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topjm [15]
3 years ago
10

Algebra help for ACT!

Mathematics
1 answer:
denis23 [38]3 years ago
3 0

Answer:

J. The equation has one real solution and two complex solutions.

Step-by-step explanation:

Complex solutions come in pairs, so there can only be an even number of them.  So we can rule out G, H, and K.

To find the other roots, we can factor using either long division or grouping.  To use long division, see the attached picture.  To use grouping:

3x³ − 4x² + x − 10 = 0

3x³ − 6x² + 2x² + x − 10 = 0

3x² (x − 2) + (2x + 5) (x − 2) = 0

(x − 2) (3x² + 2x + 5) = 0

The other factor is 3x² + 2x + 5.  The discriminant of this is (2)² − 4(3)(5) = -56.  Since the discriminant is negative, the roots are complex.

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One morning the temperature is -28 degrees in Anchorage, Alaska, and +65 degrees in Miami, Florida. Which city is warmer in the
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Answer:

B. Miami is 93 degrees warmer than Anchorage.

Step-by-step explanation:

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3 0
3 years ago
In the Tigers Football Club, there are 9 players to each coach, while in the Eagles Football Club, there are 17 players to every
vivado [14]

9514 1404 393

Answer:

  • Tigers: 8 coaches, 72 players
  • Eagles: 16 coaches, 136 players

Step-by-step explanation:

We can define a "basic unit" of each team to be the minimum number of players and coaches that can have the given ratio. For the Tigers, that is 1 coach and 9 players, for a total of 10 team members. For the Eagles, that is 2 coaches and 17 players, for a total of 19 team members. If we have t basic units of Tigers and e basic units of Eagles, then we want ...

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We want t and e to be integers, so this is a Diophantine equation. It can be solved any of several ways, including use of the Extended Euclidean Algorithm. Here, we'll make some observations based on "number sense."

The value of e must be an even number between 0 and 232/19 = 12. The product of e and 19 must be a number that ends in 2, because 10t will end in 0, and the sum with 19e must end in 2.

The only multiple of 9 that ends in 2 is 9×8 = 72, so the value of e must be a positive number less than 12 that ends in 8. We must have e=8.

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The Tigers have 8 coaches and 72 players.

The Eagles have 16 coaches and 136 players.

8 0
3 years ago
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