Answers: Using the process of completing the square:
1. Isolate the constant by <u>adding 7 to</u> both sides of the equation:
x^2-6x-7+7=0+7
x^2-6x=7
2. Add <u>9</u> to both sides of x2 – 6x = 7 to form a perfect square trinomial while keeping the equation balanced:
x^2-6x+9=7+9
x^2-6x+9=16
3. Write the trinomial x2 – 6x + 9 as squared:
<u>(x-3)^2</u> = 16
4. Use the square root property of equality to get x – 3 = ±<u>4</u> .
sqrt[ (x-3)^2 ] = ± sqrt(16)
x-3 = ±4
5. Isolate the variable to get solutions of –1 and 7.
x-3 = ±4
x-3+3 = ±4+3
x = ±4+3
x1=-4+3→x1=-1
x2=+4+3→x2=7
There are 16 boxes total, and 45 wheels total.
we know that each bicycle/tricycle is in it's own box.
i'm going to use the variable "b" for bicycle and "t" for tricycle
b + t = 16
(because b is the amount of bicycles and t is the amount of tricycles)
now we know that there are 45 wheels total.
there are 2 wheels for a bicycle and 3 wheels for a tricycle
2b + 3t = 45
now we have a system of equations
b + t = 16
2b + 3t = 45
You can solve this multiple ways, but I'm going to use substitution.
b + t = 16 can also be written as b = 16 - t (if you subtract both sides by t)
then we can substitute this b = 16 - t into the other equations
2(16 - t) + 3t = 45
32 - 2t + 3t = 45
32 + t = 45
t = 13
now you can plug that back into the original equations
b + 13 = 16
b = 3
2b + 3(13) = 45
2b + 39 = 45
2b = 6
b = 3
If you have any more questions, feel free to ask!
Answer:
The length of the badminton court is 44 feet.
Hoped this helped, have a nice day!
Answer:
Tn = 2/3^(n-1)
Step-by-step explanation:
The nth term of a geometric progression is expressed as
Tn = ar^{n-1}
a is the first term
n is the number of terms
r is t common ratio
From the sequence
a = 2/9
r = (2/3)/(2/9) = 2/(2/3) =3
Substitute
Tn = 2/9(3)^(n-1)
Tn = 2/3^(n-1)
Hence the required equation is Tn = 2/3^(n-1)
