Answer:
The answer to your question is length = 24 ft
Step-by-step explanation:
Data
Rectangular-shaped
Area = 360 ft²
lenght = x
width = 5/8x
Formula
Area = length x width
- Substitution
360 = (x)(5/8x)
- Solve for x
360 = 5/8x²
x² = 360(8)/5
x² = 2880 / 5
x² = 576
- Result
x = 24 ft
- Conclusion
The length of the living room is 24 ft and the width is 24(5/8) = 15 ft.
Answer:
99
Step-by-step explanation:
Through some clever algebra, we can combine our first two equations using the fact that

We have the a² and the b² in the equation
, and we <em>almost </em>have a 2ab in the equation
. To get that 2ab, we can simply double both sides of the first equation to get
. From there, we'll add the first two equations together, giving us the summed equation

And since
, we can equivalently say that

A suitable vector calculator can perform this arithmetic directly, as can many graphing or scientific calculators that are capable of handling complex numbers. Mine says
(8, 2π/3) - (4, π/3) = (4√3, 5π/6)
The distance is 4√3 ≈ 6.9282.If you cannot use your calculator for this purpose, you can use the Law of Cosines. You have two sides of the triangle (4 and 8) and the angle between them (2π/3 - π/3), so you have all the information needed.
c² = a² + b² -2ab·cos(C)
c² = 4² + 8² - 2·4·8·cos(π/3)
c² = 16 + 64 - 32 = 48
c = √48 = 4√3
Or, you can simply recognize that the two vectors have the ratio 1:2 and the angle between them is 60°. That is, they are one leg and the hypotenuse of a 30°-60°-90° triangle, so the other leg is 4√3.
Answer:
(x,y) (-3,4)
Step-by-step explanation:
Answer:
$5,956.2
Step-by-step explanation:
First we need to find the amount after 5years using the formula
A =P(1+r)^n
A = 9000(1+0.06)^5
A = 9000(1.06)^5
A = 9000(1.3382)
A = 12,043.8
Interest after 5 years = 12,043.8 - 9000
Interest after 5 years = 3,043.8
Since it will be worth 6% less each year, the amount after 5years will be 9000 - 3,043.8 = $5,956.2