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ICE Princess25 [194]
3 years ago
11

Divide. Express the quotient in simplest form. (x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3

Mathematics
2 answers:
e-lub [12.9K]3 years ago
6 0
R3eeeeeeeeeeeeeeeeeeeeeeee
bekas [8.4K]3 years ago
4 0

(x^2−x−12)/(2x^2)÷(x^2+x−6)/2x^3

First write the given term in the correct form by multiplying with reciprocal of denominator.


Given term =  (x^2−x−12)*2x^3/(2x^2)*(x^2+x-6)

Now we find that numerator = (x^2−x−12)*2x^3

= [tex]2x^3(x-4)(x+3)[tex]

Similarly denominator = [tex]2x^3/(2x^2)*(x^2+x-6)[tex]

=[tex](2x^3(x+3)(x-2)[tex]

Common factor in both numerator and denominator = [tex][2x^2(x+3)(xtex]

So cancel this to get

[tex]x(x-4)/(x-2)[tex]

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Satellite dishes are shaped like parabolas to optimally revive signals. The cross section of a satellite dish can be modeled by
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The cross section of the satellite dish is an illustration of a quadratic function

The quadratic function that models the cross-section is y = 1/6(x^2 - 9)

<h3>How to determie the equation of the cross-section?</h3>

The given parameters are:

Width = 6 feet

Depth = 1.5 feet

Express the width the sum of two equal numbers

Width = 3 + 3

The above means that, the equation of the cross section passes through the x-axis at:

x = -3 and 3

So, we have:

y = a(x - 3) * (x + 3)

Express as the difference of two squares

y = a(x^2 - 9)

The depth is 1.5.

This is represented as: (x,y) =(0,-1.5)

So, we have:

-1.5 = a(0^2 - 9)

Evaluate the exponent

-1.5 = -9a

Divide both sides by -9

a = 1/6

Substitute 1/6 for a in y = a(x^2 - 9)

y = 1/6(x^2 - 9)

Hence, the quadratic function that models the cross-section is y = 1/6(x^2 - 9)

Read more about quadratic functions at:

brainly.com/question/1497716

7 0
2 years ago
A table saw is on clearance for 20% off. If the sale price of the table saw is $380, what was the original price? Justify your s
Nikolay [14]

20% off means it is selling for 80% of the original price ( 100% - 20% =80%)

Divide the sale price by 80% as a decimal:

380/0.80 = 475

The original price was $475

Justify:

Multiply the original price by 20% and subtract:

475 x 0.20 = 95

475-95 = $380 which is the sale price.

5 0
3 years ago
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Answer:

Yes

Step-by-step explanation:

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8•11=88

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Answer:

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Step-by-step explanation:

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