Answer:
Step-by-step explanation:
QM is the angle bisector of ∠LMP
∠LMQ = ∠QMP
QM is the angle bisector of ∠PQL
∠PQM = ∠MQL
MQ = QM as common
By ASA, triangle MQP ≅ MQL
LM = PM and LQ = PQ as they are same side of congruent triangles
Triangle LPQ and LPM are isosceles
By angle bisector theorem, LP is perpendicular to MQ
By properties of rhombus, the two diagonals are perpendicular proves that LMPQ is a rhombus.
LM ≅ PQ
Answer:
f(x) = (x - 3)(x + 1) → Corresponds with the first (raised higher ) ∪ shaped graph
f(x) = -2(x - 1)((x + 3) → Corresponds with the ∩ shaped graph
f(x) = 0.5(x - 6)((x + 2) → Corresponds with the second (lower) ∪ shaped graph
Step-by-step explanation:
For the function f(x) = (x - 3)(x + 1)
We have;
When x = 0, y = -3
When y = 0 x = 3 or -1
Comparing with the graphs, it best suits the first ∪ shaped graph that rises here than the other ∪ shaped graph
For the function;
f(x) = -2(x - 1)((x + 3)
When x = 0, y = 6
When y = 0, x = 1 or -3
Which corresponds with the ∩ shaped graph
For the function;
f(x) = 2(x + 6)((x - 2)
When x = 0, y = -24
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = 0.5(x - 6)((x + 2)
When x = 0, y = -6
When y = 0, x = 6 or -2
Which best suits the second ∪ shaped graph that is lower than the other (first) ∪ shaped graph
For the function;
f(x) = 0.5(x + 6)((x - 2)
When x = 0, y = -6
When y = 0, x = -6 or 2
Graph not included
For the function;
f(x) = (x + 3)((x - 1)
When x = 0, y = -3
When y = 0, x = -3 or 1
Graph not included
<h3>
Answer: Third choice. 
</h3>
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Explanation:
SAS stands for Side Angle Side. Note how the angle is between the two sides. To prove the triangles congruent with SAS, we need to know two sides and an angle between them.
We already see that BC = CD as shown by the tickmarks. Another pair of sides is AC = AC through the reflexive theorem.
The missing info is the angle measures of ACB and ACD. If we knew those angles were the same, then we could use SAS to prove triangle ACB is congruent to triangle ACD.
It turns out that the angles are congruent only when they are 90 degrees each, leading to AC being perpendicular to BD. We write this as
. The upside down T symbol meaning "perpendicular" or "the two segments form a right angle".
Answer:
3602
Step-by-step explanation:
Formula = Population after n years = 2000( 1.04)^n
15 years the population will be 2000(1.04)^15
=3602.