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3 years ago

Explain how to find the quotient of: (8a3+31a2-20a-5)/(8a-1)

Mathematics

1 answer:

pashok25 [27]3 years ago

4 0

Answer:

Quotient = a²+ 4a- 2

Step-by-step explanation:

(8a3+31a2-20a-5)/(8a-1)

<u> a² +4a-2 ⇒ quotient</u>

(8a-1)√(8a3+31a2-20a-5)

8a²- a² ⇒ Multiplying (8a-1) by a²

<u> - + </u> ⇒ Changing signs

32a²- 20a- 5

32a²- 4a ⇒ Multiplying (8a-1) by 4a

<u> - + </u> ⇒Changing signs

-16a -5

- 16a +2 ⇒ Multiplying (8a-1) by -2

<u> + - ⇒</u> Changing signs

-7 ⇒ Remainder

We follow the steps of simple division to get the quotient which is a²+ 4a- 2

We multiply (8a-1) by factors such as a², +4a and -2 to get the same terms as given in the dividend.

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Solve each equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.

vodomira [7]

Answer:

x=2

Step-by-step explanation:

x^2+10x+24=0

12x=24=0

12x=24

x=2

My math is rusty so this may not be the right answer.

3 0

3 years ago

If √3 = 1.732, then √[(√3-1)/(√3+1)] is equal to

adelina 88 [10]

Step-by-step explanation:

<h3><u>Given Question :-</u></h3>

$\sf \: \sqrt{3} = 1.732, \: then \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

$\red{\large\underline{\sf{Solution-}}}$

Given expression is

$\rm :\longmapsto\: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} }$

<em>On rationalizing the denominator, we get </em>

$\rm \: = \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} \times \dfrac{ \sqrt{3} - 1}{ \sqrt{3} - 1} }$

$\rm \: = \: \sqrt{\dfrac{ {( \sqrt{3} - 1)}^{2} }{( \sqrt{3} + 1)( \sqrt{3} - 1)} }$

$\boxed{ \tt \: (x - y)(x + y) = {x}^{2} - {y}^{2} \: }$

<em>So, using this, we get </em>

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ {( \sqrt{3})}^{2} - {(1)}^{2} } }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{ 3 - 1} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} }$

$\rm \: = \: \dfrac{ \sqrt{3} - 1}{ \sqrt{2} } \times \dfrac{ \sqrt{2} }{ \sqrt{2} }$

$\rm \: = \: \dfrac{(1.732 - 1) \sqrt{2} }{2}$

$\rm \: = \: \dfrac{0.732 \times \sqrt{2} }{2}$

$\rm \: = \: 0.366 \sqrt{2}$

Hence,

$\rm :\longmapsto\: \boxed{ \rm{ \: \: \: \sqrt{\dfrac{ \sqrt{3} - 1}{ \sqrt{3} + 1} } = 0.366 \sqrt{2} \: \: \: }}$

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<h2>More Identities to know :- </h2>

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)

3 0

3 years ago

Which transformation(s) could map one triangle to the other? reflection translation reflection and translation rotation and tran

denis-greek [22]

The correct option D.

Rotation and translation transformation(s) could map one triangle to the other.

<h3>Briefing:</h3>

Triangle A is mapped to triangle B by reflecting it across the x-axis and rotating it 90 degrees counterclockwise with respect to the origin. Triangle A to triangle B will be mapped using the following set of transformations, which also highlights how similar the two figures are.

<h3>What is a geometric transformation in GIS?</h3>

When registering a digital map, satellite image, or air photo onto a projected coordinate system, geometric transformation is the process of applying a set of control points and transformation equations. Map-to-map transformation and image-to-map transformation are examples of geometric transformation in geographic information systems (GIS).

<h3>What are the three types of geometric transformation?</h3>

Mathematically speaking, a transformation is a mapping from a preimage of a shape or function to an image of the same shape or function. Translation, rotation, and reflection are the three main categories of transformations.

To know more about geometric transformation visit:

brainly.com/question/19117133

#SPJ4

I understand that the question you are looking for is:

Which transformation(s) could map one triangle to the

other?

O reflection

O translation

O reflection and translation

O rotation and translation

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1 year ago

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D = 10.2 ft, r = 0.5 ft/h find t

Margaret [11]

Answer:

20.4

Step-by-step explanation:

If you are using D = r × t

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20.4 = t

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2 years ago

In a circle graph, what percent would be represented by a 25° angle? (round to nearest whole number if needed)

vfiekz [6]

Answer:

A) 7%

Step-by-step explanation:

There are 360 degrees in a circle. Thus, a 25 degree sector would make up 25/360 of the circle. 25/360 can be simplified to .06944444. This rounds to .07, which is 7%.

8 0

4 years ago

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