How can models be used to generate and analyze patterns?
2 answers:
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Answer:
49+56x+16 ft squared.
Step-by-step explanation:
Alright, so we are given that we have a rug that has a side of 7x+4 feet. With this information, we are able to determine the area of the square rug. Considering that it is a square rug, all the sides are equal to each other because a square has four equal sides and angles.
To solve this, you can do it in two ways.
One, write it as (7x+4)2. That 2 is supposed to represent squared.
If you know the rule, this is a perfect square trinomial.
The formula is a squared plus 2ab plus b squared. 7 and 4 are your a and b values. 7x squared is 49x squared and 4 squared is 16.
2ab, multiply 2 times 7x times 4. That is 56x.
Therefore, the area is 49xsquared plus 56x+16.
Another way is to write it like this (7x+4) (7x+4).
Since it is an exponent, we are multiplying the same thing two times. Apply the Distributive Property.
E.G. 2(x+5)= 2x+10.
With this, you are distributing two numbers into another two numbers. 7x times 7x is 49x squared and 7x times 4 is 28x. Then, go to 4. 4 times 7x is also 28 x and 4 times 4 is 16. Now, combine the like terms. 49x squared plus 28x plus 28x or 56x plus 16.
This represents your area.
I hope this helps, and I hope you have a good day!