Answer:
The cost of the old ball was $100.
Step-by-step explanation:
The cost of the new ball = $300
The new ball has three times the price of his old ball.
So, let the price of the old ball be = x
As per situation, we get the equation:
![3x=300](https://tex.z-dn.net/?f=3x%3D300)
Dividing both sides by 3:
![\frac{3x}{3}= \frac{300}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B3%7D%3D%20%5Cfrac%7B300%7D%7B3%7D)
=> x = 100
Hence, the cost of the old ball was $100.
Answer:
2x + x +90= 180 We will add 2x + x=3x We get 3x + 90 =180 Now we subtract 3x = 180–90 ... x=30, for confirmation put value of x =30in equation and verify. LHS=RHS. Thats it. 68 views.
Answer:
AP = 22
Step-by-step explanation:
In a triangle, the centroid divides the median in the ratio 2:1.
It is given that AD is the median and AD = 33
It is also given that P is the centroid on the median AD.
Therefore, P divides AD in the ratio 2:1.
![\frac{AP}{PD} =\frac{2}{1}](https://tex.z-dn.net/?f=%5Cfrac%7BAP%7D%7BPD%7D%20%3D%5Cfrac%7B2%7D%7B1%7D)
AP = 2k and PD = k
AD = 33
AP + PD = 33
2k + k = 33
3k = 33
k = 11
So, AP = 2k = 2(11) = 22
Area of ABC : AB*AC/2
the maximum of the parabola is reached at x=-4/(2*(-1))=2 hence A is at (2,0) and B is at (2,(-2)^2+4*2+C)=(2,12+C)
C is the second root (x-intersect), which we can find :
determinant1 : D=16-4*(-1)*C=4(4+C) thus the second root is at x=
![\frac{-4-\sqrt{4(4+C)}}{-2}=2+\sqrt{4+C}](https://tex.z-dn.net/?f=%5Cfrac%7B-4-%5Csqrt%7B4%284%2BC%29%7D%7D%7B-2%7D%3D2%2B%5Csqrt%7B4%2BC%7D)
Hence the area of the triangle is
![AB*AC/2=(4+C)*(2+\sqrt{4+C}-2)/2=(4+C)\sqrt{4+C}/2=32](https://tex.z-dn.net/?f=AB%2AAC%2F2%3D%284%2BC%29%2A%282%2B%5Csqrt%7B4%2BC%7D-2%29%2F2%3D%284%2BC%29%5Csqrt%7B4%2BC%7D%2F2%3D32)
hence
![(4+C)\sqrt{4+C}=64](https://tex.z-dn.net/?f=%284%2BC%29%5Csqrt%7B4%2BC%7D%3D64)
.
We remark that
![64=16*4=16*\sqrt{16}](https://tex.z-dn.net/?f=64%3D16%2A4%3D16%2A%5Csqrt%7B16%7D)
Hence 4+C=16 thus
C=12