Answered

Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Points Y and Z are points of tangency. Find the value of a.

Points Y And Z Are Points Of Tangency Find The Value Of A class=

Sagot :

gmany

Answer:

a = 2

Step-by-step explanation:

If Y and Z are points of tangency, then |XY| = |XZ|.

We have

[tex]|XY|=9a^2-30\\|XZ|=3a[/tex]

Domain

[tex]a>0[/tex]

Substitute

[tex]9a^2-30=3a\qquad|\text{subtract}\ 3a\ \text{from both sides}\\\\9a^2-3a-30=0\qquad|\text{divide both sides by 3}\\\\3a^2-a-10=0\\\\3a^2-6a+5a-10=0\\\\3a(a-2)+5(a-2)=0\\\\(a-2)(3a+5)=0\iff a-2=0\ \vee\ 3a+5=0\\\\a-2=0\qquad|\text{add 2 to both sides}\\a=2\\\\3a+5=0\qquad|\text{subtract 5 from both sides}\\3a=-5\qquad|\text{divide both sides by 3}\\a=-\dfrac{5}{3}<0[/tex]

Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.