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defon
3 years ago
6

Solve using “completing the square”, thank you! x^4-4x^2+2=0

Mathematics
1 answer:
vodomira [7]3 years ago
7 0

(*)\qquad(a-b)^2=a^2-2ab+b^2\\\\x^4=x^{2\cdot2}=(x^2)^2\\\\x^4-4x^2+2=0\\\\(x^2)^2-4x^2+2=0\\\\\text{substitute}\ t=x^2 > 0\\\\t^2-4t+2=0\\\\t^2-2\cdot t\cdot2+2=0\ \ \ \ \ \ |+2^2\\\\\underbrace{t^2-2\cdot t\cdot2+2^2}_{(*)}+2=2^2\ \ \ \ \ \ |-2\\\\(t-2)^2=4-2\\\\(t-2)^2=2\to t-2=\pm\sqrt2\ \ \ \ \ |+2\\\\t=2-\sqrt2\ \vee\ t=2+\sqrt2\\\\x^2=2-\sqrt2\ \vee\ x^2=2+\sqrt2\\\\x=-\sqrt{2-\sqrt2}\ \vee\ x=\sqrt{2-\sqrt2}\ \vee\ x=-\sqrt{2+\sqrt2}\ \vee\ x=\sqrt{2+\sqrt2}

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A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the
almond37 [142]

Answer:

s = 4

Step-by-step explanation:

The equation for the line of best fit for the data is p=25s+40.

Where p is no. of points and s is no. fo strikes

We need to find the number of strikes made by a bowler with 140 points.

Put p = 140

p=25s+40

140 = 25s+40

Subtract 40 to both sides,

140-40 = 25s+40-40

100 = 25s

⇒ s = 4

So, there are 4 strikes made by a bowler with 140 points.

5 0
3 years ago
( I know the answers I just don't get why)
Over [174]
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8 0
3 years ago
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irinina [24]

Answer:

-1,7

0,-3

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5,47

Step-by-step explanation:

-x-=+

6 0
3 years ago
Read 2 more answers
What is the area of the composite figure shown.
AlekseyPX
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3 years ago
13. A smoothie shop has 40 stores, and 55% of the stores are in
S_A_V [24]

Answer:

You could answer this two ways.

Step-by-step explanation:

Method 1: Set up proportion

x/40=55/100

Cross-multiply and you will get..

2200=100x

x=22

Method 2: Use decimals

As we saw in the first method, 55 percent is equal to 55/100. 55/100 is equal to 0.55.

You can multiply 0.55 and 40 to get the answer as well.

0.55 times 40 is 22.

Hope this explanation helped! ☺️

6 0
3 years ago
Read 2 more answers
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