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MAXImum [283]
3 years ago
9

If the roots of a quadratic equation are 1±√5, then the product of the roots is

Mathematics
2 answers:
Drupady [299]3 years ago
5 0
The plus-minus sign represents that there are two possible outcomes.

In this case, we have 1 \pm \sqrt{5}. When we branch out the possibilities we got 2 values: 1 + \sqrt{5} and 1 - \sqrt{5}

Those are the roots of this equation. When they ask their product, they want you to multiply both numbers.

When we multiply them: (1 + \sqrt{5}) \times( 1 - \sqrt{5})

When we FOIL the we get: 1 \times 1 - 1 \times \sqrt{5} + 1 \times \sqrt{5} - \sqrt{5} \times \sqrt{5}

Simplify:
1 - \sqrt{5} + \sqrt{5} - 5
1 - 5 = 6

So the product of the two roots of this equation is 6.
Komok [63]3 years ago
4 0
The two roots would be 6
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2 points
miskamm [114]

The x - intercept of 5x - 3y = 15 is (3, 0)

The y -intercept of 5x - 3y = 15 is (0, -5)

<h3><u>Solution:</u></h3>

Given equation is 5x - 3y = 15

<em><u>To find: x - intercept and y -intercept</u></em>

The x intercept is the point where the line crosses the x axis. At this point y = 0

The y intercept is the point where the line crosses the y axis. At this point x = 0.

<em><u>Finding x - intercept:</u></em>

To find the x intercept using the equation of the line, plug in 0 for the y variable and solve for x

So put y = 0 in given equation

5x - 3(0) = 15

5x = 15

x = 3

So the x - intercept is (3, 0)

<em><u>Finding y - intercept:</u></em>

To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y

So put x = 0 in given equation

5(0) - 3y = 15

-3y = 15

y = -5

So the y - intercept is (0, -5)

5 0
3 years ago
How many ways can you arrange 8 objects?
Sergio [31]

Answer:

40,320

Step-by-step explanation:

The first object in the arrangement can be chosen 8 ways. The second, 7 ways (after the first one is chosen). And so on down to the last object, which will be the only remaining one. Altogether, the number of ways you can arrange the objects is ...

8·7·6·5·4·3·2·1 = 8! = 40,320

7 0
3 years ago
Read 2 more answers
The blades of a windmill turn on an axis that is 35 feet above the ground. The blades are 10 feet long and complete two rotation
Alona [7]

Answer:

h = 10sin(π15t)+35

Step-by-step explanation:

The height of the blade as a function f time can be written in the following way:

h = Asin(xt) + B, where:

B represets the initial height of the blade above the ground.

A represents the amplitud of length of the blade.

x represents the period.

The initial height is 35 ft, therefore, B = 35ft.

The amplotud of lenth of the blade is 10ft, therefore A = 10.

The period is two rotations every minute, therefore the period should be 60/4 = 15. Then x = 15π

Finally the equation that can be used to model h is:

h = 10sin(π15t)+35

5 0
3 years ago
Read 2 more answers
Approximate pi plus the square root of 70 to the nearest hundredth.
stich3 [128]

Answer:

  11.51

Step-by-step explanation:

In general, a calculator is required to evaluate the irrational sum ...

  π + √70

<h3>Calculator result</h3>

The result from a readily-available online calculator is shown in the attachment.

  π + √70 ≈ 11.51

__

<em>Additional comment</em>

You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.

For a number n = a² +b, the square root can be approximated by the continued fraction ...

  √n ≈ a +b/(2a +b/(2a +...))

Effectively, the root (r) can be iterated from the recursive formula ...

  r' = a +b/(a +r)

For √70, we have 70 = 8² +6   ⇒   a=8, b=6

If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...

  r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8

  r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131

This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...

  3.1416 +8.3664 = 11.5080 ≈ 11.51

5 0
1 year ago
(PICTURE PROVIDED)
Sonbull [250]

Answer:

A: She lined up the protractor incorrectly.

Hope it helps:)

7 0
2 years ago
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