Answer:
Step-by-step explanation:
Each successive year, he
earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as
Tn = ar^(n - 1)
Where
a represents the first term of the sequence(amount earned in the first year).
r represents the common ratio.
n represents the number of terms(years).
From the information given,
a = $32,000
r = 1 + 5/100 = 1.05
n = 20 years
The amount earned in his 20th year, T20 is
T20 = 32000 × 1.05^(20 - 1)
T20 = 32000 × 1.05^(19)
T20 = $80862.4
To determine the his total
earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as
Sn = (ar^n - 1)/(r - 1)
Therefore, the sum of the first 20 terms, S20 is
S20 = (32000 × 1.05^(20) - 1)/1.05 - 1
S20 = (32000 × 1.653)/0.05
S20 = $1057920
Answer:
2 and 3
Step-by-step explanation:
2) If two polygons are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides.
side ratio: 1/4------- area ratio: 1²/4² = 1/16 = 1:16 ratio
3)If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.
The ratio of the perimeters is the same as the scale factor.
scale 1:4
Answer:
The given triangle ABC is a SCALENE RIGHT - ANGLED TRIANGLE
Step-by-step explanation:
Here, in the triangle ABC
∠A = 90° , ∠B = y+ 40° and ∠C = 3y - 10°
Now, by ANGLE SUM PROPERTY of a triangle:
∠A + ∠B+ ∠C = 180°
or, 90° + ( y+ 40°) +( 3y - 10°) = 180°
or, 4y + 120° = 180°
⇒ 4y = 180° - 120° = 60°
or, y = 60° / 4 = 15 ⇒ y = 15
⇒ ∠B = y+ 40° = 55°
and ∠C = 3y - 10° = 3(15) -10 = 35°
Now, here ∠A = 90° , ∠B = 55° and ∠C = 35°
Since here ∠B ≠ ∠C ≠ 45°
Hence, the given triangle ABC is a SCALENE RIGHT ANGLED TRIANGLE
