Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A rectangle is shown with length x plus 10 and width 2 x plus 5. The inside of the rectangle is shaded other than an unshaded square with length x plus 1 and width x plus 1.
Write an expression for the area of the shaded region in its simplest form. Show all of your steps.
First, combine the length (x+10) and width (2x+5) of the rectangle to get 2x^2 + 25x+50. Find the area of the white square (x+1)(x+1) to get x^2 + 2x+1. Then subtract x^2+2x+1 from 2x^2+25x+50 to get x^2+23x+49. This is what I got and I'm 95% sure it's right. I'd put it in more precise wording but that's the basic work. Please try your hardest in math, it's so important.
oobleck you want other people to have a hard time because you are?
Actually I think @ooblek was help because they helped me get my equation started so ty
what happened here? Lmao
can people just stop man
I'm sorry, I'm not sure what you mean. Is there anything else you need help with?
To find the area of the shaded region, we need to subtract the area of the unshaded square from the area of the rectangle.
We are given that the length of the rectangle is x + 10 and the width is 2x + 5.
So, the area of the rectangle is (x + 10) * (2x + 5).
Now, let's find the area of the unshaded square. The length and width of the square are both x + 1.
So, the area of the square is (x + 1) * (x + 1).
To find the area of the shaded region, we subtract the area of the square from the area of the rectangle.
Area of the shaded region = Area of the rectangle - Area of the square
Area of the shaded region = (x + 10) * (2x + 5) - (x + 1) * (x + 1)
To simplify this expression, we need to distribute and combine like terms.
Area of the shaded region = (2x^2 + 5x + 20x + 50) - (x^2 + x + x + 1)
Area of the shaded region = 2x^2 + 25x + 50 - x^2 - 2x - 1
Now, let's combine like terms.
Area of the shaded region = (2x^2 - x^2) + (25x - 2x) + (50 - 1)
Area of the shaded region = x^2 + 23x + 49
So, the expression for the area of the shaded region in its simplest form is x^2 + 23x + 49.
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it's just the whole area minus the shaded area, right?
since the area of a rectangle is length * width, that gives you
(x+10)(2x+5) - (x+1)(x+1) = x^2 + 23x + 49
Now it's up to you to follow the set of instructions. Post your work if you get stuck.