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mote1985 [20]
3 years ago
12

If f(x) = x2 − 81 and g(x) = x+9/x-9, find g(x) · f(x).

Mathematics
1 answer:
dexar [7]3 years ago
3 0

Answer:

f(x) = x² - 81 = ( x+ 9)(x - 9) Difference of two squares

g(x) = x+9/x-9

g(x) . f(x) = x + 9/ x - 9 × (x+9)(x - 9)

= ( x + 9)(x +9)

= ( x + 9)²

= x² + 18x + 81

Hope this helps.

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One of the wagers in roulette is to bet that the ball will stop on a number that is a multiple of 3. (Both 0 and 00 are not incl
Arlecino [84]

Answer:

The players expectation is -0.1052

Step-by-step explanation:

Consider the Roulette numbers to from 1-36, also the two green zeroes 0 and 00,

Thus, there are 38 places on which the ball can land.

On first 36 numbers, 12 of them are divisible by 3. Also there are 26 numbers which are not divisible by 3.

The probability of a wager winning is: 12/38 or 6/19

Now the probability of a wager to loss is: 26/38 or 13/19

So for a 6/19 chance of winning $4 and a 13/19 chance of losing $2.

Therefore, the expected outcome is:

4 × 6/19 + -2 × 13/19 = 1.2632 - 1.3684 = -0.1052

The expected value comes up with a negative sign. Hence, he will lose money.

The players expectation is -0.1052

8 0
3 years ago
Which of the following expressions are equivalent to 6.53 - (-4.11) + 7.926.53?
umka21 [38]

Answer:

Choice B and Choise C.

Step-by-step explanation:

Equivalent expressions are those expressions that have the same value but they look different.

Given the following expression provided in the exercise:

6.53 - (-4.11) + 7.92

You need to remember the multiplication of signs in order to find the equivalent expressions:

(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-

Then:

- Eliminating the parentheses, you get this equivalent expression:

6.53 +4.11 + 7.92

- Since the mulplication of two negative signs gives yous a positive sign, you can rewrite the original expression in this form:

-(-6.53)+4.11-(-7.92)

This is an equivalent expression to 6.53 - (-4.11) + 7.92

8 0
3 years ago
2y+4=5x-4=<br><br> Help please
IgorLugansk [536]

Answer:

x = 2 and y = 1.

Step-by-step explanation:

If in the given quadrilateral all angles ∠A, ∠B, ∠C, ∠D are 90°and opposite sides are equal, then this property of a quadrilateral concludes that the given quadrilateral is a rectangle.

5x - 4 = 2y + 4

5x - 2y = 4+4 =8--------(1)

and 5y + 1 = 3x

3x - 5y = 1--------(2)

We multiply equation 1 by 3 and equation 2 by 5

15x - 6y = 24------(3)

15x - 25y = 5------(4)

Now we subtract equation 4 from 3

15x - 6y - (15x - 25 y) = 24-5

15x -6y -15x + 25y =19

19y = 19

y = 1

By putting y = 1 in equation 1.

5x - 2 = 8

5x = 10

x = 2

7 0
3 years ago
Read 2 more answers
Suppose that a loan of $8000 is given at an interest rate of 16% compounded each year.
mash [69]

Answer:

9280

Step-by-step explanation:

8000 x .16 + 8000

6 0
3 years ago
A paintball court charges an initial entrance fee plus a fixed price per ball.
m_a_m_a [10]

Answer : The cost of 10 balls will be, 13.5 dollars

Step-by-step explanation :

As we are given the following expression:

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where,

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n = number of balls used

Given:

n = number of balls used = 10

Now we have to determine the cost of 10 balls.

P=0.80\times n+5.50

P=0.80\times (10)+5.50

P=8+5.50

P=13.5\$

Thus, the cost of 10 balls will be, 13.5 dollars

4 0
3 years ago
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