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viktelen [127]
3 years ago
9

Hello can someone help me simplify 4) and 5)? Thank you and please include steps :)

Mathematics
1 answer:
Leni [432]3 years ago
3 0
Alrighty

remember some rules
(ab)^c=(a^c)(b^c)
and
x^{-m}=\frac{1}{x^m}
and
x^0=1 for all real values of x
and
(a^b)^c=a^{bc}
and
(\frac{a}{b})^c=\frac{a^c}{b^c}
and
(a/b)/(c/d)=(ad)/(bc)
and
(a^b)(a^c)=a^{b+c}
and
\frac{a^m}{a^n}=a^{m-n}
and don't forget pemdas
example: -x^m=-1(x^m) but (-x)^m=(-1)^m(x^m)

so

4.
(\frac{c^{-2}}{2})^{-2}=

\frac{(c^{-2})^{-2}}{2^{-2}}=

\frac{c^4}{\frac{1}{2^2}}=

\frac{c^4}{\frac{1}{4}}=

4c^4



5.

\frac{(-a)^4bc^5}{-a^2b^{-3}c^0}=

\frac{(-1)^4(a)^4bc^5}{-1(a^2)(\frac{1}{b^3}(1)}=

\frac{(1)a^4bc^5}{\frac{(-1)(a^2)}{b^3}}=

\frac{(a^4bc^5)b^3}{(-1)(a^2)}=

\frac{-a^4b^4c^5}{a^2}=

-a^2b^4c^5
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ad-work [718]

Answer:

a) 2

b) -\frac{1}{2}

c) y = 2x + 1

Step-by-step explanation:

a)

First put the equation into slope intersept form (y=mx+b) by...

  • Move the variable to the right-hand side and change its sign : -y = -4 -2x
  • Change the signs on both sides of the equation: y = 4 + 2x
  • Use the commutative property to reorder the terms : y = 2x + 4

Slope intersept form : y = 2x + 4

Parallel lines have the same slope so.... a parallel slope is 2

b)

First put the equation into slope intersept form (y=mx+b) by...

  • Move the variable to the right-hand side and change its sign : -y = -4 -2x
  • Change the signs on both sides of the equation: y = 4 + 2x
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Slope intersept form : y = 2x + 4

To find a perpendicular slope flip the slope and change the sign : -\frac{1}{2}

c)

First put the equation into slope intersept form (y=mx+b) by...

  • Move the variable to the right-hand side and change its sign : -y = -4 -2x
  • Change the signs on both sides of the equation: y = 4 + 2x
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Slope intersept form : y = 2x + 4, parellel slope : 2

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You pick a card at random from an ordinary deck of 52 cards. If the card is an ace, you get 9 points; if not, you lose 1 point.
Andreyy89

Answer:

a = 9\\b = 48\\c = -1

Step-by-step explanation:

We know that:

In a deck of 52 cards there are 4 aces.

Therefore the probability of obtaining an ace is:

P (x) = 4/52

The probability of not getting an ace is:

P ('x) = 1-4 / 52

P ('x) = 48/52

In this problem the number of aces obtained when extracting cards from the deck is a discrete random variable.

For a discrete random variable V, the expected value is defined as:

E(V) = VP(V)

Where V is the value that the random variable can take and P (V) is the probability that it takes that value.

We have the following equation for the expected value:

E(V) = \frac{4}{52}(a) + \frac{b}{52}(c)

In this problem the variable V can take the value V = 9 if an ace of the deck is obtained, with probability of 4/52, and can take the value V = -1 if an ace of the deck is not obtained, with a probability of 48 / 52

Therefore, expected value for V, the number of points obtained in the game is:

E(V) = \frac{4}{52}(9) + \frac{48}{52}(-1)

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