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horrorfan [7]
2 years ago
5

What is the equation of the line

Mathematics
1 answer:
cricket20 [7]2 years ago
6 0
The answer is
(0,0)
Goodluck
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An exponential function is expressed in the form y=axb^x. The relation represents a growth when _______ and a decay when ______.
seropon [69]

Answer:

Growth when: b>1.

Decay when: 0<b<1.

Step-by-step explanation:

Any function in the form f(x)=a{\times}b^x , where a > 0, b > 0 and b not equal to 1 is called an exponential function with base b.

If 0 < b < 1 this is an example of an exponential decay.

The general shape of an exponential with b > 1 is an example of exponential growth.

Hence,

An exponential function is expressed in the form f(x)=a{\times}b^x,   The relation represents a growth when  b >1 and a decay when 0<b<1.

5 0
2 years ago
The coordinates of point A are (p, q) and coordinates of point B are (p+2q, q+2p). Provide your complete solutions and proofs in
Dafna1 [17]

Answer:

The mid-point (p + q , q + p) of AB is the same distance from the x-axis and the y-axis

Step-by-step explanation:

*<em> Lets explain how to solve the problem</em>

- Any point will be equidistant from the x-axis and the y-axis must have

 equal coordinates

- Ex: point (4 , 4) is the same distance from the x-axis and the y-axis

 because the distance from the x-axis to the point is 4 (y-coordinate)

 and the distance from the y-axis and the point is 4 (x-coordinate)

- If (x , y) is the mid-point of a segment its endpoints are

 (x_{1},y_{1})  and (x_{2},y_{2}), then

 x=\frac{x_{1}+x_{2}}{2} and y=\frac{y_{1}+y_{2}}{2}

* <em>Lets solve the problem</em>

∵ Point A has coordinates (p , q)

∵ Point B has coordinates (p + 2q , q + 2p)

- The mid-point of AB is (x , y)

∵ x=\frac{p+p+2q}{2}

∴ x=\frac{2p+2q}{2}

- Take 2 as a common factor from the terms of the numerator

∴ x=\frac{2(p+q)}{2}

- Divide up and down by 2

∴ x = p + q

∵ y=\frac{q+q+2p}{2}

∴ y=\frac{2q+2p}{2}

- Take 2 as a common factor from the terms of the numerator

∴ y=\frac{2(q+p)}{2}

- Divide up and down by 2

∴ y = q + p

∴ <em>The mid point of AB is (p + q , q + p)</em>

- p + q is the same with q + p

∵ The x-coordinate of the mid point of AB is p + q

∵ The y-coordinate of the mid point of AB is q + p

∵ p + q = q + p

∴ The coordinates of the mid-point of AB are equal

- According the explanation above

∴ The mid-point (p + q , q + p) of AB is the same distance from the

   x-axis and the y-axis

8 0
3 years ago
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