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Ierofanga [76]
3 years ago
11

23^3 (-12)^3 +(-11)^3 without actually calculating cubes

Mathematics
1 answer:
Zigmanuir [339]3 years ago
8 0

Answer:

9108

Step-by-step explanation:

23^3+(-12)^3+(-11)^3                              remove parentheses

= 23^3-12^3-11^3                                  group difference of two cubes

= (23-12)(23^2+23*12+12^2) + 11^3      factor difference of two cubes

= 11 (23^2+23*12+12^2-11^2)                factor ou 11

= 11(23(23+12) + (12+11)(12-11))              apply difference of two squares

= 11 (23*35+23*1)                                  factor out 23

= 11(23*(35+1))                                       simplify

= 11*23*36                                             convert 11*23 into difference of 2 squares                                                                    

= (17^2-6^2)*6^2                                   expand parentheses

= 102^2-36^2                                       evaluate squares

= 10404 - 1296                                     subtraction

= 9108

(no calculator required)

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3 years ago
During a concert, $3280 was received. A total of 760 people attended. Reserved seats were $6 and general admission seats were $4
Andre45 [30]

Answer:

The number of reserved seat is 120 and number of general seat is 640.

Step-by-step explanation:

Given,

Total number of seats = 760

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Let the total number of reserved seat be x.

And  the total number of general seat be y

Hence total number of seats is the sum of total number of reserved seat and  the total number of general seats.

So the equation can be written as;

x+y=760\ \ \ \ equation\ 1

Again, total money collected is the sum of fees of one reserved seat times total number of reserved seat and fees of one general seat times the total number of general seats.

So the equation can be written as;

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Now, multiplying equation 1 by 4 and then subtract it from equation 2.

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x+y=760\\120+y=760\\y=760-120=640

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