URGENT! an artist intends to paint a 60-square-foot mural on a large wall that is 18 ft wide and 11 ft tall. find the dimensions of the mural if the artist leaves a border of uniform width around it. Pls show me how'd you get your answer
w+2a = 18
h+2a = 11
w h = 60 so w = 60/h
(60/h) + 2 a = 18
but a = (11-h)/2
60/h + 11 - h = 18
60 + 11 h - h^2 = 18 h
h^2 + 7 h - 60 = 0
check my arithmetic and solve quadratic
If you really are a retired teacher, why would you use that kind of language towards students. Besides, he only miscalculated, you don't have to act crazy about. Please control your language around students. You should know how to is you really are a "retired teacher" @Ms. Sue.
I hope you learn.
2+2?
=4
it took time and effort to solve it. your welcome.
To find the dimensions of the mural, we can subtract the dimensions of the border from the dimensions of the wall.
Let's assume the width of the border is 'x' feet. This means that the width of the mural will be 18 ft - 2x ft (subtracting the border from both sides of the wall).
Similarly, let's assume the height of the border is 'y' feet. This means that the height of the mural will be 11 ft - 2y ft (subtracting the border from the top and bottom of the wall).
Given that the area of the mural is 60 square feet, we can set up the equation:
(18 ft - 2x ft) * (11 ft - 2y ft) = 60 sq ft
Now, let's solve this equation to find the values of 'x' and 'y'.
Expanding the equation:
(18 ft) * (11 ft) - 2x(18 ft) - 2y(11 ft) + 4xy = 60 sq ft
198 ft^2 - 36x ft - 22y ft + 4xy = 60 sq ft
Rearranging the equation:
4xy - 36x - 22y = -138 ft^2
Now, there are multiple methods to solve this equation, such as substitution or factoring. Let's solve it using substitution.
First, let's solve for 'x' in terms of 'y':
4xy - 36x = -138 ft^2 + 22y
x(4y - 36) = -138 ft^2 + 22y
x = (-138 ft^2 + 22y) / (4y - 36)
Now, substitute this value of 'x' back into the equation:
4(-138 ft^2 + 22y) / (4y - 36) - 22y = -138 ft^2
Expand and rearrange the equation:
-552 ft^2 + 88y - 22y(4y - 36) - (4y - 36)(-138 ft^2) = 0
Now, we have a quadratic equation:
-4y^2 + 36y - 138 ft^2 - 552 = 0
Simplifying further:
-4y^2 + 36y - 690 = 0
At this point, we can solve this quadratic equation by using factoring, completing the square, or applying the quadratic formula.
The solutions to this equation will give us the possible values of 'y', which we can then substitute back into the equation for 'x' to find the corresponding dimensions of the mural.