The image shows the relationship between intersecting secants and their corresponding arcs which is important to understand when looking at problems like these.

The relationship states that an angle formed by two intersecting secants is equal to half the sum of its corresponding arc and its vertical angles corresponding arc.

So ∠FHG = 1/2 ( arc FG + arc EB )

* substitute the given expressions for each angle and arc *

we would then have

15x - 2 = 1/2 ( -2 + 12x + 16x + 10 )

We now solve for x

Step 1 multiply each side by 2

1/2 ( -2 + 12x + 16x + 10 ) *2 = ( the 2 and 1/2 cancels out ) -2 + 12x + 16x + 10

(15x - 2 )2 = 30x - 4

we now have -2 + 12x + 16x + 10 = 30x - 4

step 2 combine like terms

-2 + 10 = 8

12x + 16x = 28x

now we have 30x - 4 = 28x + 8

step 3 add 4 to each side

-4 + 4 cancels out

8 + 4 = 12

Now we have 30x = 28x + 12

step 4 subtract 28x from each side

30x - 28x = 2x

28x - 28x cancels out

now we have 2x = 12

step 5 divide each side by 2

2x / 2 = x

12 / 2 = 6

we're left with x = 6

4 0

3 years ago

Solve by graphing 2x+y=-4

olga_2 [115]

Hey there!
Graphing can be tricky, but I’m happy to help!

The slope is -2 with a Y intercept of -4.
I included my graph from the equation to give you a visual of what it will look like.

Just let me know if you need further assistance or have more questions!
~Brooke❤️

3 0

4 years ago