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Julli [10]
3 years ago
7

School A and B are competing in an academic contest. at the beginning of the final round, school A has 174 points and school B h

as 102 points, in the final round, correct answers earn 10 points and incorrect answers loose 6 points. school A hives the same number of correct and incorrect answers during the final round. school B gives no incorrect answers and the same number of correct answers as school A. the contest ends with te two schools tied. which equation models the scoring in the final round and outcome of the contest?
Mathematics
1 answer:
7nadin3 [17]3 years ago
5 0

X = number of correct answers

Y = number of incorrect answers

School A has 174 points and school B has 102 points.

A = 174

B = 102

School A has the same number of correct and incorrect answers during the final round.

A = 174 + 10X - 6Y

School B gives no incorrect answers and the same number of correct answers as school A.

B = 102 + 10X

The contest ends with the two schools tied.

Score = 174 + 10X - 6Y = 102 + 10X

174 + 10X - 6Y = 102 + 10X

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Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29. Writ
zepelin [54]

Part A)

So we need the graph to pass through these points:

time = 2 and price=$14 -> (2,14)

time= 5 and price = $29 -> (5,29)

Standard form:

Ax+By = C

Let’s replace the points:

A*2+B*14=C

A*5+B*29=C

Let’s eliminate variables:

(A*2+B*14)-(A*5+B*29)=C-C

A*2+B*14-A*5-B*29=0

-3A-15B=0

-3A=15B

A=15B/-3

A=-5B

There are several numbers that verify this proportion. For example, if B=1, A=-5 (you can try others, there is not only 1 correct answer).

So we can make this equation:

-5x+y=C

Then we can calculate C using one point:

-5*2+14=C

-10+14=C

4=C

So one of the possible equations is: -5x+y=4

(Remember there are multiple correct answers for this item)

You can verify it with the other point:

-5*5+29=-25+29=4 ->OK

 

Part B)

Whatever you have found in Part A, you will find the same in Part B when you convert it to function notation. All you have to do is clear y:

-5x+y=4

y=4+5x

So the equation is: f(x)=4+5x


Part C)

First of all, you have to find f(0)

f(x)=4+5x

f(0) =4+5*0=4+0=0

f(0) is ALWAYS the constant not multiplied by x.

So you know it has to cross the y axes in y=4

Now let’s put 0 as y-value:

4+5x=0

5x=0-4=-4

x=-4/5

So now you know it has to cross the x axes in x=-4/5.

So you can put those intersections in the graph and you draw the line through those points. Labels: horizontal axes is x, and in this case represents time; vertical axes is y, and in this case represents price.

Remember there are other methods, too :)

5 0
3 years ago
Mr. Littles is building a triangular sandbox using three boards. He already has two boards that measure 9 feet and 12 feet. Sele
Bess [88]

Answer:

  • 9 feet, 15 feet, 19 feet

Step-by-step explanation:

<u><em> Options are: </em></u>

  • <em>2 feet </em>
  • <em>3 feet </em>
  • <em>9 feet </em>
  • <em>15 feet </em>
  • <em>19 feet </em>
  • <em>21 feet </em>
  • <em>30 feet</em>

<em>-------------------------------------</em>

Use the triangle inequality theorem: sum of any two side must be greater than the third side by length

  • 2 feet     ⇒  no, as 2 + 9 < 12
  • 3 feet     ⇒  no, as 3 + 9 = 12
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  • 15 feet    ⇒  yes
  • 19 feet    ⇒  yes
  • 21 feet    ⇒  no, as 9 + 12 = 21
  • 30 feet  ⇒  no, as 9 + 12 < 30

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ladessa [460]

Answer:

|x |-7 = -5     ( x = -3 )

Step-by-step explanation:

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svlad2 [7]
2x = 44
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Multiply and simplify: b3 • b • b4 • b2
Luden [163]
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b^3 * b^1 * b^4 * b^2  
3 + 1 + 4 + 2 = 10

Answer: b^10
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