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Montano1993 [528]
3 years ago
5

Solve x2 = 12x – 15 by completing the square. Which is the solution set of the equation? Solve x2 = 12x – 15 by completing the s

quare. Which is the solution set of the equation?
Mathematics
2 answers:
Helga [31]3 years ago
8 0

Answer:

D on edge

Step-by-step explanation:

Svetlanka [38]3 years ago
6 0

Answer: 6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}

Step-by-step explanation:

Given

Quadratic equation is

x^2-12x+15=0

Solving by completing the square method

\Rightarrow x^2-2\cdot 6\cdot x+15=0\\\text{add and subtract 36}\\\Rightarrow x^2-2\cdot 6\cdot x+15+36-36=0\\\Rightarrow x^2-2\cdot 6\cdot x+36+(-36+15)=0\\\text{using}\ (a-b)^2=a^2+b^2-2ab\\\Rightarrow (x-6)^2-21=0\\\Rightarrow (x-6)^2=21\\\Rightarrow x-6=\pm \sqrt{21}\\\Rightarrow x=6\pm \sqrt{21}

The solution set of the equation is 6+\sqrt{21}\ \text{and}\ 6-\sqrt{21}

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Since we are only allotting one out of the 10 numbers for the yellow marbles, then we should also find a set of marbles wherein the ratio of the yellow marbles to the total marbles is 1/10. Out of the options, the situation with 30 red marbles, 40 blue marbles, 20 green marbles, and 10 yellow marbles match the ratio.

CARD #2: Use the numbers 0 through 4 to represent the yellow marbles and 5 through 9 to represent the other marbles.

We will follow the same logic as the previous pair. Since we used 5 numbers out of the 10 for yellow marbles, then we should find a situation wherein the ratio of the yellow marbles to the total marbles is 1/2. From the options, the situation with 16 red marbles, 32 blue marbles, 32 green marbles, and 80 yellow marbles satisfy the ratio.

CARD #3: Use the numbers 0 through 2 to represent the yellow marbles and 3 through 9 to represent the other marbles.

For this card, 3 out of the 10 numbers are allotted for the yellow marbles. Thus, the ratio of the yellow marbles to the total marbles should be 3/10. We can see that the only situation that satisfies this is the one with 60 red marbles, 120 blue marbles, 30 green marbles, and 90 yellow marbles.

CARD #4: Use the numbers 0 through 3 to represent the yellow marbles and 4 through 9 to represent the other marbles.

Lastly, we will apply the same logic for this card. The 4 numbers allotted for yellow marbles will tell us that the ratio of the yellow marbles to the total marbles should be 2/5. The only situation that satisfies this would be the one with 20 red marbles, 30 blue marbles, 10 green marbles, and 40 yellow marbles.
8 0
3 years ago
Plz answer it what are the multiples for 345 and 567?
kobusy [5.1K]
1)1, 3, 5, 15, 23, 69, 115, 345
<span>2)1,3,7,9,21,27,63,81,189,567</span>

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Answer:

(-4,3)

Step-by-step explanation:

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Please help!!! <br><br> Which number line shows the solutions to n &gt; -2?
PolarNik [594]

Answer: the first one

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
3 divided by 225 patrial quotients
Karolina [17]

Answer:

0.0133

Step-by-step explanation:

Set up the long division.

225 | 3

2 Calculate 300 ÷ 225, which is 1 with a remainder of 75.

0 . 01

_____

225 | 3.  

2 . 25

__

     75

3 Bring down 0, so that 750 is large enough to be divided by 225.

0 . 01

_____

225 | 3.  

2 . 25

__

     750

4 Calculate 750 ÷ 225, which is 3 with a remainder of 75.

0 . 013

______

225 | 3.  

2.25

__

750

675

___

 75

5 Bring down 0, so that 750 is large enough to be divided by 225.

0. 0 1 3

_______

225 | 3.    

2.25

__  

750

675

_____

   75

6 Calculate 750 ÷ 225, which is 3 with a remainder of 75.

0 . 0133

_______

225 | 3.    

2. 25

__  

750

675

___

750

675

___

75

7 Therefore, 3 ÷ 225 ≈ 0.0133.

Answer: 0.0133

4 0
3 years ago
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