The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 5 feet, find the horizantal run length that the ramp must start. (Round to one decimal place)

1. Draw out a diagram as a triangle with one side as the 5' rise, the other side as the horizontal run, and the hypotenuse as the ramp.

2. Put the 5 ° in as the angle between the run and the ramp.

3. Let the run = x. Using trigonometry (needed!) the tangent angle (tan) of 5° = opposite/adjacent = 5/x.

4. So x = 5/tan(5°). you will need a scientific calculator to solve.

(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

mx+89b(-98)nb

step-by-step explanation: