Jason drove 8 4/5 miles to a subway station. He then 15 /6 miles by taxi to attend a meeting. How many total miles did he travel?

Option A: (23 + 29/30) miles

Step-by-step explanation:

Here we just need to add two mixed numbers.

(8 + 4/5) miles and (15 + 1/6) miles.

To add these, we just separate between the whole part and the fraction part:

(8 + 4/5) miles + (15 + 1/6) miles

= (8 + 4/5 + 15 + 1/6) miles

= (8 + 15 + 4/5 + 1/6) miles

= (23 + 4/5 + 1/6) miles

Now we need to find a common multiple between 6 and 5.

So, only analyzing the fraction part of the sum, we can rewrite:

4/5 + 1/6

= 4/5*(6/6) + 1/6*(5/5)

(notice that we are multiplying both numbers by one, so we do not change the expression's value)

= (4*6)/(5*6) + (1*5)/(6*5)

= 24/30 + 5/30

So now both fractions have the same denominator.

Then, replacing that in the sum equation we get:

(23 + 4/5 + 1/6) miles =  (23 + 24/30 + 5/30) miles

= (23 + 29/30) miles

Then the correct option is option A.

(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

a

b

d

step-by-step explanation: