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Kamila [148]
4 years ago
10

How to factor x^3 - 4x^2 - 9x + 36 by grouping

Mathematics
2 answers:
const2013 [10]4 years ago
6 0

Answer:

(x-4) (x-3) (x+3)

Step-by-step explanation:

x^3 - 4x^2 - 9x + 36

Make 2 groups

x^3 - 4x^2            - 9x + 36

We can factor out x^2 from the first group and -9 from the second group

x^2 (x-4)    - 9(x-4)

Now factor out (x-4)

(x-4) (x^2 -9)

This may be an answer choice but we can still factor

(x^2 -9) is the difference of squares

(x^2-9) = (x-3) (x+3)

Replacing this

(x-4) (x-3) (x+3)

alukav5142 [94]4 years ago
4 0

Answer:

(x - 4)(x - 3)(x + 3)

Step-by-step explanation:

x³ - 4x² - 9x + 36

x²(x - 4) - 9(x - 4)

(x - 4)(x² - 9)

(x - 4)(x² - 3²)

(x - 4)(x - 3)(x + 3)

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Answer:

$16,000

Step-by-step explanation:

For easier understanding and calculation; we created a table for solving this question.

Destination →  Dallas     Atlanta     Denver      Availability

Source

<u>↓                                                                                           </u>

<u>Houston          $ 8         $ 12             $ 13          850          </u>

<u />

<u>Phoenix           $ 10       $ 14             $ 8           800            </u>

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<u>Memphis         $ 11         $ 8             $ 14          350            </u>

<u>Requirement    800       700            250                             </u>

<u />

Minimum Shipping Cost to Dallas is from Houston and they have 850 air conditioners, Dallas need 800, so ship all required 800 air conditioners from Houston itself

Minimum shipping cost of Atlanta is from Memphis and they have 350 air conditioners, but Atlanta need 700, so ship all the 350 air conditioners that Memphis have to Atlanta

Minimum shipping cost to Denver is from Phoenix and they have 800 air conditioners, but Denver need 250, so ship all the required 250 air conditioners to Denver itself.

Destination →  Dallas     Atlanta     Denver      Availability

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<u>↓                                                                                           </u>

Houston          $ 8         $ 12             $ 13          850          

<u>                         (800)                                                           </u>

Phoenix           $ 10       $ 14             $ 8           800        

<u>                                                         (250)                             </u>

<u />

Memphis         $ 11         $ 8             $ 14          350            

<u>                                       (350)                                               </u>  

<u>Requirement    800       700            250                             </u>

Still Atlanta need 350 air conditioners more, the second minimum shopping cost to Atlanta is from Houston and they have 50 air conditioners left .

So, ship all the 50 air conditioners that Houston have to Atlanta

Also, sent the remaining 300 air conditioners that Atlanta need from Phoenix

Destination →  Dallas     Atlanta     Denver      Availability

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<u>                         (800)      (50)                                                 </u>

Phoenix           $ 10       $ 14             $ 8           800        

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<u />

Memphis         $ 11         $ 8             $ 14          350            

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The total cost of shipping = ($ 8 × 800) +( ( $ 12 × 50)+($ 14 × 300) +( $ 8 × 350) ) + ( $ 8 × 250)

= ( $ 6, 400) + $ ( 600 + 4, 200 + 2, 800 ) + $ 2, 000

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Therefore, the total cost = $ 16,000

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Answer:

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Adopting:

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Note: Now, let's find the volume of a hemisphere.

Data: (hemisphere volume)

V (volume) = ?

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Adopting:

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Formula: (Volume of the hemisphere)

Solving:

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