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Ksenya-84 [330]
3 years ago
10

tom determines the system of equations below has two solutions, one of which is located at the vertex of the parabola. equation

1: (x – 3)2 = y – 4 equation 2: y = -x bin order for this solution to be reasonable, which qualifications must be met?
Mathematics
1 answer:
stiks02 [169]3 years ago
8 0
( x -3 )² = y - 4
y = ( x - 3 )² + 4
One solution is located at the vertex: ( 3, 4 ).
y = - x + b
4 = - 3 + b
b = 7
( x - 3 )² = - x + 7 - 4
x² - 6 x + 9 = - x + 3
x² - 5 x + 6 = 0
x² - 2 x - 3 x + 6 = 0
x ( x - 2 ) - 3 ( x - 2 ) = 0
( x - 2 ) ( x - 3 ) = 0
x 1 = 2,  x 2 = 3
y 1 = 5,  y 2 = 4.
In order for this solution to be reasonable, the 2nd equation must be:
y = - x + 7

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Answer:

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60c = 4(90)       product means/extremes

60c = 360

c = 6

 Or  90 is 1.5 times 60, therefore you need 1.5 times 4 cups.

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Write the following sentence as linear equation. Adding 16 to 5 times a number x is 40.
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Answer:

x = 24/5

Step-by-step explanation:

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Can you explain how to solve this problem ​
iVinArrow [24]

Answer:

Step 1:

Start by setting it up with the divisor 10 on the left side and the dividend 179 on the right side like this:

             

 1 0 ⟌ 1 7 9

Step 2:

The divisor (10) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

       0    

 1 0 ⟌ 1 7 9

Step 3:

Multiply the divisor by the result in the previous step (10 x 0 = 0) and write that answer below the dividend.

       0    

 1 0 ⟌ 1 7 9

      0    

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

       0    

 1 0 ⟌ 1 7 9

     - 0    

       1    

Step 5:

Move down the 2nd digit of the dividend (7) like this:

       0    

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

Step 6:

The divisor (10) goes into the bottom number (17), 1 time(s). Therefore, put 1 on top:

       0 1  

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

Step 7:

Multiply the divisor by the result in the previous step (10 x 1 = 10) and write that answer at the bottom:

       0 1  

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

       1 0  

Step 8:

Subtract the result in the previous step from the number written above it. (17 - 10 = 7) and write the answer at the bottom.

       0 1  

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

     - 1 0  

         7  

Step 9:

Move down the last digit of the dividend (9) like this:

       0 1  

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

     - 1 0  

         7 9

Step 10:

The divisor (10) goes into the bottom number (79), 7 time(s). Therefore put 7 on top:

       0 1 7

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

     - 1 0  

         7 9

Step 11:

Multiply the divisor by the result in the previous step (10 x 7 = 70) and write the answer at the bottom:

       0 1 7

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

     - 1 0  

         7 9

         7 0

Step 12:

Subtract the result in the previous step from the number written above it. (79 - 70 = 9) and write the answer at the bottom.

       0 1 7

 1 0 ⟌ 1 7 9

     - 0    

       1 7  

     - 1 0  

         7 9

     -   7 0

           9

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 179 divided by 10 calculated using Long Division is:

17

9 Remainder

Step-by-step explanation:

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