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Tatiana [17]
3 years ago
13

-8(r-2)=40 what is the answer to this equation

Mathematics
1 answer:
Elena-2011 [213]3 years ago
6 0
The answer is r=-3. You use the distributive property which is basically multiplying -8 with all the numbers inside the parenthesis. So -8 x r and -8 x -2. This results to -8r+16=40 (Two negative numbers multiplied together will form a positive number). We use inverse operations to subtract 16 from both sides. 16-16 is 0 and 40-16 is 24. So we are left with -8r=24. We want to be left with only r, so we once again use inverse operations to divide -8 from both sides. -8/-8 is 1, and 24/-8 is -3. So we end up with r=-3. Hope this helped :]
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Understanding Mathematics, Resource 2, Chapter Nine.
VikaD [51]

Answer:

  6.  6 is the number I thought of

  8.  -15 is the number I thought of

Step-by-step explanation:

6. Let x represent the number you thought of.

  x/2 . . . halve it

  x/2 -5 . . . take away 5 (from the previous result)

  x/2 -5 +3x . . . then add on 3 times the number I thought of

  = . . . I end up with ...

  4 + . . . four more than ...

  4 + 2x . . . ... twice the number I first thought of.

So, the equation is ...

  x/2 -5 +3x = 4 +2x

Subtracting 2x we have

  x/2 -5 +3x -2x = 4

Adding 5 and collecting terms, we get

  (3/2)x = 9

Multiplying by the inverse of the coefficient of x, we get ...

  x = (2/3)(9)

  x = 6

The number I first thought of was 6.

__

<em>Check</em>

After I halve it, take away 5 and add back 3 times 6, I have ...

  3 -5 +18 = 16

After I add 4 to twice the number, I have ...

  4 +2·6 = 16

So, the first set of manipulations gives the same result as the second. 6 is the answer.

_____

8. Let x represent the number I thought of.

  x +4 . . . add 4

  5(x +4) . . . multiply the answer by 5

  = . . . . I could get the same final answer by ...

  4x . . . multiplying my number by 4

  4x +5 . . . then adding 5

So, the equation is ...

  5(x +4) = 4x +5

  5x +20 = 4x +5 . . . . eliminate parentheses

  x + 20 = 5 . . . . . . . . subtract 4x

  x = -15 . . . . . . . . . . . subtract 20

The number I thought of was -15.

__

<em>Check</em>

Add 4 and multiply the result by 5: 5(-15+4) = 5(-11) = -55.

Multiply the result by 4 and add 5: 4(-15)+5 = -60+5 = -55, the same final answer.

The answer of -15 checks with the problem statement.

6 0
4 years ago
HELP ASAP Find the equation of a line that goes through the points (8, -9) and (-4, 15).
Leona [35]

Answer:

Your answer is: y= -2x+7

Step-by-step explanation:

Hope this helped : )

7 0
3 years ago
Which of the following represent the same ratio?
eduard
Answer:2/3 and 2:3
Explanation
5 0
3 years ago
The function y=e−3x is vertically stretched by a factor of 4, reflected across the y-axis, and then shifted up 5 units, find the
olya-2409 [2.1K]

Answer:

Step-by-step explanation:

y = e^(-3x)

Stretch by factor of 4

y = 4e^(-3x)

Reflect across y axis

y = 4e^(3x)

Shift up by 5

y = 4e^(3x) + 5

8 0
3 years ago
A train travels at a constant speed of 35 feet per second. How many minutes will it take the train to travel exactly 70 miles? (
olga_2 [115]

176 minutes,

70x5,280= 369,600 divide by 35= 10,560 divide by 60=176

3 0
4 years ago
Read 2 more answers
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