Answer:
5x-12 > with the _ on the bottom 6+2x
Step-by-step explanation:
x is the number/variable
Siras ! Don't try to picture this all in your head !
You'll wear out your brain.
You MUST sketch it on a piece of paper.
Draw an x-axis and a y-axis, then draw the two circles.
I'm drawing myself a picture right now, and I'm
supposed to be some kind of a genius.
a). In order to move Circle-Q so that both centers are
at the same point, you need to move the center of Q
4 units down and 2 units to the right.
When you do that, you'll have the little circle inside the
big circle, with their centers both at the same place.
b). The radius of Q is 2.
The radius of P is 20.
What do you have to multiply 2 by, in order to get 20 ?
THAT's the scale factor to dilate Q so that it has the same
radius as P.
When you do that, suddenly it'll look like you only have one circle
on the paper ... they'll both have the same radius and their centers are
at the same place, so you can't tell them apart.
c). All circles are similar !
I went online (you could easily go there too). I searched the question
"Are circles similar ?" and a lot of interesting stuff came up. (you could
do that too). I saw a lot of ways to prove that all circles are similar.
The best one says:
Two figures are "similar" if you can make one of them
exactly fit on top of the other one (make them congruent)
with translations and dilations.
You just did that with P and Q !
-- Translation is moving them around.
You moved Q and put the centers of both circles at the same place.
-- Dilation is blowing it up or blowing it down, so its size changes
but its shape doesn't change.
You blew Q up so that it had the same radius as P.
Then the two circles exactly fit over/under each other.
So the two circles are similar.
Answer:
<em>Her annual salary is $62,400</em>
Step-by-step explanation:
Michelle Hong noticed that her gross pay per period increased by 2,800 when her employer changed from a bi weekly pay plan to a monthly pay plan.
Bi weekly is a check every 2 weeks, so she would get 26 checks per year.
Monthly would be 12 checks per year.
When she gets paid monthly her pay increased by $2,800 each check.
Let x be one bi-weekly paycheck.
The equation we get is:
12(x+2800) = 26x
Multiply the bracket by 12:
12x +33600 = 26x
Subtract 12x from both sides
33600 = 14x
Divide both sides by 14:
x = 33600/14
<em>x = 2400</em>
Her pay increased by 2800 each period:
2400 + 2800 = 5200 per check.
5200 x 12 months = 62400
<em>Her annual salary is $62,400</em>
16+5=21
21/3=7
I believe that is the correct answer]
