Answer:
The set of factors of 20 is {1, 2, 4, 5, 10, 20} and the set of factors of 16 is {1, 2, 4, 8, 16}. {1, 2, 4, 5, 10, 20} ∩ {1, 2, 4, 8, 16} = {1, 2, 4} which has greatest value 4. So, GCF(20, 16) = 4.
Step-by-step explanation:
Add -7 to both sides so that the equation becomes -3x^2 + 6x + 2 = 0.
To find the solutions to this equation, we can apply the quadratic formula. This quadratic formula solves equations of the form ax^2 + bx + c = 0
x = [ -b ± √(b^2 - 4ac) ] / (2a)
x = [ -6 ± √((6)^2 - 4(-3)(2)) ] / ( 2(-3) )
x = [-6 ± √(36 - (-24) ) ] / ( -6 )
x = [-6 ± √(60) ] / ( -6)
x = [-6 ± 2*sqrt(15) ] / ( -6 )
x = 1 ± -sqrt(15)/3
The answers are 1 + sqrt(15)/3 and 1 - sqrt(15)/3.
Answer:
(a) x + 3(x + 4) = 5(x + 2) - 5
(b) youngest: 7 years old
middle: 9 years old
oldest: 11 years old
Step-by-step explanation:
(a)
We know that x is the youngest child's age. Since the sisters' ages are consecutive odd integers, we know that the ages differ by 2. So, the middle sister's age is x + 2 and the oldest sister's age is x + 4.
Our equation to model the sentence "the sum of the age of the youngest and three times the age of the oldest is five less than five times the middle sister's age" would be:
x + 3 * (x + 4) = 5 * (x + 2) - 5
x + 3(x + 4) = 5(x + 2) - 5
(b)
Now, we can just solve the equation above:
x + 3(x + 4) = 5(x + 2) - 5
x + 3x + 12 = 5x + 10 - 5
4x + 12 = 5x + 5
x = 12 - 5 = 7
So, the youngest sister is 7 years old.
That means the middle sister is 7 + 2 = 9 years old, and the oldest sister is 9 + 2 = 11 years old.
The ages, then, are:
youngest: 7 years old
middle: 9 years old
oldest: 11 years old
The area of the disk is approximately 314 inches
Answer:
(x-1)^2 + y^2 = 25
Step-by-step explanation:
center C ( ( xA + xB)/2 , (yA+yB)/2 ) = ( 1 , 0)
AB = 10
radius = AB / 2 = 5
equation formula: (x - xC)^2 + (y-yC)^2 = radius^2
Hence:
(x-1)^2 + y^2 = 25
