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3 years ago

If f(1) = 2 and f(n+1) = f(n)^2 – 3 then find the value of f(3).

Mathematics

1 answer:

Inga [223]3 years ago

4 0

Answer:

The value of f(3) = -2.

Step-by-step explanation:

First of all, let's find f(2).

$f(n+1)=f(n)^{2}-3$

$f(1+1)=f(1)^{2}-3$

$f(2)=f(1)^{2}-3=2^{2}-3=1$

Now, we can find f(3):

$f(2+1)=f(2)^{2}-3$

$f(3)=f(2)^{2}-3=1^{2}-3=-2$

Therefore, the value of f(3) = -2.

I hope it helps you!

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Answer:

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3 years ago

(X-3) (2x-3)= (x-3) (x+1) solve for x

yanalaym [24]

$(x - 3)(2x - 3) = (x - 3)(x + 1)$

Do the multiplication both sides,

$2 {x}^{2} - 9x + 9 = {x}^{2} - 2x - 3$

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$2 {x}^{2} - {x}^{2} - 9x + 2x + 9 - 3 = 0 \\ {x}^{2} - 7x + 6 = 0$

Factorise this polynomial

${x}^{2} - 6x - 6x + 6 = 0 \\ x(x - 6) - (x - 6) = 0 \\ (x - 1)(x - 6) = 0$

So what we notice here is when you're multiplying two numbers you're getting 0 as answer.

So one of them must be 0.

If (x-1) is 0
then x = 1

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3 years ago

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Which statement(s) is (are) correct?

Anna71 [15]

Answer:

<em>statements 3 and 4 are correct.</em>

Step-by-step explanation:

(1)

The probability of choosing cured pasta and bear= probability that the card is king.

Hence, The probability of choosing cured pasta and bear= $\dfrac{4}{52}=\dfrac{1}{13}$

Probability of choosing baked cucumber and lime mutton=probability that the card is 3.

as there are 4 cards that are '3'.

Hence Probability of choosing baked cucumber and lime mutton= $\dfrac{4}{52}=\dfrac{1}{13}$

as both the probabilities are equal.

Hence statement 1 is incorrect.

(2)

The probability of choosing gooseberry & passion fruit cheesecake= Probability taht the card is ace.

as there are 4 cards which are ace out of 52 cards.

Hence, The probability of choosing gooseberry & passion fruit cheesecake= $\dfrac{4}{52}=\dfrac{1}{13}$

probability of choosing poached fennel & lemon alligator=Probability that the card is a face card.

As there are 12 face cards out of 52 cards.

Hence, probability of choosing poached fennel & lemon alligator= $\dfrac{12}{52}=\dfrac{3}{13}$

Hence, the probability of choosing gooseberry and passion fruit cheesecake is smaller than the probability of choosing poached fennel & lemon alligator.

Hence statement 2 is false.

(3)

The probability of choosing a praline wafer=probability that the card is a diamond.

as there are 13 diamond cards out of 52 cards.

The probability of choosing a praline wafer= $\dfrac{13}{52}=\dfrac{1}{4}$

the probability of choosing poached fennel & lemon alligator=Probability that the card is a face card.

As there are 12 face cards out of 52 cards.

Hence, probability of choosing poached fennel & lemon alligator= $\dfrac{12}{52}=\dfrac{3}{13}$

Hence, The probability of choosing a praline wafer is greater than the probability of choosing poached fennel & lemon alligator.

Hence statement 3 is correct.

(4)

The probability of choosing pressure-cooked mushroom & garlic chicken =probability that the card is red.

As there are 26 red cards out of 52 cards.

Hence,

The probability of choosing pressure-cooked mushroom & garlic chicken = $\dfrac{26}{52}=\dfrac{1}{2}$

probability of choosing an oven-baked apple & lavender calzone =probability that the card is black.

As there are 26 red cards out of 52 cards.

Hence, probability of choosing an oven-baked apple & lavender calzone= $\dfrac{26}{52}=\dfrac{1}{2}$

Hence, The probability of choosing pressure-cooked mushroom & garlic chicken and the probability of choosing an oven-baked apple & lavender calzone are the same.

Hence statement 4 is true.

(5)

The probability of choosing pressure-cooked mushroom & garlic chicken =probability that the card is red.

As there are 26 red cards out of 52 cards.

Hence,

The probability of choosing pressure-cooked mushroom & garlic chicken = $\dfrac{26}{52}=\dfrac{1}{2}$

the probability of choosing a praline wafer=probability that the card is a diamond.

as there are 13 diamond cards out of 52 cards.

The probability of choosing a praline wafer= $\dfrac{13}{52}=\dfrac{1}{4}$

Hence, the probability of choosing pressure-cooked mushroom & garlic chicken and the probability of choosing a praline wafer are not same.

Hence, statement 5 is not correct.

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4 years ago

What is a parallel slope for the line y = 2x + 2?

ArbitrLikvidat [17]

Answer: 2

Step-by-step explanation:

The slope is equal to 2 by it being in the slope place of y=mx+b

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3 years ago