The probability of obtaining an odd number is 1/2 or 50%.
Answer: B. 2 inch
Step-by-step explanation:
Let x represent the uniform width of the frame.
The original dimensions of the picture is 5 in x 7 in. This means that the new width of the picture together with the frame is (5 + 2x) in and the new length of the picture together with the frame is (7 + 2x) in.
The formula for determining the area of a rectangle is expressed as
Area = length × width
The area of the picture and the frame together is 99 in2. Therefore,
(5 + 2x)(7 + 2x) = 99
35 + 10x + 14x + 4x² = 99
4x² + 24x + 35 - 99 = 0
4x² + 24x - 64 = 0
Dividing through by 4, it becomes
x² + 6x - 16 = 0
x² + 8x - 2x - 16 = 0
x(x + 8) - 2(x + 8) = 0
x - 2 = 0 or x + 8 = 0
x = 2 or x = - 8
The width cannot be negative. So
x = 2 in
5^2(4+6)/2
25(10)/2
250/2
= 125
Answer:
g(x)= (1/6)x+5/6 is the inverse function of f(x)
Step-by-step explanation:
We have y= 6x-5
Then, we take x depending on y like:
6x-5=y
6x-5 +5 = y + 5
6x= y+5
6x/6=y/6 + 5/6
x= y/6+ 5/6
Now, we replace x by the function g(x) and y by the variable x, then we have
g(x)= (1/6)x+5/6 is the inverse function of f(x).
Hope that you understand.
Parameterize this surface (call it 
) by
with 
and 
. Take the normal vector to to be
Then the area of is
