Two figures are similar if one is the scaled version of the other.
This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.
To be more precise, you only need two steps to prove that every two circles are similar:
- Translate one of the two circles so that they have the same center
- Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well
Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.
Recapping, we have:
- Start with circle X and radius r
- Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
- Scale the radius of circle X' until it becomes
. This new circle, say X'', is similar to X' because you only scaled it
So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.
Answer: b is the correct option
Step-by-step explanation:
Tamara earns her living as a salary plus commission employee. This means that the total amount she earns is not fixed.
Her annual salary is $48,000. There are 12 months in a year. This means
that her her monthly salary is 48000/12 = $4000
she earns 4% commission on all sales she makes.
If Tamara wants to make a total of $6,000 this month, it means that she wants to make an extra $2000($6000-$4000) this month. She can only make this from commission based on sales
Let the sales be x
4% of x = 2000
4/100 × x = 2000
0.04x = 2000
x= 2000/0.04 = $50000
When tow solids of similar shape that is assuming to be a box in this case, having a length ratio of 2:9, we get the ratio of the surface areas equal to the<span>square of the ratio of their edges. This is becaue the surface area is equal to the area of the base (square) which is the square of the side. Answer is B.</span>
The options of the problem are
we have
we know that
<u>The Rational Root Theorem </u>states that when a root 'x' is written as a fraction in lowest terms
p is an integer factor of <u>the constant term</u>, and q is an integer factor of <u>the coefficient of the first monomial</u>.
So
in this problem
the constant term is equal to 
and the first monomial is equal to 
-----> coefficient is 
therefore
<u>the answer is the option </u>
D. 
Answer:
9x²y¹⁴
Step-by-step explanation:
