Lydias hotel room number has three digits. The hundreds digit has a value of 40 Tens. The Tens digit is greater than 6. Which could be Lydias hotel room number?

Any 3 digit number can be expressed in the form of:

Where represent any natural number from 0 to 9.

We are told the hundreds number (this means in the expression above) is equal to the value of 40 tens, 40 tens is 400. Then, we know the digit in the tens is greater then 6, this means in the expression above.

So, there are multiple numbers the room number could be, namely:

where can be 7, 8, or 9; and can be  0, 1, 2, 3, 4, 5, 6, 7, 8, or 9. So, there's 30 possible room numbers Lydia may be.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,