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3 years ago

Find the solution to the inequality 2x - 6 ≥ 3x -4 _________.

Mathematics

2 answers:

Alona [7]3 years ago

5 0

Answer:x<=-2

Step-by-step explanation:

pochemuha3 years ago

5 0

Answer:

Step-by-step explanation:

2x - 6 ≥ 3x -4 means : 3x -4 ≤ 2x-6

add 4 from both sides : 3x ≤ 2x -2

add 2 from both sides : 3x+2 ≤ 2x

subtract 2x from both sides : x+2≤0

subtract 2 from both sides : x ≤-2

set of solution is : ]-∞;-2]

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3 years ago

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3 years ago

Read 2 more answers

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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3 years ago

A polynomial p has zeros when I = 0.2 = -

Rainbow [258]

Answer:

p(x) = (5x - 1) (x + 3)

Step-by-step explanation:

I apologize if I couldn't answer correctly, the question was a bit hard to understand because of the formatting.

Also I didn't see my answer in the list of answer choices but here it is:

if the polynomial has zeros at 0.2 and -3 the equation would have to be:

p(x)=(x-0.2)(x+3)

This is because plugging either of those numbers into the polynomial would cause it to equal 0.

(x-0.2) can be simplified by multiplying everything in the parenthesis by 5, getting rid of all of the decimals, making the final answer:

p(x) = (5x - 1) (x + 3)

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3 years ago