Answer: the athlete's salary for year 7 of the contract is $3795957
Step-by-step explanation:
The player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4%. This means that the amount he gets each year is 1.04 times of the previous year's amount. The rate at which his salary increases is in geometric progression. The nth term of a geometric progression is expressed as
Tn = ar^n-1
Where
Tn is the salary for the nth year
a is the salary for the first year
r is the rate at which the salary is increasing. So
a = 3,000,000
n = 7
r = 1.04
We want to determine T7. It becomes
T7 = 3000000 × 1.04^(7-1)
T7 = 3000000 × 1.04^6
Tn = $3795957
It depends if it is
1. 3x+(1/14)=(2x)/8 or
2. (3x+1)/14=(2x)/8
if it is 1
1.
3x+(1/14)=2x/8
simplify 2x/8
2x/8=x/4
3x+(1/14)=x/4
find least common multiple of 14 and 4
factors of 14=2 and 7
factors of 4 are 2 and 2 so LCM=2 times 2 times 7=28
multiply both sides by 28
84x+2=7x
subtract 7x from both sides
77x+2=0
subtract 2 from both sides
77x=-2
divide both sides by 77
x=-2/77
2.
(3x+1)/14=2x/8
simpify 2x/8
2x/8=x/4
(3x+1)/14=x/4
find least common multiple of 14 and 4
factors of 14=2 and 7
factors of 4 are 2 and 2 so LCM=2 times 2 times 7=28
multiply both sides by 28
(2)(3x+1)=7x
distribute
6x+2=7x
subtract 6x from both sides
2=x
475,805 rounded to the nearest ten thousand would be 476,000.
The area of a kite is (1/2) * x * y, where x and y are the length of the two diagonals. In this case, the length of the two diagonals are 10 ft and 2 ft.
<span>Plug that in the equation, we get 1/2 * 2 * 10. We multiply the 2 and 10 first to get 20, that leaves us with 1/2 x 20, which is 10, so the area of this kite is 10 ft squared.</span>
