-3n<_15
the "<_" is a "less than or equal to" sign i just couldn't type it how it looks
Answer:
Part 7) ![AB=27\ units](https://tex.z-dn.net/?f=AB%3D27%5C%20units)
Part 8) ![x=1.7\ units](https://tex.z-dn.net/?f=x%3D1.7%5C%20units)
Step-by-step explanation:
Part 7) Find the length of AB
we know that
The<u><em> two tangent theorem</em></u> states that if we draw two lines from the same point which lies outside a circle, such that both lines are tangent to the circle, then their lengths are the same
so
In this problem, applying the two tangent theorem
AB=BC
substitute the given values
![15x-3=10x+7](https://tex.z-dn.net/?f=15x-3%3D10x%2B7)
solve for x
![15x-10x=7+3\\5x=10\\x=2](https://tex.z-dn.net/?f=15x-10x%3D7%2B3%5C%5C5x%3D10%5C%5Cx%3D2)
Find the length of AB
![AB=15x-3](https://tex.z-dn.net/?f=AB%3D15x-3)
substitute the value of x
![AB=15(2)-3=27\ units](https://tex.z-dn.net/?f=AB%3D15%282%29-3%3D27%5C%20units)
Part 8) we know that
If CD is tangent to circle E at point C
then
Line segment CD is perpendicular to line segment EC (radius) and CDE is a right triangle
so
Applying the Pythagorean Theorem in the right triangle CDE
![DE^2=CD^2+EC^2](https://tex.z-dn.net/?f=DE%5E2%3DCD%5E2%2BEC%5E2)
substitute the given values
![2^2=x^2+1^2](https://tex.z-dn.net/?f=2%5E2%3Dx%5E2%2B1%5E2)
solve for x
![4=x^2+1\\x^2=3\\x=1.7\ units](https://tex.z-dn.net/?f=4%3Dx%5E2%2B1%5C%5Cx%5E2%3D3%5C%5Cx%3D1.7%5C%20units)
Answer:
x = 24 , y = 19
Step-by-step explanation:
(2x + 13) and 47 + 3x are same- side interior angles and sum to 180° , so
2x + 13 + 47 + 3x = 180 , that is
5x + 60 = 180 ( subtract 60 from both sides )
5x = 120 ( divide both sides by 5 )
x = 24
Then 3x = 3 × 24 = 72
5y - 23 and 3x are corresponding angles and are congruent , then
5y - 23 = 72 ( add 23 to both sides )
5y = 95 ( divide both sides by 5 )
y = 19
Answer:
x= -1
y= 1
Step-by-step explanation:
Set both equations equal to each other
2x+3=x^2+3x+3 then solve for x
2x=x^2+3x the 3 on either side cancel out
-x=x^2
-1=x
Then plug -1 in for one of the equations to solve for y
Y=2(-1)+3
Y=1
Answer and Step-by-step explanation:
Half of
is
.
<em><u>#teamtrees #PAW (Plant And Water)</u></em>