A carpenter is putting a skylight in a roof. If the roof measures 10x + 9 by 7x + 7 and the skylight measures x + 5 by 3x + 3, what is the area of the remaining roof after the skylight is built?
A.) 67x^2 + 115x + 48**
B.) 73x^2 + 151x + 78
C.) 70x^2 + 133x + 63
A IS THE ANSWER, I just took the test
67x^2…. Is the answer
remaining area: roof-skylight
= (10x+9)(7x+7)- (x+5)(3x+3)
you need to multiply these out, but there is a shortcut here: just do the x^2 terms
= 70x^2 + ...-3x^2= 67x^2 + .....
you are correct.
Thank you.
still correct <3
Well, it seems like the carpenter is working hard to let some sunlight into that roof! To find the area of the remaining roof after the skylight is built, we need to subtract the area of the skylight from the area of the original roof.
The area of the original roof is given by (10x + 9) * (7x + 7), which simplifies to 70x^2 + 133x + 63.
The area of the skylight is given by (x + 5) * (3x + 3), which simplifies to 3x^2 + 18x + 15.
To find the area of the remaining roof, we subtract the area of the skylight from the area of the original roof:
70x^2 + 133x + 63 - (3x^2 + 18x + 15).
Simplifying that, we get:
67x^2 + 115x + 48.
So, the area of the remaining roof is A) 67x^2 + 115x + 48.
Now, that's called doing some math and letting the light shine through!
To find the area of the remaining roof after the skylight is built, we need to subtract the area of the skylight from the area of the original roof.
First, let's calculate the area of the original roof. We can find the area of a rectangle by multiplying its length by its width.
The length of the original roof is 10x + 9, and the width is 7x + 7. Hence, the area of the original roof is (10x + 9) * (7x + 7).
Next, let's calculate the area of the skylight. The length of the skylight is x + 5, and the width is 3x + 3. Therefore, the area of the skylight is (x + 5) * (3x + 3).
Finally, to find the area of the remaining roof, we subtract the area of the skylight from the area of the original roof:
Remaining Area = Area of Original Roof - Area of Skylight
= (10x + 9) * (7x + 7) - (x + 5) * (3x + 3)
Simplifying this expression will give us the final answer.