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1. it takes the earth 24 h to complete a full rotation. it takes mercury approximately 58 days, 15 h, and 30 min to complete a full rotation. how many hours does it take mercury to complete a full rotation? show your work using the correct conversion factors.
2. a vine called the mile-a-minute weed is known for growing at a very fast rate. it can grow up to 0.5 ft per day. how fast in inches per hour can the mile-a-minute weed grow up to? show your work using the correct conversion factors
3. the total cost after tax to repair deborah’s computer is represented by , where h represents the number of hours it takes to repair deborah’s computer. what part of the expression represents the amount of tax deborah has to pay? explain.

1.

1 day = 24 hours

24*58= 1392hours  58/1 * 24/1        +           30/1* 1/60

1392+15=1407hours  

1407hours+30min= 1407.5hours

2.

24h=1day 12inches=1ft

0.5/24 = 0.02083

0.02083*12= 0.25 inches per hour

3.

50h means $50 per hour and 0.08 stands for 8% sales tax so the which means she is pay 8% of the total cost so the answer is 0.08(50h)

-6 is the correct option from the above given options

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!