Answer:
ΔLMN ≅ ΔLQP by (SAA)
Step-by-step explanation:
It is given that line (NM) is congruent to the line (PQ), meaning they have the same measure. This is signified by the small red line on each of these sides.
Moreover, it is also given that angle (MNL) is congruent to angle (QPL), this is shown by the red arc around these angles.
Finally one can figure out that angle (NLM) is congruent to angle (PLQ) by the vertical angles theorem. The verticle angles theorem states that when two lines intersect, the opposite angles are congruent.
Thus the two triangles are congruent by side-angle-angle postulate, abbreviated as (SAA).
Answer:
x=-5, y=-1
Step-by-step explanation:
Substitute x=-4+y into -2x-5y=15. So we have
-2(-4+y)-5y=15
8-2y-5y=15
-7y=7
y=-1
And x is -4+y so x= -4+(-1)= -5.
Solve for m:3 m + 7/2 = 5/2 - 2 m
Put each term in 3 m + 7/2 over the common denominator 2: 3 m + 7/2 = (6 m)/2 + 7/2:(6 m)/2 + 7/2 = 5/2 - 2 m
(6 m)/2 + 7/2 = (6 m + 7)/2:(6 m + 7)/2 = 5/2 - 2 m
Put each term in 5/2 - 2 m over the common denominator 2: 5/2 - 2 m = 5/2 - (4 m)/2:(6 m + 7)/2 = 5/2 - (4 m)/2
5/2 - (4 m)/2 = (5 - 4 m)/2:(6 m + 7)/2 = (5 - 4 m)/2
Multiply both sides by 2:6 m + 7 = 5 - 4 m
Add 4 m to both sides:6 m + 4 m + 7 = (4 m - 4 m) + 5
4 m - 4 m = 0:6 m + 4 m + 7 = 5
6 m + 4 m = 10 m:10 m + 7 = 5
Subtract 7 from both sides:10 m + (7 - 7) = 5 - 7
7 - 7 = 0:10 m = 5 - 7
5 - 7 = -2:10 m = -2
Divide both sides of 10 m = -2 by 10:(10 m)/10 = (-2)/10
10/10 = 1:m = (-2)/10
The gcd of -2 and 10 is 2, so (-2)/10 = (2 (-1))/(2×5) = 2/2×(-1)/5 = (-1)/5:Answer: m = (-1)/5
