Given that
log (x+y)/5 =( 1/2) {log x+logy}
We know that
log a+ log b = log ab
⇛log (x+y)/5 =( 1/2) log(xy)
We know that log a^m = m log a
⇛log (x+y)/5 = log (xy)^1/2
⇛log (x+y)/5 = log√(xy)
⇛(x+y)/5 = √(xy)
On squaring both sides then
⇛{ (x+y)/5}^2 = {√(xy)}^2
⇛(x+y)^2/5^2 = xy
⇛(x^2+y^2+2xy)/25 = xy
⇛x^2+y^2+2xy = 25xy
⇛x^2+y^2 = 25xy-2xy
⇛x^2+y^2 = 23xy
⇛( x^2+y^2)/xy = 23
⇛(x^2/xy) +(y^2/xy) = 23
⇛{(x×x)/xy} +{(y×y)/xy} = 23
⇛(x/y)+(y/x) = 23
Therefore, (x/y)+(y/x) = 23
Hence, the value of (x/y)+(y/x) is 23.
A
Step-by-step explanation:
90 Degree Rotation. When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). ...
180 Degree Rotation. When rotating a point 180 degrees counterclockwise about the origin our point A(x,y) becomes A'(-x,-y). ...
270 Degree Rotation.
The spinner is divided into four equal sections: 2, 4, 7, 9. This represents 4 possibilities
If the spinner is spun twice, the sample space is:

For product less than 30, the number of outcomes is shown below:
The number of outcomes that have a product less than 30 = 10
The sample space that shows possibilities of an odd number combination:
The number of outcomes that contains at least one odd number = 12
The number of outcomes that have a product less than 30 and contain at least one odd number is shown below. These outcomes are outcomes circled in both cases shown above,
The outcomes circled represents the number of outcomes that has a product less than 30 and contains at least one odd number
Answer: 6 (option B)