If triangles PQR and STU are similar then PQ corresponds to ST and PR corresponds to SU. Therefore, PQ/ST=PR/SU
Considering that, PQ= 7-x, ST= 13-x, PR= x²+5 and SU= x² +20
therefore, (7-x)/(13-x)= (x²+5)/(x²+20)
cross multiplying,
7x² +140-x³+20x =13x²+65-x³-5x
combining the like terms,
6x² +15x -75=0
solving for x,
x = 5/2 or -5
Answer:
Two quantities have a proportional relationship if they can be expressed in the general form y = kx, where k is the constant of proportionality. In other words, these quantities always maintain the same ratio--that is, when you divide any pair of the two values, you always get the same number k.
Answer: First option.
Step-by-step explanation:
You can idenfity in the figure that 
is formed by two secants that intersect outside of the given circle.
It is important to remember that, by definition:
Knowing this, you can set up the following equation:
Therefore, you must substitute values into the equation and then evaluate, in order to find the measure of the angle .
This is:
The measure off DF is 11.
In a circle inscribed within a triangle, the distance from each vertex of the triangle to the two nearest touchpoints (points of tangency on the circle) are equal. Since SD=4, DT=4 as well. Since UF=7, then FT=7.
DF=DT+TF=4+7=11.
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