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Vedmedyk [2.9K]
3 years ago
10

Please solve equations by completing square

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
8 0
x^2-4x+1=0\\
x^2-4x+4-3=0\\
(x-2)^2=3\\
|x-2|=\sqrt3\\
x-2=\sqrt3 \vee x-2=-\sqrt3\\
x=2+\sqrt3 \vee x=2-\sqrt3

x^2+6x-9=0\\
x^2+6x+9-18=0\\
(x+3)^2=18\\
|x+3|=\sqrt{18}=3\sqrt2\\
x+3=3\sqrt2 \vee x+3=-3\sqrt2\\
x=-3+3\sqrt2 \vee x=-3-3\sqrt2\\

x^2+20x+3=0\\
x^2+20x+100-97=0\\
(x+10)^2=97\\
|x+10|=\sqrt{97}\\
x+10=\sqrt{97} \vee x+10=-\sqrt{97}\\
x=-10+\sqrt{97} \vee x=-10-\sqrt{97}

x^2-2x-5=0\\
x^2-2x+1-6=0\\
(x-1)^2=6\\
|x-1|=\sqrt6\\
x-1=\sqrt6 \vee x-1=-\sqrt6\\
x=1+\sqrt6 \vee x=1-\sqrt6
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You multiply each side of the equation by 16 .
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3 years ago
X/4 - y/3 =1 X and Y axis standard form
Semenov [28]

Answer:

Step-by-step explanation:

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3x - 4y = 12 <== standard form

=====================================

if it makes it easier for u, x/4 is the same as (1/4)x and y/3 is the same as (1/3)y

so ur problem can be written as : (1/4)x - (1/3)y = 1....multiply by 12

12(1/4)x - 12(1/3)y = 12(1)

(12/4)x - (12/3)y = 12.....reduce

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5 0
3 years ago
I will give brainlest please answer and explain
Artemon [7]

Answer:

c

Step-by-step explanation:

There is 6 students in the 8hr zone.

Gosh, do I have to explain?  A is a, c is c!

4+6+6+6.5+6.5+6.5+6.5+7+7+7+7+7.5+7.5+7.5+8+8+8+8+8+8.5=141.

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3 0
3 years ago
Elena went on a 6-mile walk. She completed the first half of the walk 1 mi/h faster than usual and the second half of the walk 2
xxTIMURxx [149]

Answer:

Her usual rate is 0.8333 miles per hour.

Step-by-step explanation:

The velocity formula is given by:

v = \frac{d}{t}

In which d is the distance and t is the time.

She completed the first half of the walk 1 mi/h faster than usual

Her usual rate is v. 1mph faster is v + 1.

The second half of the walk 2 mi/h slower than the first half.

The first half is v + 1.

2mph slower is v + 1 - 2 = v - 1. Then

Total rate:

7.2 hours, and 6 miles. So

One half is v+1 and the other is v - 1. This is why each is multiplied by 0.5.

0.5(v + 1) + 0.5(v - 1) = \frac{6}{7.2}

0.5v + 0.5 + 0.5v - 0.5 = 0.8333

v = 0.8333

Her usual rate is 0.8333 miles per hour.

8 0
3 years ago
Aisha measures the length of a sheet of paper and finds that it is 29 cm long. The label on the package indicates that the paper
Masteriza [31]

Answer:

just do the step by step and you'll probably get it because it's quite simple but hard for me to explain so just read this!

Step-by-step explanation:

In making any measurement, the chances are that our results will not be absolutely accurate.  We can often compare our results with some standard or accepted value to see how closely they agree.  But how much error can be allowed before the result becomes meaningless?

As you may guess, the amount of error that is acceptable varies with the situation.  Suppose you measure the distance on a map between your Scarsdale and Mamaroneck and you get a result of 5 miles.  If the actual distance is 5 1/2 miles, the chances are this error will have no effect on the trip between the two towns. But if the same degree of error existed in the calculations used to send astronauts to the moon, those people would be in big trouble!

Percentage Error =  <u>measured value - accepted value</u>  x 100%

                                             accepted value          

Suppose, you measured the length of a table and obtained a measurement of 202 cm.  A friend also measures the table and obtains a result of 198 cm. To calculate the percentage error in each of the measurements, you need to know the "correct' or “accepted value” of the length of the table. After consulting the manufacturer’s catalog, you find that the table's length is listed as 200 cm in length. This will be used as the accepted value in our calculation.

The calculations of percentage error for the two measurements are shown below. Both measurements show an error of 1%. Your friend has made a measurement which is on the low side of the accepted value and is therefore, negative. You, on the other hand, have made an error on the high side of the accepted value and it is positive.

I dont know the answer but I hope this helped!

(sorry for the inconvenience)

6 0
3 years ago
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