Answer: Veronica is not correct
Explanation:
The AAA theorem, aka the AA theorem, only applies to similar triangles. We cannot use it to prove two triangles are congruent or not. We would need to know info about at least one pair of sides. So based on this diagram, we don't have enough information to know if triangle HAT is congruent to triangle PAM or not.
A similar example to this is to consider two equilateral triangles. Let's call them triangle A and triangle B. If equilateral triangle A has side lengths of 2, and has side lengths of 10, we can see that the triangles are not congruent. However, the triangles are similar because the corresponding angles equal one another. One triangle is a scaled copy of the other. This example is a counterexample as to why the AAA theorem is not a valid congruence theorem.
Shipment = 72 cases of books + 94 cases of magazines
1 case of books = 35 pounds
1 case of magazines = 23 pounds
Shipment = 72 × 35 + 94 × 23 pounds
72 × 35 = 2520
94 × 23 = 2162
Shipment = 2520 + 2162 pounds
Shipment = 4682 pounds
Hello from MrBillDoesMath
Answer:
[email protected] = - sqrt(7)/ 4
which is choice B
Discussion:
This problem can be solved by drawing triangles and looking at ratios of sides or by using the trig identity:
([email protected])^2 + (sin2)^2 = 1
If [email protected] = 3/4
, the
([email protected])^2 + (3/4)^2 = 1 => (subtract (3/4)^2 from both sides)
([email protected])^2 = 1 - (3/4)^2 = 1 - 9/16 = 7/16
So...... taking the square root of both sides gives
[email protected] = +\- sqrt(7)/ sqrt(16) = +\- sqrt(7)/4
But is [email protected] positive or negative? We are told that @ is in the second quadrant and cos(@) is negative in this quadrant, so our answer must be negative
[email protected] = - sqrt(7)/ 4
which is choice B
Thank you,
Mr. B
0.15c>10+0.10c
0.05c>10
c>200
