The formula for a diagonal of a rectangle is <span>√w^2+h^2, with w and h being the width and height. Plug in your numbers to get </span><span>√7^2+5.5^2. Simplify that into </span><span>√49+30.25, then to </span><span>√79.25. Use your calculator to get 8.9022. The diagonal is 8.9 feet.</span>
If
, then
. So, in the first gap you can write 5 and in the second you can write -4.
Since
, the minimum value of y is when
. The solution of the last equation is x=-5 and then y=-4 -- these are numbers, which you can write in the third and fourth gaps.
The slope:
m = ( y2 - y1 ) / ( x2 - x1 ) = ( 8 2 ) / ( 3 - 2 ) = 6 / 1
m = 6 ( we have the same slope for AB and A`B` )
AB = √[( 3 - 2 )² + ( 8 - 2 )²] = √37
A`B` = 3.5 √37 = 21.29
Answer: the total amount that you can earn in 15 years is $737245. Option C
Step-by-step explanation:
You receive an annual salary of $32,900 and each year, you are assured of a 5.5% raise. Assuming there was no raise, you get 100% of your previous salary each year. With a raise of 5.5%, you will get 100 + 5.5 = 105.5% of your previous salary for each year. This is a geometric progression and we want to determine the sum of 15 terms(15 years).
The formula for the sum of terms in a geometric progression is
Sn = [a(r^n - 1)]/ r - 1
Sn = sum of n terms
a = the first term
n = number of terms
r = common ratio
From the information given,
a = 32900
n = 15
r = 105.5/100 = 1.055
S15 = [32900(1.055^15 - 1)] / 1.055 - 1
S15 = [32900(2.23247649 - 1)] / 0.055
S15 = 32900 × 1.23247649) / 0.055
S15 = 737245.0277
S15 = $737245
