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spin [16.1K]
2 years ago
9

Factor the polynomial completely. 4x3 – 12x2 7x – 21 4x2(x – 3) 7(x – 3) Which is the completely factored polynomial? 4x2(x 4) 3

x2(x – 3) (4x2 – 7)(x 3) (4x2 7)(x – 3).
Mathematics
1 answer:
bixtya [17]2 years ago
7 0

Answer:

  (d)  (4x² +7)(x -3)

Step-by-step explanation:

This polynomial can be factored by factoring pairs of terms.

  = (4x³ -12x²) +(7x -21)

  = 4x²(x -3) +7(x -3)

  = (4x² +7)(x -3)

__

<em>Additional comment</em>

The answer choices suggest we're not interested in irrational or complex factors. The quadratic (4x² +7) could be factored into linear terms involving irrational complex numbers. The form for "difference of squares" would be used for the purpose.

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Choose 5 cards from a full deck of 52 cards with 13values (2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K, A) and 4 kinds(spade, diamond, h
Delvig [45]

Answer:

a) 182 possible ways.

b) 5148 possible ways.

c) 1378 possible ways.

d) 2899 possible ways.

Step-by-step explanation:

The order in which the cards are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question, we have that:

There are 52 total cards, of which:

13 are spades.

13 are diamonds.

13 are hearts.

13 are clubs.

(a)Two-pairs: Two pairs plus another card of a different value, for example:

2 pairs of 2 from sets os 13.

1 other card, from a set of 26(whichever two cards were not chosen above). So

T = 2C_{13,2} + C_{26,1} = 2*\frac{13!}{2!11!} + \frac{26!}{1!25!} = 182

So 182 possible ways.

(b)Flush: five cards of the same suit but different values, for example:

4 combinations of 5 from a set of 13(can be all spades, all diamonds, and hearts or all clubs). So

T = 4*C_{13,5} = 4*\frac{13!}{5!8!} = 5148

So 5148 possible ways.

(c)Full house: A three of a kind and a pair, for example:

4 combinations of 3 from a set of 13(three of a kind ,c an be all possible kinds).

3 combinations of 2 from a set of 13(the pair, cant be the kind chosen for the trio, so 3 combinations). So

T = 4*C_{13,3} + 3*C_{13.2} = 4*\frac{13!}{3!10!} + 3*\frac{13!}{2!11!} = 1378

So 1378 possible ways.

(d)Four of a kind: Four cards of the same value, for example:

4 combinations of 4 from a set of 13(four of a kind, can be all spades, all diamonds, and hearts or all clubs).

1 from the remaining 39(do not involve the kind chosen above). So

T = 4*C_{13,4} + C_{39,1} = 4*\frac{13!}{4!9!} + \frac{39!}{1!38!} = 2899

So 2899 possible ways.

4 0
3 years ago
Pedro's Diner is open six days a week. His income for the first five days this week was
S_A_V [24]

Answer:

$330

Step-by-step explanation:

What is mean/average?

It is the "sum of all the numbers" divided by the "number of numbers".

An average of 200 for 6 numbers means:

Average=\frac{SUM}{NumberOfNumbers}\\200=\frac{SUM}{6}\\SUM=200*6\\SUM=1200

THus, if we were to add the 6 numbers, we would get "1200". Let the 6th number be x, so we can write:

120 + 110 + 200 + 300 + 140 + x = 1200

870 + x = 1200

x = 1200 - 870

x = 330

To make the average $200, Pedro needs to make $330 on 6th day.

6 0
3 years ago
Evaluate the expression 8^7/8^7
Kisachek [45]
<span>8^7/8^7
=</span><span>8^0
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answer is 1</span>
6 0
3 years ago
(4 x 1) + (0 x 1/10) + (7 x 1/100) + (6 x 1/1000)
sergiy2304 [10]

Answer:

1019/250 x

Step-by-step explanation:

4x1+

0x1

10

+

7x1

100

+

6x1

1000

3 0
2 years ago
Read 2 more answers
Solve:<br>2x + 4 - 3x = -11
JulijaS [17]

Answer:

15

Step-by-step explanation:

-1x+4=-11

subtract 4 on both sides

-1x=-15

divide

15

4 0
3 years ago
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