Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
2 answers:
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).
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Exponental law
so
√(81y^5)=√81 times √(y^5)
√81=9 or -9
√(y^5)=y^2 times√y
answer is 9y^2 times √y or -9y^2 times √y
√(81y^5)=√81 times √(y^5)
√81=9 or -9
√(y^5)=y^2 times√y
answer is 9y^2 times √y or -9y^2 times √y
Given:
Consider the inequality is and its solution set is
.
To find:
The statement that verify the solution set.
Solution:
Any value into the inequality form the solution set , will create a true statement and any value into the inequality not form the solution set
, will create a false statement.
To verify the solution set set, we need to put any value form solution set into the given inequality.
Substituting a value into the inequality from the solution set, such as -2, will create a true statement.
Therefore, the correct option is A.