I’m pretty sure it will be 7+12 and 12+7
Answer:
See proof below
Step-by-step explanation:
Two triangles are said to be congruent if one of the 4 following rules is valid
- The three sides are equal
- The three angles are equal
- Two angles are the same and a corresponding side is the same
- Two sides are equal and the angle between the two sides is equal
Let's consider the two triangles ΔABC and ΔAED.
ΔABC sides are AB, BC and AC
ΔAED sides are AD, AE and ED
We have AE = AC and EB = CD
So AE + EB = AC + CD
But AE + EB = AB and AC+CD = AD
We have
AB of ΔABC = AD of ΔAED
AC of ΔABC = AE of ΔAED
Thus two sides the these two triangles. In order to prove that the triangles are congruent by rule 4, we have to prove that the angle between the sides is also equal. We see that the common angle is ∡BAC = ∡EAC
So triangles ΔABC and ΔAED are congruent
That means all 3 sides of these triangles are equal as well as all the angles
Since BC is the third side of ΔABC and ED the third side of ΔAED, it follows that
BC = ED Proved
Answer:
(D) 11: 00
Step-by-step explanation:
We have been given that Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike.
This means that Cassie leaves 1/2 hour before Brian.
Since Cassie bikes at a uniform rate of 12 miles per hour, so distance covered in half hour would be half of 12 miles that is 6 miles.
Since total distance is 62 miles, so distance left between both at 9:00 Am would be
.
We are told that Brian bikes at a uniform rate of 16 miles per hour and Cassie bikes at a uniform rate of 12 miles per hour, so distance traveled by both in one hour would be
miles.
Let us divide 56 by 28 to find time taken to complete 56 miles.
.
Since it will take them 2 hours to cover 56 miles, therefore, they will meet 2 hours after 9:00 AM that is 11:00 AM.
Answer:
4 students
Step-by-step explanation:
As shown in the diagram, let U=[The total number of students questioned]

A=[Those who liked peanut butter ]

B=[Those who liked jam ]

x = those who like both peanut butter and jam.
Also 6 liked neither peanut butter nor jam.
From the diagram we can write the mathematical equation as follow and solve for x


We add x and subtract 30 to both sides.


Therefore 4 students like both peanut butter and jam.
Consider the number xy where:
xy = 10 . x + y
x . y = 35
xy + 18 = yx
10.x + y + 18 = 10.y + x
10.x - x = 10.y - y - 18
9.x = 9.y - 18
x = y - 2
(y - 2) . y = 35
y^2 - 2y - 35 = 0
Using the Bhaskara formula:
y = 7 (the negative solution is discarded)
x = 7 - 2
x = 5
Response: the xy number is 57.
;-)