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lana66690 [7]
3 years ago
6

1.) Reggie lost 3 spaceships in level 3 of a video game.He lost 30 points for each spaceship.When he complete level 3 he earned

a bonus of 200 points.By how much did he score change?
2.) Simplify: -6(13)-21

3.) Bella pays 7 payments of $5 each to a game store.She returns one game and receive $20 back. What is the change to the amount of money she has?

4.) Ron lost 10 points seven times playing a video game. He then lost an additional 100 points for going over the time limit. What was the total change in his score?

9.) Ned took a test with 25 questions. He lost 4 points for each of the 6 questions he got wrong and earned an additional 10 points for answering a bonus question correctly. How many points did ned receive or lose overall?

10.) mr. Harris has some money in his wallet. He pays the babysitter $12 an hour for 4 hours of babysitting. His wife gives him $10 and he puts the money in his wallet. By how much does the amount in his wallet change?
Mathematics
2 answers:
lions [1.4K]3 years ago
8 0
1. The score changed by 110. Since 30 x 3= 90 you do 200 - 90= 110

2. -78-21=-99

3. $15 35-20 = 15

4. He lost 70 points for going over the time limit  and lost and additional 100 points 100-70=30 its a 30 point difference

9. He lost 14 points 4 x 6= 24 - 10=14

10. So he pays $48 for babysitting and the wife gives him $10 so $48 - $10= $38 so im guessing this means how much he has in the wallet so its $38
GenaCL600 [577]3 years ago
8 0

Answer:

1. 110

2. -99

3. $35

4.  $30

9. 14 points

10. Amount in his wallet reduced by $38

Step-by-step explanation:

1.

Number of points lost = 30 × 3 = 90

Number of points earned at the end of level 3 = 200

Therefore, the score changed by 200 - 90 = 110

2. - 6(13)-21 = - 78 - 21 = - 99

3. Amount paid by Bella = 7×5 = $35

Amount received by Bella = $20

Therefore, change in amount of money with Bella = 35 - 20 = $15

4. Points lost by Ron playing a video game= 10 ×7 =70

Points lost for going over the time limit = 100

Therefore, total change in his score = 100 - 70 = $30

9. Number of questions in a test = 25

Points lost = 4 x 6= 24

Points earned = 10

Therefore, he lost 24 - 10 = 14 points

10. Amount given to babysitter = $12 × 4 = $48

However his wife gives him $10, so he has to pay just $48 - $10 = $38

Therefore, amount in his wallet reduced by $38

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This is one pathway to prove the identity.

Part 1

\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{1}{\tan(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\cot(\theta) = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)}{1-\cos(\theta)}-\frac{\cos(\theta)}{\sin(\theta)} = \frac{1}{\sin(\theta)}\\\\\frac{\sin(\theta)*\sin(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)(1-\cos(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\

Part 2

\frac{\sin^2(\theta)}{\sin(\theta)(1-\cos(\theta))}-\frac{\cos(\theta)-\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-(\cos(\theta)-\cos^2(\theta))}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{\sin^2(\theta)-\cos(\theta)+\cos^2(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\

Part 3

\frac{\sin^2(\theta)+\cos^2(\theta)-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1-\cos(\theta)}{\sin(\theta)(1-\cos(\theta))} = \frac{1}{\sin(\theta)}\\\\\frac{1}{\sin(\theta)} = \frac{1}{\sin(\theta)} \ \ {\checkmark}\\\\

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We use other previously established or proven trig identities to work through the steps. For example, I used the pythagorean identity \sin^2(\theta)+\cos^2(\theta) = 1 in the second to last step. I broke the steps into three parts to hopefully make it more manageable.

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