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gtnhenbr [62]
3 years ago
9

Which of these values for p and a will cause the function f(x)=Pa^x to be an exponential growth function?

Mathematics
2 answers:
Lera25 [3.4K]3 years ago
8 0
Grouth is when a>1
if a=1, theer is no change
if a<1, it is exponetial decay


B is answer
finlep [7]3 years ago
4 0

The <em><u>correct answer</u></em> is:

B.P=1/4;a=5  

Explanation:

In order to represent exponential growth, a must be a positive number larger than 1.  If it is a fraction less than 1, we are basically taking a percent (less than 100) of the number; this makes it smaller, which would be decay.  If a is a negative, the values would alternate between positive and negative.

The only option where a is a positive number larger than 1 is P=1/4 and a=5.

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The endpoints of one diagonal of a rhombus are (-7, -2) and (-1, -4). If the coordinates of the 3rd vertex are (-6, -9), what ar
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The coordinates of the 4th vertex of the rhombus are (-2,3)

<h3>How to determine the coordinates of the 4th vertex?</h3>

The diagonals are given as:

(-7, -2) and (-1, -4)

The 3rd vertex is given as: (-6,-9)

Calculate the distance between the vertices of the diagonals and the 3rd vertex using:

d = \sqrt{(x_2 -x_1)^2 + (y_2 - y_1)^2}

So, we have:

d_1 = \sqrt{(-7 + 6)^2 + (-2 + 9)^2} =\sqrt{50

d_2 = \sqrt{(-1 + 6)^2 + (-4 + 9)^2} =\sqrt{50

Let the 4th vertex be (x,y)

So, we have:

d_3 = \sqrt{(-7 - x)^2 + (-2 - y)^2} =\sqrt{50

d_4 = \sqrt{(-1 - x)^2 + (-4 - y)^2} =\sqrt{50

Equate d3 and d4

\sqrt{(-1 - x)^2 + (-4 - y)^2} = \sqrt{(-7 - x)^2 + (-2 - y)^2}

Take the square of both sides

(-1 - x)^2 + (-4 - y)^2 = (-7 - x)^2 + (-2 - y)^2

Expand

1 + 2x + x^2 + 16 + 8y + y^2 = 49 + 14x + x^2 + 4 + 4y + y^2

Evaluate the like terms

1 + 2x  + 16 + 8y  = 49 + 14x + 4 + 4y

Collect like terms

14x - 2x + 4y - 8y = 1 + 16 - 49 - 4

12x - 4y = -36

Divide through by 4

3x - y = -9

Next, we test the options in the above equation

Point (-8,13) means x = -8 and y = 13

So, we have:

3x - y = -9

3(-8) - 13 = -9

-37 = -9 --- this is false

Point (-2, 3) means x = -2 and y = 3

So, we have:

3x - y = -9

3(-2) - 3 = -9

-9 = -9 --- this is true.

Hence, the coordinates of the 4th vertex are (-2,3)

Read more about rhombus at:

brainly.com/question/20627264

#SPJ1

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1 year ago
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