Answer:
x=8
Step-by-step explanation:
8-2=6
8x7=42
(checked)
About 4.1 seconds. How long was the ball in the air? We are told that t represents time in seconds since the ball was thrown, so it started to be 'in the air' at t = 0 To answer the question, then, we need to know the time when it stopped being in the air. We are told that the ball hit the ground. So that's what happened when it stopped being airborne. We need to relate that event to the mathematics we're working with. What can we say about h , the height of the ball when the ball hits the ground? Answer: The height will be 0 when the ball stops being in the air. Now translate this back to the mathematics: The ball is in the air from t = 0 until the time t when h = 0 . Find the time t that makes h = 0 . That means: solve: − 5 t 2 + 20 t + 2 = 0 We can solve this by solving: 5 t 2 − 20 t − 2 = 0 (Either multiply both sides of the equation by − 1 , or add 5 x 2 − 20 x and − 2 to both sides and then re-write it the other way around) That's a quadratic equation, so try to factor first. But don't spend too much time trying to factor, because not every quadratic is easily factorable and that's OK, because we still have the quadratic formula if we need it. We do need it. t = − ( − 20 ) ± √ ( − 20 ) 2 − 4 ( 5 ) ( − 2 ) 2 ( 5 ) = 20 ± √ 440 10 = 20 ± √ 4 ( 110 ) 10 = 20 ± 2 √ 110 10 = 2 ( 10 ± √ 110 ) 2 ( 5 ) = 10 ± √ 110 5 We can see that 10 < √ 110 < 11 . In fact ( 10 + 1 2 ) 2 = 10 2 + 10 + 1 4 = 110.25 Using 10.25 as an approximation for √ 110 , we get : for the solution t = 10 − √ 110 5 we'll get a negative t . That doesn't make sense. The other solution gives t ≈ 10 + 10.25 5 = 20.5 5 = 4.1 seconds. So the ball was in the air from t = 0 until about t = 4.1 . The elapsed time is the difference, 4.1 seconds.
Answer:
The slope is 5x, and the y-intercept is -4
If it was bought after 10% discount, it means it was bought at 90% of the original price:
90% = $450
1% = $5
100% = $5 x 100
100% = $500
The original price of the Play Station was $500.
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Charlie's Carpets:
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Carpet : $18/yd
Installation: $2/yd
Discount: 20% x $18 = 0.2 x 18 = $3.60
Carpet Price after discount = $18 - $3.60 = $14.40/yd²
Carpet Price with installation $14.40 + $2 = $16.40/yd²
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Cindy's Carpet
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Carpet = $18/yd²
Discount = 10% = 0.1 x $18 = $1.80
Price after Discount = $18 - $1.80 = $16.20/yd²
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Summary:
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Charlie's Carpet = $16.40/yd²
Cindy's Carpet = $16.20/yd²
CIndy's Carpet is cheaper.
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Find Cost:
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Length = 19 x 1/3 = 19/3 yards
Width = 12 x 1/3 = 4 yards
19/3 x 4 = 25 1/3 yd²
Cost = 25 1/3 x $16.20 = $410.40
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Answer: Cindy's Carpet is cheaper and it will cost $410.40.
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