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>
Answer:
x = -1 and x = 5
Step-by-step explanation:
<em>What are the solutions of the equation (x – 3)² + 2(x – 3) -8 = 0? Use u substitution to solve.</em>
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(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)
To solve this problem, we will follow the steps below;
let u = x-3
we will replace x-3 by u in the given equation:
(x – 3)² + 2(x – 3) -8 = 0
u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)
We will now solve the above quadratic equation
find two numbers such that its product gives -8 and its sum gives 2
The two numbers are 4 and -2
That is; 4×-2 = -8 and 4+(-2) = 2
we will replace 2u by (4u -2u) in equation (2)
u² + 2u -8 = 0
u² + 4u - 2u -8 = 0
u(u+4) -2(u+4) = 0
(u+4)(u-2) = 0
Either u + 4 = 0
u = -4
or
u-2 = 0
u = 2
Either u = -4 or u = 2
But u = x-3
x = u +3
when u = -4
x = u + 3
x = -4 + 3
x=-1
when u = 2
x = u + 3
x = 2 + 3
x=5
Therefore, x = -1 and x =5
x
Answer:
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
A = $2700
P = $20300
n = 2004 - 1997 = 7 years
Therefore,
20300 = 2700(1 - r)^7
20300/2700 = (1 - r)^7
7.519 = (1 - r)^7
Taking log of both sides, it becomes
Log 7.519 = 7 log(1 - r)
0.876 = 7 log(1 - r)
Log (1 - r) = 0.876/7 = 0.125
Taking inverse log of both sides, it becomes
10^log1 - r = 10^0.125
1 - r = 1.33
r = 1.33 - 1 = 0.33
The expression would be
A = 20300(1 - 0.33)^t
A = 20300(0.67)^t
Therefore, in 2007,
t = 2007 - 1997 = 10 years
The value would be
A = 20300(0.67)^10
A = $370
Answer:
3,872.32
Step-by-step explanation:
the nearest hundredth is 2 numbers on the right of the decimal sign. So you round up from 5 to get answer above.
There are 14 possibilities for first place.
There are 13 possibilities for second place, since a dog can't get both first and second place.
There are 12 possibilities for third place, since a dog can't get both first, second, and third place.
There are 11 possibilities for fourth place, since a dog can't get both first, second, third, and fourth place.
Multiply them together and get 24024 possibilities.
Hope this helps!
