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nikklg [1K]
2 years ago
15

Which of the following is an equivalent equation obtained by completing the square of the expression below? x^2+6x−8=0 A (x+3)^2

=8 B (x+3)^2=17 C (x+3)^2=1 D x^2+6x+6=14
Mathematics
1 answer:
valentina_108 [34]2 years ago
7 0

Answer:

Solving the equation x^2+6x-8=0 by completing the square method we get \mathbf{(x+3)^2=17}

Option B is correct option.

Step-by-step explanation:

We need to solve the equation x^2+6x-8=0 by completing the square method.

For completing the square method: we need to follow: a^2+2ab+b^2=(a+b)^2

We are given:

x^2+6x-8=0

Solving by completing the square

x^2+2(x)(?)+(?)^2-8=0

We need to find ? in our case ? is 3 because 2*3= 6 and our middle term is 6x i,e 2(x)(3)=6x.

So, adding and subtracting (3)^2

x^2+2(x)(3)+(3)^2-8-(3)^2=0\\(x+3)^2-8-9=0\\(x+3)^2-17=0\\(x+3)^2=17

So, solving the equation x^2+6x-8=0 by completing the square method we get \mathbf{(x+3)^2=17}

Option B is correct option.

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The 90% confidence interval for the mean one-way commuting time in New York City is
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Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

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Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

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(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

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C. I = (5.147 ; 6.053)

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