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EastWind [94]
3 years ago
15

Select the equations that are equivalent to the equation y – 2 = 3(x + 6). Select all that apply.

Mathematics
1 answer:
amm18123 years ago
3 0
The correct answer for the exercise shown above is the first option and the las option, which are:

 <span>y = 3x + 20
 3x - y = -20
</span>
 The explanation is shown below:

 1. You have the folllowing expression given in the problem above:

 y-2=3(x+6)

 2. If you solve it for y, you have:

 y-2=3x+18
 y=3x+18+2
 y=3x+20

 3. And if you move the variables to the left member, you have:

 3x-y=-20

 Therefore, as you can see, the correct answer are the options mentioned above.

 
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35 quarters

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This situation has two unknowns - the total number of dimes and the total number of quarters. Because we have two unknowns, we will write a system of equations with two equations using the two unknowns.

  • d+q=60 is an equation representing the total number of coins
  • 0.10d+0.25q=11.25 is an equation representing the total value in money based on the number of coin. 0.10 and 0.25 come from the value of a dime and quarter individually.

We write the first equation in terms of q by subtracting it across the equal sign to get d=60-q. We now substitute this for d in the second equation.

0.10(60-q)+0.25q=11.25\\6-0.10q+0.25q=11.25\\6+0.15q=11.25

After simplifying, we subtract 6 across and divide by the coefficient of q.

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