A local diner must build a wheelchair ramp to provide handicap access to the restaurant. Building codes require that a wheelchair ramp must have a maximum rise of 1 in. for every horizontal distance of 12 in. (a) What is the maximum allowable slope for a wheelchair ramp? Assuming that the ramp has maximum rise, find a linear function H that models the height of the ramp above the ground as a function of the horizontal distance x? H(x) = (b) If the space available to build a ramp is 150 in. wide, how high does the ramp reach? in

(a) Maximum slope,

(b) 12.5 in.

Step-by-step explanation:

The given condition is the wheelchair ramp must have a maximum rise of 1 in. for every horizontal distance of 12 in.

(a) Let m be the maximum allowable slope for the ramp.

.

Let x be the distance in the horizontal direction as shown in the figure.

So, for slope m, the linear function H for the height is

, where C is constant.

Now, at the starting of the ramp, x=0, and H=0.

Putting this condition back to the equation, we have

.

Hence, the required equation is

(b) The ramp is 150 in. wide,

So, height gained by the ramp at the end is,

in.

idk

step-by-step explanation:

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3