Answer:
Long = 6√3
Step-by-step explanation:
Reference angle = 30°
Hypotenuse = 12
Long = Adjacent = ?
Apply CAH:
Cos 30 = Adj/Hyp
Cos 30 = Long/12
12*cos 30 = Long
12*√3/2 = long (cos 30 = √3/2)
6√3 = long
Long = 6√3
Answer:
x=10 and y=12
Step-by-step explanation:
To solve this quadratic equation we will use two method
1. Elimination method
2. substitution method
first of we use elimination method
we either eliminate x or y
we will be eliminating y
83x-20y=590..........(eq1)
60x+18y=816...........(eq2)
y will be eliminated by multiplying
(eq1) by 9
(eq2) by 10
which will give
747x-180y=5310.........(eq3)
600x-180y=8160.........(eq4)
see that y has the same value that is (-180y and +180y)
so to eliminate y completely you have to add eq1 and eq2 because if you don't add them together you wont eliminate y
747x-180y=5310
+
600x+180y=8160
=
1347x+0=13470
1347x=13470
x=13470/1347
x=10
Now to find y we use substitution method ie put x=10 in any of the equation above(eq1,eq2,eq3, eq4) you will get the same answer
eq1
83x-20y=590..... where (x=10)
83(10)-20y =590
830-20y=590
like terms
-20y=590-830
-20y= -240
divide both sides with -20
y= -240/-20
y=12
OR
eq2
60x+18y=816..... where x=10
60(10)+18y=816
600+18y=816
like term
18y=816-600
18y=216
y=216/18
y= 12
or eq3 or eq4 you will still get the same answer......
Answer:
The money was invested for 8 years.
Step-by-step explanation:
Given that a principal of $ 20,000 is invested at 6.25% and earns $ 10,000 simple interest, to determine how many years has the money been invested, the following calculation has to be performed:
(20,000 x 0.0625) x X = 10,000
1,250X = 10,000
X = 10,000 / 1,250
X = 8
Thus, the money was invested for 8 years.
Given:
P = $8000, the principal
r = 5.99% = 0.0599, the interest rate
t = 60 months = 5 years, the duration
Assume n = 12, monthly compounding.
n*t = 12*5 = 60
r/n = 0.0599/12 = 0.004992
The total value of the loan is
A = P(1 + r/n)⁶⁰
= 8000(1.004992)⁶⁰
= 10785.434
Monthly payment = 10785.434/60 = $179.76
Answer: $179.46
cosine ( CAH) = Adjacent/ hypothenus
cos9 = x/ 2
let x represent the horizontal distance
2 cos 9 = x
x = 2 (0.98768834)
x = 1.975
x = 1.97
therefore the horizontal dstance jade covers is 1.97km
