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3 years ago

Fins the value of (15)^3 + (-9)^3 + (-6)^3 , without actually cubing the numbers

Mathematics

1 answer:

Hatshy [7]3 years ago

8 0

a³ + b³ + c³ + 3abc = ( a + b + c)(a² + b² + c² + ab + bc + ca)

if a + b + c = 0. then a³ + b³ + c³ = 3abc

here a + b + c = 15 + (-9) + (-6)

a + b + c = 15 - 15

a + b + c = 0

so a³ + b³ + c³ = 3abc

15³ + (-9)³ + (-6)³ = 3(15)(-9)(-6)

= 2430

so the answer is 2430

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3 years ago

Round 45.983 to the nearest whole number, tenth and hundredth.

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Answer:

Step-by-step explanation:

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3 years ago

Three candidates were running for president of a student council. Altogether, 1524 students cast a vote in the election. The sec

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Answer:

48%

Step-by-step explanation:

The total number of votes casted = 1524 votes = 100%

Let a = votes of first place candidate

b = votes of second place candidate

c = votes of third place candidate

The second place candidate had 140 votes less than the winner

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

a + b + c = 1524 votes....... Equation 5

If a = b + 140 and c = b - 395

The number of votes by b(second place candidate ) =

b + 140 + b + b - 395 = 1524 votes

3b = 1524 + 395 - 140

3b = 1779

b = 1779/3

b = 593 votes.

Therefore, the second place candidate had 593 votes.

Now we can calculate how many votes, the other candidates had.

The second place candidate had 140 votes less than the winner

Votes for the winner( first place candidate)

b = a - 140 votes...... Equation 1

Hence,

a = b + 140.......... Equation 2

Since b = 593

a = 593 + 140

a = 733 votes

Votes for the last place candidate

Since, Second place candidate has 395 votes more than the last place candidate

b = c + 395.......Equation 3

Hence,

c = b - 395......Equation 4

b = 593

c = 593 - 395

c = 198

From the above calculation,

a = votes of first place (winner) candidate = 733

b = votes of second place candidate = 593

c = votes of third(last) place candidate = 198

In the above question, we were asked to calculate the percentage of all the votes cast were received by the winner.

This is calculated as

= Voted received by winner/ Total number of votes casted × 100

= 733/1524 × 100

= 48.09711286%

Approximately to the nearest percent = 48%

Therefore, the percentage of all the votes cast were received by the winner = 48%

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3 years ago

Rory is driving 584 miles to a family reunion. She will drive 300 miles by her self the first day.The second day, Rory and her c

gogolik [260]

Answer:

Total distance Rory drive = 300 +142 = 442 miles

and total distance her cousin drive = 142 miles.

Step-by-step explanation:

Total distance traveled by Rory and her cousins = 584 miles

Distance drive by Rory herself first day = 300 miles

Distance left to travel = total distance - distance drive by Rory

= ( 584-300 ) miles

= 284 miles.

According to the question, The second day, Rory and her cousin will share driving equally.

Let the distance traveled by cousin is S miles, then, Rory also drive S miles.

⇒ S + S = 284

⇒ 2S = 284

⇒ S = 142

So they will divide the remaining distance of 284 miles among them equally that is they both drive 142 miles.

Total distance Rory drive = 300 +142 = 442 miles

and total distance her cousin drive = 142 miles.

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4 years ago

Fins the value of (15)^3 + (-9)^3 + (-6)^3 , without actually cubing the numbers​

Fins the value of (15)^3 + (-9)^3 + (-6)^3 , without actually cubing the numbers