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3 years ago

Find the zeros of the function y=x^2-1

Mathematics

1 answer:

scoundrel [369]3 years ago

7 0

Answer: 1, -1

Step-by-step explanation: This is a difference of squares when factored,

(x+1)(x-1)

Let's check using FOIL(First, outside, inside, last)

x * x =x^2

1 *x =x

x * (-1) =-x

1* -1 =-1

so x^2 +x -x -1

=x^2 -1

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4 years ago

Solve the equation x² + 6x + 1 = 0. give your answer to two decimal places

Alexandra [31]

Answer:

x ≈ - 5.83 , x ≈ - 0.17

Step-by-step explanation:

x² + 6x + 1 = 0 ( subtract 1 from both sides )

x² + 6x = - 1

Using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(3)x + 9 = - 1 + 9

(x + 3)² = 8 ( take square root of both sides )

x + 3 = ± $\sqrt{8}$ ( subtract 3 from both sides )

x = - 3 ± $\sqrt{8}$

Then

x = - 3 - $\sqrt{8}$ ≈ - 5.83 ( to 2 dec. places )

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5 0

3 years ago

Sequence: 49, 36, 25, 16, 8, 4, 1 * Is this a arithmetic or geometric sequence? and if it is arithmetic find the common differen

timurjin [86]

Answer:

Step-by-step explanation:

The sequence is nor properly written. This is correct sequence

49, 36, 25, 16, 9, 4, 1...

Merely looking at the sequence, we can see that it doesn't form an arithmetic sequence nor does it form a geometric sequence.

The values of the sequence are all perfect squares.

Rewriting the sequence;

7², 6², 5², 4², 3², 2², 1²...

Now we can see that the base values for an arithmetic sequence as shown:

7, 6, 5, 4, 3, 2, 1...

We find the common difference of this sequence as shown

d = T2-T1 = T3-T2 = T4-T3

Given T1 = 7, T2 = 6, T3 = 5, T4 = 4

Substitute

d = 6-7 = 5-6 = 4-5 = -1

d = -1

Get the nth term using the sequence

Tn = a+(n-1)d

a is the first term

d is the common difference

n is number of terms

Tn = 7+(n-1)(-1)

Tn = 7+(-n+1)

Tn = 7+1-n

Tn = 8-n

Since their power are constant i.e squared, hence we will square the ntj term as well to get the nth term of the original sequence as;

Tn = (8-n)²

To conclude, we can say that the sequence is neither arithmetic nor geometric sequence since the terms of the sequence are prefect squares.

3 0

3 years ago