The length of BC = 72
Solution:
Given ΔABC and ΔDEF are similar triangles.
ΔABC 
ΔDEF
AB = 54, BC = n, EF = 12, DE = 9
Similar triangle theorem:
If two triangles are similar then the corresponding sides are proportional to each other.
Substitute the given values, we get
Do cross multiplication.
Divide both sides of the equation by 9.
⇒ BC = 72
Option B is the correct answer.
The length of BC = 72.
We have the following equation:
x2 + y2 + 42x + 38y - 47 = 0
We rewrite the equation:
x2 + 42x + y2 + 38y - 47 = 0
x2 + 42x + y2 + 38y = 47
Rewriting we have:
x2 + 42x + (42/2) ^ 2 + y2 + 38y + (38/2) ^ 2 = 47 + (42/2) ^ 2 + (38/2) ^ 2
x2 + 42x + 441 + y2 + 38y + 361 = 47 + 441 + 361
Rewriting we have:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
The center of the circle is:
(x, y) = (-21, -19)
The radio is:
r = root (849)
r = (849) ^ 2
A circle of the same radius is given by:
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
Let's check:
x ^ 2 - 50x + y ^ 2 - 30y + 1 = 0
x ^ 2 - 50x + y ^ 2 - 30y = - 1
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + (-30/2) ^ 2 + (-50/2) ^ 2
x ^ 2 - 50x + (-50/2) ^ 2 + y ^ 2 - 30y + (-30/2) ^ 2 = - 1 + 225 + 625
(x-25) ^ 2 + (y-15) ^ 2 = 849
Answer:
(x + 21) ^ 2 + (y + 19) ^ 2 = 849
(x, y) = (-21, -19)
r = (849) ^ 2
x ^ 2 + y ^ 2 - 50x - 30y + 1 = 0
1/2 = 2m
2m/2 = 1/2 divided by 2
1/2 * 1/2 = 1/4
m = 1/4
m = 0.25
Answer: m = 1/4 or 0.25
Overall, the goal is to find the value of x and then use this and the given total to find the percentage of x. First, to do this, we must set up our equations based on the given information.
x + y + z = 510
z = (3/2)y
y = 3x
Now, we can begin to solve with substitution. The ultimate goal is to get the first equation to be regarding one variable and them work backwards using that found value.
Substitute the 3rd equation into the second.
z = (3/2)(3x) ----> Simply
z = (9/2)x
Now, when we plug in z and y into the first equation, only x will be present.
x + (3x) + (9/2)x = 510 ---> Combine like terms.
4x + (9/2)x = 510 ---> Get a common denominator.
(8/2)x + (9/2)x = 510
(17/2)x = 510 -----> Multiply both sides by 2/17
Now, if you understand what you are looking at, you know that you just found your answer which is 2/17 because you are about to multiply that by the total.
2/17 = .12 × 100 = 12%
If you did not know that, you can continue solving and then find the answer using part over whole or the total books of school x divided by the total books from all schools. You will get the same answer!
x = (2/17)×510
x = 60
60/510 = .12 × 100 = 12%
I hope this helps!
An Easy Way to do this is to write out the sample space.
5 10
5 25
10 5
10 25
25 5
25 10
Then, check which ones, add to over 20
5 25
10 25
25 5
25 10
Therefore, it's 4/6 or 2/3
