Using the properties of alternate angles, the value of x = 8 and ∠ A = 30
<h3>What are Alternate Angles?</h3>A transversal that crosses two parallel lines produces alternate exterior angles. They form two pairs (four total angles) of alternate outside angles since they are situated "outside" the two parallel lines but on different sides of the transversal.
For the given question,
∠A=6x−18
∠B=14x+38
As, both parallel lines are intersected by a transversal,
the value of angle ∠A and ∠180 - B is same as they are alternate angles,
⇒ 6x−18 = 180 - 14x - 38
⇒ 6x + 14x = 142 + 18
⇒ 20x = 160
⇒ x = 8
∠A = 6x−18
⇒ ∠ A = 30
To learn more abut alternate angles from given link
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Correct question -
Inequality is 6t ≤ 44 and Jim can rent a boat for 7.33 hrs or less
<u> Solution:</u>
Given that
Maximum amount Jim can spend to rent a boat = $34
Rental cost of boat for 1 hour = $6
Also Jim has a discount coupon for $8 off.
Need to determine possible number of hours Jim could rent a boat.
Let’s assume possible number of hours Jim could rent a boat be represented by variable "t"
Cost of renting boat for 1 hour = 6
So Cost of renting a boat for t hours = t x renting boat for 1 hour = t x 6 = 6t
Also Maximum amount Jim can spend to rent a boat = $34
As Jim has a discount coupon for $8 off, so Total amount Jim can spend to rent a boat = $ 34 + $ 8 = $ 44
So cost of renting a boat for t hours must be less that of equal to Total amount Jim can spend to rent a boat
=> 6t ≤ 44
On solving above equality for "t" we get ,
Hence inequality is 6t ≤ 44 and Jim can rent a boat for 7.33 hrs or less.