Two main facts are needed here:
1. The logarithm 
, regardless of the base of the logarithm, exists for 
.
2. The square root 
exists for 
.
(in both cases we're assuming real-valued functions only)
By (2) we know that 
exists if 
, or 
.
By (1), we know that 
exists if 
, or 
. But as long as the square root exists, it will always be positive, so this condition will always be met.
Ultimately, then, we only require , so the function has domain 
.
To determine the range, we need to know that, in their respective domains, and increase monotonically without bound. We also know that 
at minimum, at which point the square root term vanishes, so the least value the function takes on is 
. Then its range would be 
.
96 ---> 100%
60 ----> x
x=(60*100%)/96=62.5%
We know that
<span>Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.
</span>we have that
<span>Circle 1 is centered at (4,3) and has a radius of 5 centimeters
</span><span> Circle 2 is centered at (6,-2) and has a radius of 15 centimeters
</span>
step 1
<span>Move the center of the circle 1 onto the center of the circle 2
</span>the transformation has the following rule
(x,y)--------> (x+2,y-5)
so
(4,3)------> (4+2,3-5)-----> (6,-2)
so
center circle 1 is now equal to center circle 2
<span>The circles are now concentric (they have the same center)
</span>
step 2
A dilation is needed to increase the size of circle 1<span> to coincide with circle 2
</span>
scale factor=radius circle 2/radius circle 1-----> 15/5----> 3
radius circle 1 will be=5*scale factor-----> 5*3-----> 15 cm
radius circle 1 is now equal to radius circle 2
A translation, followed by a dilation<span> will map one circle onto the other, thus proving that the circles are similar</span>
43 as you substitute 6 in place of x, and then get 36+6+1=43
Answer:
Answer B, AB is parallel to CD
Step-by-step explanation:
I'm 99% sure this is the answer.
