Answer:
The solution is (-2,-11)
Step-by-step explanation:
The given system is
![-5x+y=-1](https://tex.z-dn.net/?f=-5x%2By%3D-1)
and
![y-4x=-3](https://tex.z-dn.net/?f=y-4x%3D-3)
Make y the subject in the first equation to get;
![y=5x-1](https://tex.z-dn.net/?f=y%3D5x-1)
Put
into the second equation.
![5x-1-4x=-3](https://tex.z-dn.net/?f=5x-1-4x%3D-3)
Group similar terms;
![5x-4x=-3+1](https://tex.z-dn.net/?f=5x-4x%3D-3%2B1)
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Put
into
.
This implies that;
![y=5(-2)-1](https://tex.z-dn.net/?f=y%3D5%28-2%29-1)
![y=-10-1](https://tex.z-dn.net/?f=y%3D-10-1)
![y=-11](https://tex.z-dn.net/?f=y%3D-11)
The solution is (-2,-11)
Hypotenuse of the triangle containing < theta = sqrt (60^2 + 11^2) = sqrt 3721 = 61
H = 61 , O = 60 and A = 11
sin theta = O/H = 60/61, cos theta = A/H = 11/61
csc theta = H/O = 61/60, sec theta = H?A = 61/11 and cot theta = 11/60
It's C
It's easy once you spot the ones that can cross cancel!
Say we have the fractions 8/10 and 20/23.
(it's easier to see on top of each other)
If you look diagonally , so 8 and 23 and 10 and 20, you can see that 10 and 20 have a common factor. So we divide it by the highest common factor to reduce those numbers, making it easier to multiply. 10 and 20 can become 1 and 2, dividing by 10. So now we are left with 8/1 and 2/23, and now we multiply normally going across so 16/23.
This works going both diagonals and simplifying both, but in that case it would be easier to try and simplify the fractions before cross multiplying them.
Basically: look for those diagonals and if they can be divided down by the highest common factor, go for it to make it easier to multiply normally afterwards.
Hope I helped!
Answer:
The probability is ![\frac{16}{43}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B43%7D)
Step-by-step explanation:
The psychology class has 9 freshman male, 15 freshman females, 8 sophomore male and 12 sophomore female.
Total population constitution of the class=
17 males and 27 females and 44 students in total.
If on selecting on the first attempt, a male has been picked up then the number of males for the picking up in the second attempt has to decrease by one.
Also, the total number of students from which it has to be selected also decreases by 1, because one child has already been selected.
Therefore for Second Attempt, Total 43 students and 16 males.
Probability=![\frac{No.OfFavorableOutcomes}{TotalNo.OfOutcomes}](https://tex.z-dn.net/?f=%5Cfrac%7BNo.OfFavorableOutcomes%7D%7BTotalNo.OfOutcomes%7D)
Probability=![\frac{16}{43}](https://tex.z-dn.net/?f=%5Cfrac%7B16%7D%7B43%7D)