pratice final A, TI-89 titatnium calculator may be used if needed. whichever is easier for me. please help

Question

Answer 1

(26)

The function is f(x) = x(x-1)

g(x) = x

Condition is f(x) < g(x)

x(x-1) < x

x(x-1) - x < 0

x(x-1 - 1) < 0

x(x-2) < 0

Then the condition is 0 < x < 2

Therefore the values of x lies between 0 < x < 2.

Option (d) is the correct answer.

Answer 2

(27)

The function is

To find the values of x such that f(x) = 4

Let f(x) = 5-x     for x ≤ 3

5 - x = 4

x = 5 - 4

x = 1 < 3

Then x = 1

Let f(x) = -x² + 10x -8     for x > 3

-x² + 10x -8 = 4

x² - 10x + 8 + 4 = 0

x² - 10x + 12 = 0

Roots of the quadratic equation are x = 8.60  and 1.39

The function is valid for x > 3 then x = 8.60.

Therefore the values of x are 1 and 8.60.

Option (d) is the correct answer.

Answer 3

(28)

The system of equation are given in matrix form

The augmented matrix is

now apply

As the rank of Augmented matrix = 3

Rank of the Matrix A is 3

Rank of A = Rank of [A|B] then it has finite solutions

From the augmented matrix,we can say

z = 9

y = 5

-2x+8y + z = 1

-2x + 8*5 + 9 = 1

-2x = -48

x = 24

Therefore the solutions are

Option (d) is the correct answer.

Comments

Did you use a calculator for this? I don't understand.

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No, we do not make use of calculator.

We make use of Augmented matrix [A|B] to solve the system of linear equations AX = B.