Since BD bisects angle ABC, that means angle ABD and angle CBD are equal to each other. With that set up the equation to solve for x like this:
-4x+33 = 2x+81
-2x -2x
————————
-6x +33 = 81
-33 -33
————————
-6x = 48
————- (divide by -6)
-6
x = -8
Now substitute that to ABD
-4(-8) +33
32 +33
=65
here’s CBD
2(-8) + 81
-16 + 81
=65
Finally angle ABC will be double the amount of ABD or CBD so 65 times 2 is 130.
ANSWERS: (angles)
ABD and CBD: 65
ABC: 130
The bisector of the angle at A (call it AQ) divides the segment BC into segments BQ:QC having the ratio AB:AC. Use this fact to find x.
.. 9:15 = (2x -1):3x
.. 15(2x -1) = 9*3x . . . . . the product of the means equals the product of extremes
.. 30x -15 = 27x
.. 3x = 15
.. x = 5
___
According to the value of x, the bisector AQ divides the triangle into two isosceles triangles: ABQ, ACQ.
Let's assume
x represent the number of trips that the larger truck makes
so, we are given
If the smaller truck makes 18 more trips than the larger
so,
number of trips for larger truck =x
number of trips for smaller truck =x+18
The capacities of two trucks are 3 tons and 4 tons respectively
so, capacity of smaller truck per trip =3 tons / trip
total ton carried by smaller truck = (number of trips for smaller truck)*(capacity of smaller truck per trip)
now, we can plug values
total ton carried by smaller truck =3*(x+18)
total ton carried by larger truck = (number of trips for larger truck)*(capacity of larger truck per trip)
total ton carried by larger truck =4x
it can deliver 12 more tons of freight than the larger
so, we get
we can move 4x on left side
we get
...............Answer
Answer:
The answer is D
Step-by-step explanation:
Remember:
Contrapositive means that if you reverse the hypothesis and the conclusion the statement will mean the same thing
Answer:
C)
Step-by-step explanation:
if the shapes were rotated it would be easier to prove that the shape are congruent. Hope this helps :)
