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Ksenya-84 [330]
4 years ago
11

1. The missing value that makes the polynomial x^2-6x+? A perfect square quadratic is...___

Mathematics
1 answer:
Lera25 [3.4K]4 years ago
6 0

Answer:

1. The missing value is 9

2. The missing value is 81

Step-by-step explanation:

1. To find the missing value of a perfect square you divide the center term (-6 as is -6x) by two to get 3 then square the three to get 9

To check this write it as the simplified form (x-3)^2 and multiply it out again using foil.   x times x is x^2,  -3 times x is -3x ( this happens twice adding up to the -6x), and -3 times -3 is 9 making it x^2 -6x +9

2. Follow the steps for the previous problem to get the same answer for this one. Divide 18 (middle term) by 2 making 9. Then square the 9 making 81.

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4 years ago
There is a beaker of 3.5% acid solution and a beaker of 6% acid solution in the science lab. Mr. Larson needs 200 milliliters of
oksian1 [2.3K]
Et x = the volume of the 3.5% solution 
<span>Let y = the volume 6% solution </span>

<span>(3.5%)x + (6%)y = (4.5%)(200) </span>
<span>0.035)x + 0.06y = 0.045(200) </span>
<span>0.035x + 0.06y = 9 ( Equation 1 )</span>

<span>x + y = 200 ( Equation 2 )</span>
<span>x = 200 - y </span>

<span>Substitute x = 200 - y into equation 1: </span>
<span>0.035x + 0.06y = 9 </span>
<span>0.035(200 - y) + 0.06y = 9 </span>
<span>7 - 0.035y + 0.06y = 9 </span>
<span>0.06y - 0.035y = 9 - 7 </span>
<span>0.025y = 2 </span>
<span>y = 2/(0.025) </span>
<span>y = 80 mL (the volume of 6% solution.)</span>

<span>Substitute y = 80 into equation 2: </span>
<span>x + y = 200 </span>
<span>x + 80 = 200 </span>
<span>x = 200 - 80 </span>
<span>x = 120 mL (the volume of the 3.5% solution.)</span>

<span>Therefore, Mr. Larson should combine 120 mL of the 3.5% solution </span>
<span>and 80 mL of the 6% solution to make 200 mL of 4.5% solution. </span>

<span>Answer is 120 mL of the 3.5% solution & 80 mL of the 6% solution

Hope I helped :)</span>
5 0
4 years ago
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