Answer:
Carter family = 25 hours
Davis family = 31 hours
Step-by-step explanation:
Let's say the number of hours the Carter family used their sprinkler is x and the number of hours the Davis family used their sprinkler for is y.
So combined:
x + y = 45 hours
and we are also told that:
40x + 15y = 1300 L
So we can do simultaneous equations to solve the problem.
With some rearranging, we can figure out that:
y= 45 - x
and by substituting that into the second equation:
40x + 15 (45 -x) = 40x + 675 - 15x = 1300L
25x = 1300 - 675
25x = 625
x = 25 = hours that the Carter family used their sprinkler
and we can substitute that back into the original equation to find how many hours the Davis family used their sprinkler so:
25 + y = 56
y = 31
The Davis family used their sprinkler for 31 hours whilst the Carter family used their sprinkler for 25 hours.
The ΔABR ≅ ΔACR are congruent by SAS theorem
Option D is the correct answer.
The missing diagram is attched with the answer.
<h3>What is a Triangle ?</h3>
A triangle is a polygon with three sides , three vertices and three angles.
SAS will be used to prove the congruence of ΔABR ≅ ΔACR
In both the triangle we have a common side , AR
AB = AC (given)
∠ B A R = ∠R A C ( given equal)
So as the two side and the included angle is equal
Therefore the ΔABR ≅ ΔACR are congruent by SAS theorem
Option D is the correct answer.
To know more about Triangle
brainly.com/question/2773823
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