Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Experience the convenience of finding accurate answers to your questions from knowledgeable professionals on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

Could someone please help on this question? I’m giving 20 points and brainliest but I need it quickly so please help!

Could Someone Please Help On This Question Im Giving 20 Points And Brainliest But I Need It Quickly So Please Help class=

Sagot :

Answer:  HF = 5

=============================================

Explanation:

Refer to the diagram below. I'm adding in points A and B, which are marked in blue. I'm also adding in variables x, y, and z.

The goal is to find HF, so let's make that equal to x. This is also equal to HB because they are radii of the same circle.

Let y be the length of segments JA and JB.

Let z be the length of segments CF and CA.

So in short we have

  • x = HF = HB
  • y = JA = JB
  • z = CF = CA

We know that

  • CH = 13
  • HJ = 19
  • CJ = 22

This must mean

  • CH = CF+HF = z+x = 13
  • HJ = HB+JB = x+y = 19
  • CJ = CA+JA = z+y = 22

Or in short,

  • z+x = 13
  • x+y = 19
  • z+y = 22

Let's solve the first equation for z to get z = -x+13. I subtracted x from both sides.

Now plug this into the third equation to get

z+y = 22

(z) + y = 22

(-x+13) + y = 22 ... replace z with -x+13

-x+13+y = 22

-x+y+13 = 22

-x+y = 22-13 .... subtract 13 from both sides

-x+y = 9

------------------------------------

So we have this reduced system of equations of two variables and two equations

  • x+y = 19 ... found earlier
  • -x+y = 9 .... what we just found above

Add the equations straight down. This is the elimination property.

Doing so leads to the x terms canceling out since x + (-x) = 0x = 0

The y terms add to y+y = 2y

The terms on the right hand side add to 19+9 = 28

We are left with 2y = 28 which solves to y = 28/2 = 14.

If y = 14, then,

x+y = 19

x+14 = 19

x = 19-14

x  = 5

In which we can then say

z = -x+13

z = -5+13

z = 8

Though we don't need to find z (unless you're curious about it).

Since x = 5, and we set HF equal to x, this means that HF = 5.

View image jimthompson5910
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.