PLEASE ANSWER ASAP

Mathematics

1 answer:

mote1985 [20]3 years ago

8 0

Answer:

y = 2 $(3)^{x}$

Step-by-step explanation:

For the exponential function in the form

y = a $b^{x}$

Use ordered pairs from the table to find a and b

Using (0, 2 ), then

2 = a $b^{0}$ ( $b^{0}$ = 1 ) , thus

a = 2, so

y = 2 $b^{x}$

Using (1, 6 ) , then

6 = 2b ( divide both sides by 2 )

b = 3

Thus the exponential function is

y = 2 $(3)^{x}$

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What is the constant term of the quotient when 2x^3-3x^2 + 4x-2 is divided by x^2-x+2?

AlladinOne [14]

Answer:

-1

Step-by-step explanation:

See the attachment for the polynomial long division. The constant in the quotient is -1.

_____

Here, there is a remainder of -x. If there were no remainder the constant in the quotient is the ratio of the constant in the dividend to the constant in the divisor: -2/2 = -1.

That could be a first guess in a "guess and check" solution approach.

<em>Guess</em>: first term of binomial quotient is (2x^3)/x^2 = 2x; last term of binomial quotient is -2/2 = -1. So, the quotient is guessed to be (2x -1).

<em>Check</em>: (2x -1)(x^2 -x +2) = 2x^3 -3x^2 +5x -2

Subtracting this from the actual dividend gives a remainder of -x. This has a lower degree than the divisor, so no further adjustment of the quotient is required.