Answer:
B) 8 and 24.
Step-by-step explanation:
Just by looking at the answer choices, since one number must be three times the other, we can determine that the correct answer is B.
Regardless, let's work this out mathematically. Let the first number be <em>a</em> and the second number be <em>b</em>.
Their difference is 16. Hence:
![a-b=16](https://tex.z-dn.net/?f=a-b%3D16)
The first number is three times the second number. So:
![a=3b](https://tex.z-dn.net/?f=a%3D3b)
Substitute:
![3b-b=16](https://tex.z-dn.net/?f=3b-b%3D16)
Solve for <em>b</em>. Subtract:
![2b=16](https://tex.z-dn.net/?f=2b%3D16)
And divide both sides by two:
![b=8](https://tex.z-dn.net/?f=b%3D8)
So, the second number is 8.
And since the first number is three times the second, the first number is 24.
Our answer is B as expected.
Answer:
Step-by-step explanation:
the quotient of is the result of dividing two terms
The first term is - Twice a number t: 2t
The second term is - and 12: 12 2t÷12or 2t12
Sin= p/h , cos= b/h , tan= p/b
Answer:
46
Step-by-step explanation:
Let
represent a number with
in the ten's position and
is the one's position.
This means
actually has value of
.
We are given the sum of those digits of
is 10; this means
.
It says if 18 is added to the number
, then the result is
.
So
has value
and
has value
.
We are given then:
![(ab)+18=(ba)](https://tex.z-dn.net/?f=%28ab%29%2B18%3D%28ba%29)
![10a+b+18=10b+a](https://tex.z-dn.net/?f=10a%2Bb%2B18%3D10b%2Ba)
Subtract
on both sides:
![b+18=10b+a-10a](https://tex.z-dn.net/?f=b%2B18%3D10b%2Ba-10a)
Simplify:
![b+18=10b-9a](https://tex.z-dn.net/?f=b%2B18%3D10b-9a)
Subtract
on both sides:
![18=10b-b-9a](https://tex.z-dn.net/?f=18%3D10b-b-9a)
![18=9b-9a](https://tex.z-dn.net/?f=18%3D9b-9a)
Divide both sides by 9:
![2=b-a](https://tex.z-dn.net/?f=2%3Db-a)
Rearrange by commutative property:
![2=-a+b](https://tex.z-dn.net/?f=2%3D-a%2Bb)
So the system of equations we want to solve is:
![a+b=10](https://tex.z-dn.net/?f=a%2Bb%3D10)
![-a+b=2](https://tex.z-dn.net/?f=-a%2Bb%3D2)
-------------------------Add equations together (this will eliminate the variable
and allow you to go ahead and solve for
:
![0+2b=12](https://tex.z-dn.net/?f=0%2B2b%3D12)
![2b=12](https://tex.z-dn.net/?f=2b%3D12)
Divide both sides by 2:
![b=\frac{12}{2}](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B12%7D%7B2%7D)
Simplify:
![b=6](https://tex.z-dn.net/?f=b%3D6)
If
and
, then
.
since 4+6=10.
So the original number is (46).
18 more than 46 is 18+46=(64) which is what we wanted.
We also have the sum of 4 and 6 is 10 as well.