Answer:
A) AAS; B) LA; C) ASA
Step-by-step explanation:
AAS is the Angle-Angle-Side congruence statement. It says that if two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of a second triangle, then the triangles are congruent. In these triangles, ∠E≅∠K, ∠F≅∠L, and DE≅JK. These are two angles and a non-included side; this is AAS.
LA is the leg-acute theorem. It states that if a leg and acute angle of one triangle is congruent to the corresponding leg and acute angle of another triangle, then the triangles are congruent.
The leg we have congruent from each triangle is DE and JK. We also have ∠E≅∠K and ∠F≅∠L, both pairs of which are acute. This is the LA theorem.
ASA is the Angle-Side-Angle congruence statement. It says that if two angles and an included side of one triangle are congruent to the corresponding two angles and included side of another triangle, then the triangles are congruent.
We have that ∠D≅∠J, DE≅JK and ∠E≅∠K. This gives us two angles and an included side, or ASA.
6(-3-4y)
-18-24y
(Multiply 6 by both numbers)
<span>nth term = 7n - 3
n = 1,2,3,4....</span>
Answer:
It will take about 7.3 years for his money to triple.
Step-by-step explanation:
Identify the variables in the formula.
A = 150,000
P = 50,000
r = 0.15
t = ?
A = Pe^rt
Substitute the values into the formula.
150,000 = 50,000e^0.15*t
Solve for t. Divide each side by 50,000.
3 = e^0.15*t
Take the natural log of each side.
ln 3 = ln e^0.15*t
Use the power property and then simplify.
ln 3 = 0.15*t ln e
ln 3 = 0.15-t
Divide each side by 0.15.
(ln 3)
/(0.15) = t
Approximate the answer.
t ≈ 7.3
