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mote1985 [20]
3 years ago
10

Use completing the square to solve this quadratic equation.

Mathematics
1 answer:
borishaifa [10]3 years ago
7 0

Step-by-step explanation:

x² + 6x + 9 = 2

(x + 3)² = 2

x + 3 = ±sqrt(2)

x = -3 ± sqrt(2)

so, B and D are correct.

control :

(-3 + sqrt(2))² + 6(-3 + sqrt(2)) + 9 = 2

9 + 2 - 6sqrt(2) - 18 + 6sqrt(2) + 9 = 2

2 = 2

correct

(-3 - sqrt(2))² + 6(-3 - sqrt(2)) + 9 = 2

9 + 2 + 6sqrt(2) - 18 - 6sqrt(2) + 9 = 2

2 = 2

correct

(3 + sqrt(2))² + 6(3 + sqrt(2)) + 9 = 2

9 + 2 + 6sqrt(2) + 18 + 6sqrt(2) + 9 = 2

38 + 12sqrt(2) = 2

wrong.

(3 - sqrt(2))² + 6(3 - sqrt(2)) + 9 = 2

9 + 2 - 6sqrt(2) + 18 - 6sqrt(2) + 9 = 2

38 - 12sqrt(2) = 2

wrong.

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The area of shaded region.
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Answer:

160π cm²

Step-by-step explanation:

The area of the shaded region is

area of outer circle - area of inner circle

A = πr₁² - πr₂²

r₁ is the radius of the outer circle = 10 + 3 = 13 cm

r₂ is the radius of the inner circle = 3 cm

A = π × 13² - π × 3²

  = π(169 - 9) = 160π cm² ≈ 502.65 cm² ( to 2 dec. places )

5 0
3 years ago
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What divided by what equals 2.82?
kenny6666 [7]
Well.....2.82 divided by 1 = 2.82
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4 years ago
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Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of adults who retir
matrenka [14]

Answer:

<u>Type I error: </u>D. Reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually true.

<u>Type II error: </u>A. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than or equal to 62 % when it is actually false.

Step-by-step explanation:

A type I error happens when a true null hypothesis is rejected.

A type II error happens when a false null hypothesis is failed to be rejected.

In this case, where the alternative hypothesis is that "the percentage of adults who retire at age 65 is greater than 62%", the null hypothesis will state that this percentage is not significantly greater than 62%.

A type I error would happen when the conclusion is that the percentage is greater than 62%, when in fact it is not.

A type II error would happen when there is no enough evidence to claim that the percentage is greater than 62%, even when the percentage is in fact greater than 62% (but we still don't have evidence to prove it).

5 0
4 years ago
600 times 23 times 60 times 6565
ivanzaharov [21]

Answer:

5,435,820,000 is your answer

7 0
4 years ago
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The graph below shows the distance, y, in miles, of a bird from its nest for a certain amount of time, x, in minutes:
Montano1993 [528]

Answer:

0.2 miles per minute represents the speed of the bird and 3 miles represents the original distance of the bird from its nest.

Step-by-step explanation:

As there is no graph mentioned here but the information are quite sufficient to answer the question.

We have points (0,3), (5,4),(10,5)...

From these points we can find the slope of the line .

From point slope formula y-y_1=m(x-x_1)

And assigning (x,y) (0,3) and (x_1,y_1) (5,4)

m=\frac{y_1-y}{x_1-x} =\frac{4-3}{5-0} =\frac{1}{5}=0.2

This slope is also the speed of the bird which is 0.2\ miles\ per\ minute.

As by plugging the values of any coordinate point we can confirm this.

Lets put (10,5), y-axis is the distance so in 10 minutes the the distance covered by the bird must be equal to to y-axis value which is 5 miles.

y=0.2(x),y=0.2(10)=5\ miles

Now as in t=0 the bird has started from y-intercept value 3 so we can say that,the original distance of the bird from its nest is 3\ miles.

So the correct choices are:B and D

The birds speed is 0.2\ miles per minute and is 3\ miles away from its nest.

7 0
3 years ago
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