<span>Congruence between two triangles means six items, all three sides and all three angles, are congruent. Thus the statement ABC DEF has a very precise meaning. It succinctly summarizes the six statements (assume lines atop these segments): ABDE, BCEF, ACDF, AD, BE, and CF. It is very important to maintain the vertices in the proper order. Not doing so is a common mistake.</span>
Answer:
The first, second, and fifth statements are correct.
Step-by-step explanation:
We are given a circle with the equation:

And we want to select the statements that are true.
First, we can convert the equation into standard form. We can group each variable:

And complete the square for the first term:

Factor and simplify:

We can rewrite our equation as:

So, this tells us that we have a circle centered on (1, 0) with a radius of 3 units.
In this case, the first statement, second statement (the point (1,0) is on the x-axis), and fifth statements are correct (the square root of 9 is also 3).
Answer: The answer is 9x-8y²+4y+34
Step-by-step explanation: Since the equation is 12x+4y-3x+2-8y^2 + 32
1. combine like terms so- combine 12x-3x= 89x
2. look for other like terms- 2+32= 34
3. since 8y^2 and 4y are not the same you can combine them
4. put them all together- 9x-8y^2+4y+3
That's you answer. Hope this helped