6th grade math
drusilla replaces the light bulb in the hall closet every 9 months and replaces the air filter every 6 months. she just replaced both items this month. after how many months will she replace both the light bulb and the air filter?

They will both be replaced the 18th month.

She will replace both at the same time in 18 months

Step-by-step explanation:

The first thing you have to do to find when she will change them at the same time, is to try with multiples of both, untill they match.

Hall Closet = every 9 months

Air Filter = every 6 months

1) 9-18-27-36-45

2)6-12-18

We find that in the 18th month he will change both of them.

7. 153.86 ft

8. 12.56 ft

9. 78.5 m

10. 379.94 in

11. 132.665 m

12. 12.56 yd

13. 226.865 ft

14. 113.04 ft

15. 63.585 ft

16. 254.34 m

17. 50.24 cm

step-by-step explanation:

7.

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17.

(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