Circle P is shown. Line segment P Q is a radius and has a length of 9. Line Q R is a tangent that intersects the circle at point Q and has a length of 12. A line connects points R and P. The distance between point R and the circle is x, and the point on the circle to point P is a radius.
What value of x would make Line R Q tangent to circle P at point Q?

x =

X=6

Step-by-step explanation:

We need to remember the theorem that Tangent always makes a right angle at the point of contact with the circle.

Given details-  

PQ=9= circle radius  

QR=12  

As given in the question  

PQ is the radius  

PQ=PY (since both are the radius to the circle)  

⇒If the line QR = tangent than ∠ PQR must be 90°  

Hence Δ PQR is a right-angled triangle with hypotenuse PR  

PQ²+QR²=PR² (Pythagoras theorem)  

∴Substituting the value of PQ, QR  

⇒We get (9)² +(12)² = PR²

PR²= 225  

⇒PR=15  

As clear in figure PR= PY+YR  

∴15=9+x  

⇒ YR(x)= 6cm  

0.6, 3/5, and 6% are the 3 same portion.

but, when they're all changed to a decimal they would equal to 0.6.

hope this , good luck!

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1