Stella models a product with algebra tiles. Write a number sentence that best describes her model. Fill in the blanks.
2 answers:
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Answer:
Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
Answer:
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Step-by-step explanation:
The perimeter of a rectangle is the sum of it's side lengths.
A rectangle has 4 sides where it's opposite sides are congruent.
So if one side has measurement w, then there is another side that has measurement w.
If there is one side that has measurement l, then there is another side that has measurement l.
So if you add w+w+l+l you get 2w+2l.
They are giving us that the perimeter is P, so P=2w+2l.
we are being asking to solve for l.
P=2w+2l
First step: Isolate term that contains the l, so get 2l by itself first.
We are going to subtract 2w on both sides giving us:
P-2w=2l
2l=P-2w
Now that we have 2l by itself it is time to perform the last step in getting l by itself.
Second step: Divide both sides by 2.
This gives us:
l=(P-2w)/2
You may separate the fraction like so:
.
I don't know your options but I have solve for l in terms of P and w
and got .
Please let me know if you have further questions with this problem.