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3 years ago

Factorise 2xsquared X 7x +3

Mathematics

1 answer:

Monica [59]3 years ago

5 0

Answer:

(-2x - 1) • (x + 3)

Step-by-step explanation:

3.2 Factoring 2x2 + 7x + 3

The first term is, 2x2 its coefficient is 2 .

The middle term is, +7x its coefficient is 7 .

The last term, "the constant", is +3

Step-1 : Multiply the coefficient of the first term by the constant 2 • 3 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is 7 .

-6 + -1 = -7

-3 + -2 = -5

-2 + -3 = -5

-1 + -6 = -7

1 + 6 = 7 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 6

2x2 + 1x + 6x + 3

Step-4 : Add up the first 2 terms, pulling out like factors :

x • (2x+1)

Add up the last 2 terms, pulling out common factors :

3 • (2x+1)

Step-5 : Add up the four terms of step 4 :

(x+3) • (2x+1)

Which is the desired factorization

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You roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any o

amm1812

Answer: -1
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Explanation:

Define the three events
A = rolling a 7
B = rolling an 11
C = roll any other total (don't roll 7, don't roll 11)

There are 6 ways to roll a 7. They are
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
Use this to compute the probability of rolling a 7
P(A) = (number of ways to roll 7)/(number total rolls) = 6/36 = 1/6
Note: the 36 comes from 6*6 = 36 since there are 6 sides per die

There are only 2 ways to roll an 11. Those 2 ways are:
5+6 = 11
6+5 = 11
The probability for event B is P(B) = 2/36 = 1/18

Since there are 6 ways to roll a "7" and 2 ways to roll "11", there are 6+2 = 8 ways to roll either event.
This leaves 36-8 = 28 ways to roll anything else
P(C) = 28/36 = 7/9

-----------------------------

In summary so far,
P(A) = 1/6
P(B) = 1/18
P(C) = 7/9

The winnings for each event, let's call it W(X), represents the prize amounts.
Any losses are negative values
W(A) = amount of winnings if event A happens
W(B) = amount of winnings if event B happens
W(C) = amount of winnings if event C happens
W(A) = 18
W(B) = 54
W(C) = -9

Multiply the probability P(X) values with the corresponding W(X) values
P(A)*W(A) = (1/6)*(18) = 3
P(B)*W(B) = (1/18)*(54) = 3
P(C)*W(C) = (7/9)*(-9) = -7

Add up those results
3+3+(-7) = -1

The expected value for this game is -1.
The player is expected to lose on average 1 dollar per game played.

Note: because the expected value is not 0, this is not a fair game.

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