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nikitadnepr [17]
3 years ago
8

If a 25 in. by 32 in. picture has a wooden frame "x" in. wide surrounding it, which equation can be used to find the total area

of the picture and frame?
Mathematics
2 answers:
djyliett [7]3 years ago
6 0
The frame is at each side of the picture so the area is (25 + 2x) times (32 +2x), (which multiplies out to 4x^2 + 114x + 800 square inches). ie if the frame <span>is an inch and a half wide then the area is 28 x 35 sq ins, ie 980 sq ins.</span>
Pavel [41]3 years ago
3 0

Answer: The required equation is,

A = 4x^2+114x+800

Step-by-step explanation:

Given,

The dimension of the picture is 25 in. by 32 in,

Also, there is a  wooden frame "x" in. wide surrounding it,

So, the dimension of the combined figure of picture and wooden frame would be obtained after adding 2x in the each measure of the picture,

Thus, the dimension of the combined figure is (25+2x) in by (32+2x) in,

The total area of the picture and frame is,

A=(25+2x)(32+2x)

=(25+2x)(32)+(25+2x)(2x)

=25(32)+2x(32)+25(2x)+(2x)(2x)

=800+64x+50x+4x^2

=800+114x+4x^2

Hence, the equation that can be used to find the total area of the picture and frame would be,

A=4x^2+114x+800

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Hi there!  

»»————- ★ ————-««

I believe your answer is:  

3v + 8 \geq  22

»»————- ★ ————-««  

Here’s why:

⸻⸻⸻⸻

\boxed{\text{Breaking down the phrase...}}\\\\\text{Three times a number, v, added to eight is greater than or equal to twenty-two. }\\------------------\\\rightarrow \text{"Three times a number, v..."} - 3v \text{ This expresses the product of '3' and 'v'.}\\\\\rightarrow \text{"added to eight..."} - + 8 \text{ The product gets added to eight.}\\\\--------------\\\text{The First Part Is:}}\\\\3v + 8\\---------------\\\rightarrow \text{is greater than or equal to twenty-two. } - \geq 22

\text{The value of '3v + 8' is greater than or equal to 22.}\\---------------\\\text{\underline{Putting it together, we would have:}}\\\\\boxed{3v + 8 \geq 22}}

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

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