Answer:
d
Step-by-step explanation:
Answer:
y=4
Step-by-step explanation:
2(y+1)-2=4+y
2y+2-2=4+y
2y=4+y
2y-y=4
y=4
Let x be the number of weeks; therefore, the two linear equations are
Where T stands for the punches on the tea punch card and C for the punches on the coffee punch card.
Solving by substitution. Set T=C, then
Thus, substitute the value of x=3 into the first equation,
Thus, after 3 weeks, Josiah will have the same number of punches on each card, and he will have 23 punches on each card.
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
