Ahomeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. the building code allows for a deck to have a maximum area of 800 square feet. if the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased.

10.6 feet

Step-by-step explanation:

Length = 22ft

width= 14ft

Maximum area = 800 sq. ft

Let X be increase in the number of feet for the length and width.

The new length = (22 + x) ft

New width= (14 + x) ft

Area = (22+x)(14+x) ≤ 800

308 + 36x + x^2 ≤ 800

x^2 + 36x + 308 - 800 ≤ 0

x^2 + 36x - 492 ≤ 0

Solve using quadratic equation

x = (-b +/- √b^2 - 4ac) / 2a

a= 1, b = 36, c= 492

x = (-36 +/- √36^2 - 4*1*-492)/ 2*1

= (-36 +/- √1396 + 1968) / 2

= (-36 +/- √3264) / 2

= (-36 +/- 57.13) / 2

x = (-36 + 57.13)/2 or (-36 - 57.13)/2

x = 21.13/2 or -93.13/2

x = 10.6 or -31.0

x = 10.6 ft

The length and width must increase by 10.6 ft each

she will most likely have 33  

step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!