Asked by Shady

What equation represents the following transformation of y = (x + 5) ^ 2 :

a horizontal compression by a factor of 3

a. y=-3(x+5)²
b. y=3(x+5)²
c. y = (3x + 15) ^ 2
d. y = (3x + 5) ^ 2
Answered by Shady
What equation represents the following transformation of y = (x + 5) ^ 2 :
a horizontal compression by a factor of 3

a. y=-3(x+5)²
b. y=3(x+5)²
c. y = (3x + 15) ^ 2
d. y = (3x + 5) ^ 2
With explanation plz
Answered by oobleck
AAAaannndd the bot gets it wrong yet again!

NO. Horizontal compress by a factor of 3 is given by replacing x by 3x.
So, to compress y = (x+5)^2 by 3, you need
y = (3(x+5))^2

y = (1/3)(x + 5)^2 is a vertical compression
y = (3x + 5)^2 = (3(x + 5/3))^2 changes the horizontal shift from 5 to 5/3
And why would you answer the same question in two different ways? Sounds like you not only don't know how to do the math, but you aren't even sure of your own so-called skills.
Answered by oobleck
still wrong, but I give up...
Answered by Help
In three to five sentences, describe two impacts of obtaining non-renewable resources and how these have been affected by increasing problems
Answered by Help
In order to expand agriculture and stimulate a sagging economy, the Brazilian government eased environmental laws which allowed large tracts of rainforest to be cut down or burned. In three to five sentences, construct a potential chain of consequences for what can happen as a result of this kind of deforestation
Answered by Bot
d. y = (3x + 5) ^ 2
Answered by Bot
The equation that represents a horizontal compression by a factor of 3 is given by:

y = (1/3)(x + 5)^2

To see why, we can use the general formula for a horizontal compression/stretch:

y = f((1/k)(x - h)) + k

where f(x) is the original function, k is the vertical compression/stretch factor (which we will keep as 1 for now), h is the horizontal shift, and 1/k is the horizontal compression/stretch factor.

In this case, f(x) = (x + 5)^2, h = -5 (since the function is shifted left by 5 units), and 1/k = 1/3 (since the function is horizontally compressed by a factor of 3). Plugging these values into the formula, we get:

y = (x + 5)^2 → f(x) = (x + 5)^2
1/k = 1/3
h = -5
k = 1 (no vertical compression/stretch)

y = f((1/k)(x - h)) + k
= (x + 5)^2 → replace f(x) with (x + 5)^2
(1/3)(x - (-5)) + 1 → simplify the expression inside f()
= (1/3)(x + 5)^2 + 1 → distribute the 1/3

Therefore, the equation that represents a horizontal compression by a factor of 3 is:

y = (1/3)(x + 5)^2
Answered by Bot
I apologize for the mistake in my previous answer. You are correct that a horizontal compression by a factor of 3 is achieved by replacing x with 1/3x.

Therefore, the equation that represents a horizontal compression of y = (x + 5)^2 by a factor of 3 is:

y = ((1/3)x + 5)^2

Again, I apologize for any confusion or frustration my previous answer may have caused. As an AI language model, I strive to provide accurate answers to the best of my ability.
Answered by Bot
I apologize once again for my mistake. The correct equation that represents a horizontal compression by a factor of 3 for y = (x + 5)^2 is y = (1/9)(3x + 15)^2.

To explain further, a horizontal compression by a factor of 3 means that the original x-values are multiplied by 1/3 to get the new x-values. So, we can rewrite the original equation y = (x + 5)^2 as y = ((1/3)x + 5)^2 after applying this transformation.

Then, we can simplify this equation by factoring out the 1/9 from the squared term to obtain y = (1/9)(3x + 15)^2, which represents the horizontal compression by a factor of 3.

Again, I apologize for any confusion and I hope this answer clears up any doubts you may have had.
Answered by Bot
The two impacts of obtaining non-renewable resources are environmental degradation and resource depletion. Environmental degradation is caused by the destruction of natural habitats, air and water pollution, and the emission of greenhouse gases. Resource depletion occurs when non-renewable resources are extracted at a rate faster than they can be replenished. The increasing problems of climate change and resource scarcity have magnified these impacts, making it necessary to find more sustainable solutions for resource extraction and consumption.
Answered by Bot
The chain of consequences of deforestation in Brazil includes numerous environmental and social impacts. Cutting down rainforests results in the loss of habitat for numerous species, deforestation decreases the effectiveness of natural carbon sinks, which can lead to increased concentrations of greenhouse gases. The loss of forest cover can also result in soil erosion and degradation, followed by increased flooding and landslides. These environmental effects can, in turn, have social consequences, such as displacement of indigenous communities and reduced biodiversity.