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alina1380 [7]
3 years ago
11

All the numbers that are highlighted

Mathematics
1 answer:
liberstina [14]3 years ago
5 0
3b) 4 tickets/$16 = 0.25 tickets/$1
4a & 4b) You didn’t provide a photo of the problems that I need to solve them
4c) ($4/1 ticket) x (1000 tickets) = $4000
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9 times the quantity of 12 less than a number x is 24. Write in an algebraic expression.
kiruha [24]

Answer:

9(x-12)=24

Step-by-step explanation:

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Answer:

Step-by-step explanation:

A

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Lisa paid 43.95 for 16.1 gallons of gasoline.What was the cost per gallon,rounded to the nearest hundredth?Show your work
GrogVix [38]

Cost per gallon is found by dividing the cost by the number of gallons.

$43.95/16.1 ≈ $2.7298137

Rounded to hundredths, this is $2.73.

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3 years ago
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3 years ago
Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
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