

10rupee notes are 11

20rupee notes are 22

Step-by-step explanation:

Let 10-rupee note be x

20-rupee note will be x + 11

The equation will be

10x + 20(x + 11) = 550

10x + 20x + 220 = 550

30x = 330

x = 330/30 = 11 = 10rupee notes

y = 11+11 = 22 = 20rupee notes

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3 years ago