Solve the problem using the six-step method: a pharmacist found at the end of the day she had 7/4 as many prescriptions for antibiotics as tranquilizers. she had 33 prescriptions altogether. how many did she have for tranquilizers?

1 (female) pharmacist counting prescriptions at the end of the day

(prescriptions for antibiotics) = (7/4)×(prescriptions for tranquilizers)

33 = (prescriptions for tranquilizers) + (prescriptions for antibiotics)

The number of (prescriptions for tranquilizers)

Let x represent the number of prescriptions for tranquilizers. Then the number of prescriptions for antibiotics is (7/4)x, and the total number of prescriptions is

... 33 = x + (7/4)x . . . . . . . . . . put the given information in the given relation

... 33 = (4/4)x + (7/4)x . . . . . . rewrite 1 as 4/4 so we can add to 7/4

... 33 = ((4+7)/4)x = (11/4)x . . . simplify

... 33×(4/11) = (4/11)×(11/4)x . . . multiply by the reciprocal of the coefficient of x

... 12 = x . . . . . . . . . . . . . . . . . simplify

The pharmacist had 12 prescriptions for tranquilizers.

The pharmacist had 33-12 = 21 prescriptions for antibiotics.

There was 1 pharmacist and 33 prescriptions.

(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

i think it will be zero as slope has a formula of difference between initial and final distance divided by itz time interval