MATHEMATICS MIDDLE SCHOOL

What are the real and complex solutions of the polynomial equation X^3-216=0

Answers

Answer 1
Answer:

Answer:

6,\ -3+3√(3)i,\ -3-3√(3)i

Step-by-step explanation:

Factor the equation x^3-216=0 using formula for difference of the cubes:

x^3-216=(x-6)(x^2+6x+36),

then

x-6=0\ or\ x^2+6x+36=0.

1. The equation x-6=0 has real solution x=6.

2. The equation x^2+6x+36=0 has negative discriminant D=6^2-4\cdot 36=36-144=-108, then it has two complex solutions

x_(1,2)=(-6\pm 6√(3)i)/(2)=-3\pm3√(3)i.

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A box is filled with pennies, nickels, and dimes in a ratio of 2:3:4. If the total number of coins in the box is 1620, how many pennies are in the box

Answers

We could say that the number of pennies is 2x, nickels are 3x, and dimes are 4x. Adding all of them together, we get 2x+3x+4x=9x. We also know that 9x=1620 because the total amount of coins is 1620. Dividing by 9 on both sides we get x=180.
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rick won 27 tickets playing a game to get the prize he needs to win at least 30 tickets how many more tickets can he win to get a prize?

Answers

i believe 3. because if he needs at least 30 to win any prize and he already has 27, then he only needs 3 more tickets.
The answers going to be 3

What's the estimate of 189,729

Answers

It's might be.....180,000 I'm sure
It will be 180,000!!!!

Maria's favorite candy bar has 230 calories.The nutrition label states that 7/8 of the calories come from fat.How many calories in the candy bar come from fat?

Answers

230/8= 28.75
28.75x 7= 201.25
201.25 calories come from fat.

Raffle tickets are sold and 6 prizes are available for the lucky draw. A total of 1,356 raffle tickets are sold for 4/5 dollars each and the 6 prizes cost 8 3/10 each. How much money was raise from the raffle tickets?

Answers

Answer:

US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Number of raffle tickets sold = 1,356

Cost of each raffle ticket = US$ 4/5

Number of prizes = 6

Cost of each prize = US$ 8 3/10

2. How much money was raised from the raffle tickets?

For easier calculation, let's convert the fraction numbers to decimal numbers:

Cost of each raffle ticket = US$ 4/5 = US$ 0.80

Cost of each prize = US$ 8 3/10 = US$ 8 + 0.30 = US$ 8.30

Now, we use this formula to calculate how much money was raised and the profits:

Profits = (Number of tickets sold * Cost of each ticket) - (Number of prizes * Cost of each prize)

Replacing with the real values, we have:

Profits = 1,356 * 0.80 - 6 * 8.30

Profits = 1,084.80 - 49.80

Profits = 1,035

US$ 1,084.80 were raised from the raffle tickets and US$ 1,035 are the profits after paying the prizes.

X and Y are continuous values, both measured to 2 significant figures. X=230 and Y=400. work out the greatest possible value of X/Y^2.(this is on an upper and lower bounds sheet)

Answers

"Two significant figures" means that a digit after the second one could actually be anything ... it wasn't measured. 'X' could be anything from 230 to 239. 'Y' could be anything from 400 to 409.The greatest possible value of that fraction is. (239)/(409 squared) .
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