Skylar owns a trucking company. for every truck that goes out, skylar must pay the driver $11 per hour of driving and also has an expense of $3 per mile driven for gas and maintenance. on one particular day, the driver drove an average of 30 miles per hour and skylar's total expenses for the driver, gas and truck maintenance were $909. write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. define the variables that you use to write the system.

The set of needed equations is

h = 30 m

11 m +  3  h = 909  where

the driver drove for m hours.

h : distance covered in m hours

Step-by-step explanation:

Here, according to the question:

The per hour rate of driver  = $11

The gas maintenance expense = $3 per mile.

The total distance covered by drives is 30 miles per hour.

The total  expenses paid to driver  = $909

Now, let us assume the driver drove for m hours.

The average speed of driver was 30 miles / hour

⇒ Driver covers 30 miles in 1 hour

SO, distance covered in m hours  = h = m x 30 = 30 m

or, h = 30 m

So,according to the question, the total amount paid :

Charges of m hours driving + maintenance charges for h miles

= 11 m + 3( h)

or, 11 m +  3  h = $909

Hence the set of needed equations is

h = 30 m

11 m +  3  h = 909

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

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step-by-step explanation: