Rectangle has an
The area of a rectangle can be expressed by 2^2- 7x - 4.
area of 45, find the positive value for x.

The positive value for x is 7

Explanation:

Given that the area of a rectangle is expressed by

The area of the rectangle is 45.

We need to determine the positive value for x.

The value for x:

The value of x can be determined by equating both the values of area of a rectangle.

Thus, we have,

Subtracting both sides by 45, we have;

Let us solve the equation using the quadratic formula.

Thus, we get;

Simplifying, we get;

Thus, the two values of x are given by

  and  

  and  

  and  

Since, x cannot take negative values, then

Thus, the value of x is 7.

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'.