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3 years ago

Hello, how can I do this equation?

1 answer:

4 0

(9^x) - 3 = 2*3^x
(9^x) - 3 - (2*3^x) = (2*3^x) - (2*3^x)
(9^x) - (2*3^x) - 3 = 0
(3^2)^x - 2*(3^x) - 3 = 0
3^(2x) - 2*(3^x) - 3 = 0
3^(x*2) - 2*(3^x) - 3 = 0
(3^x)^2 - 2*(3^x) - 3 = 0
z^2 - 2*z - 3 = 0 ............ let z = 3^x
(z - 3)(z + 1) = 0

If z-3 = 0, then z = 3 when we isolate z
If z = 3, and z = 3^x, then
z = 3
3^x = 3
3^x = 3^1
x = 1
which is a solutin in terms of x

If z+1 = 0 then z = -1
If z = -1 and z = 3^x, then there are NO solutions for this part of the equation
The quantity 3^x is never negative no matter what the x value is

---------------------------------------------------------------

Answer: x = 1

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The x intercept of the given graph of the company's profit is where the curve of the graph crosses the x-axis.

<h3>How to determine the x-intercept</h3>

From the figure, the graph crosses the x-axis at x values of 0 and 6

This represents the profit is 0 when the price is $0 and $6, respectively

<h3>The increasing and the decreasing interval</h3>

From the graph, the graph increases from x = 0 to x = x = 3, and it decreases from x = 3 to x = 6

These intervals represent when the profit increases, and when it decreases

<h3>The maximum value</h3>

This represents the maximum profit that can be made.

From the graph, the maximum profit is $120

<h3>The average rate of change</h3>

This is calculated as:

$m = \frac{f(b) - f(a)}{b - a}$

So, we have:

$m = \frac{f(3) - f(1)}{3 - 1}$

$m = \frac{f(3) - f(1)}{2}$

Substitute known values

$m = \frac{120 - 60}{2}$

$m = \frac{60}{2}$

Simplify

$m = 30$

Hence, the average rate of change from x = 1 to x = 3 is a profit of $30 per unit sale

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2 years ago

The figure below shows two triangles on the coordinate grid:

madreJ [45]

Answer:

Option A

Step-by-step explanation:

A translation 5 units down, followed by a 180-degree counterclockwise rotation about the origin

Correct

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Incorrect. It would work with 180-degree rotation.

A 180-degree counterclockwise rotation about the origin, followed by a translation 5 units down

Incorrect. It would work with the translation 5 units up.

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3 years ago

If 1 kilometer equals 1,000 meters, how many meters are equal to 6 kilometers?

Andreas93 [3]

Answer:

6000

Step-by-step explanation:

if 1 kilometer equals 1000 meters then 6 kilometers is equal to 6000 kilometers

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3 years ago

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Step-by-step explanation:

$- 24 \div 4 = - 6$

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3 years ago

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Round 104229 to the nearest ten thousand

saul85 [17]

That is a one hundred thousand number. To round it you need to know this: 5 or more make it go up (make it the next number. For example: 19,530. It would be rounded to 20,000 because of the 5) 4 or less let it be (EXAMPLE : 8,213. It would be 8,000. Because of the 4.)

Then you need to find the ten thousand. In this case it is the 0. (104,229) Then you round it off to 100,000. The answer is 100,000.

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4 years ago