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2 answers:
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Answer:
always true
Step-by-step explanation:
Original inequality:
Distribute the -6
Combine like terms:
As you can see the expression on the left side is constant, so it is always true, since the constant (60) is less than 180
Answer:
The radius is .
Step-by-step explanation:
The standard equation for a circle is .
I like to call this form center-radius form because it tells you the center (h,k) and the radius r.
So we put it in this form to determine r, the radius, which is the desired value here.
We will need to complete the square.
Thankfully there is a formula to take more thinking out of the process:
.
Let's begin:
Reorganize the equation so the x's are together and the y's are together.
Now time to being completing the square. Keep in mind whatever you add to one side you need to add the other side to keep the equation equivalent to what it once was.
Use the other side of the formula I mentioned for completing the square:
So the center is (3,-4).
The radius is .
You can actually simplify the radius since 99 contains a factor that is a perfect square.
Y = 
x + 3
y = x - 4
Since both equations are equal to y, you can set the two values equal to each other and solve for x.
x + 3 = x - 4 Multiply both sides by 2
x + 6 = 2x - 8 Add x to both sides
6 = 3x - 8 Add 8 to both sides
14 = 3x DIvide both sides by 3
4
= x
Now, plug the x value into one of the original equations, I'll plug it into y = x - 4.
y = x - 4 Plug in the x value
y = 4 - 4 Subtract
y =
x = 4 and y =
y = x - 4
Since both equations are equal to y, you can set the two values equal to each other and solve for x.
x + 6 = 2x - 8 Add x to both sides
6 = 3x - 8 Add 8 to both sides
14 = 3x DIvide both sides by 3
4
Now, plug the x value into one of the original equations, I'll plug it into y = x - 4.
y = x - 4 Plug in the x value
y = 4
y =
x = 4