Answer:
See proof
Step-by-step explanation:
Statements Reasons
1. 
bisects 
Given
2. 
Definition of angle bisector
3. 
Reflexive property of equality
4. 
AAS postulate
5. 
Congruent triangles have congruent corresponding sides
6. 
Reflexive property of equality
7. 
SAS postulate
8. 
Congruent triangles have congruent corresponding sides
Step 1
Given;
Required; To find the similarity postulate or theorem that applies.
Step 2
Both triangles share one side AG
They also have a common angle;
Side AG = 10 units and ∠AGT ≅ ∠AGB.
Thus, options A and B are discarded.
Step 3
Now, as for the SAS criteria, we need two sides to be congruent and their included angles to be congruent.
But, as no other information is given, we cannot determine whether the given triangles are congruent or not.
Therefore, the answer is; Option D
Let A be the angle of 79 degrees
B be the angle of (5y-4) degrees
C be the angle of (x+5) degrees
D be the angle of (9z-7) degrees
According to the property of parallelogram
Opposite angles are equal
We get, angle A = angle C
Since angle A = 79 degrees
And angle C = (x+5) degrees
We get, x+5=79
=> x=79-5=74.
Angle B = Angle D
(5y-4)=(9z-7)
Since there’s two variables here, we can’t use the property of “opposite angles are equivalent”
We have to use another property which is adjacent angles are equal
Therefore, we can find angle D
Angle D + Angle A=180
=> 9z-7 =180-79
z=108/9
z=12
Since (5y-4)=(9z-7)
Substitute z=12 in
We get, 5y-4=101
y= 105/5
y= 21
Therefore, x=74, y=21 and z=12.
Start off by making a ratio and write down the given. From there solve and multiply. Hopefully the picture helps :)
Answer:
6194.84
Step-by-step explanation:
Using the formula for calculating accumulated annuity amount
F = P × ([1 + I]^N - 1 )/I
Where P is the payment amount. I is equal to the interest (discount) rate and N number of duration
For 40 years,
X = 100[(1 + i)^40 + (1 + i)^36 + · · ·+ (1 + i)^4]
=[100 × (1+i)^4 × (1 - (1 + i)^40]/1 − (1 + i)^4
For 20 years,
Y = A(20) = 100[(1+i)^20+(1+i)^16+· · ·+(1+i)^4]
Using X = 5Y (5 times the accumulated amount in the account at the ned of 20 years) and using a difference of squares on the left side gives
1 + (1 + i)^20 = 5
so (1 + i)^20 = 4
so (1 + i)^4 = 4^0.2 = 1.319508
Hence X = [100 × (1 + i)^4 × (1 − (1 + i)^40)] / 1 − (1 + i)^4
= [100×1.3195×(1−4^2)] / 1−1.3195
X = 6194.84
