Answer:
16 - Original number of chocolates in the box.
Step-by-step explanation:
C = 6 / (3/8) =6 x (8/3) =48 / 3 = 16
Answer:
= 32.440
Step-by-step explanation:
Change the divisor 12.5 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.
We then have the equations:
4055 ÷ 125 = 32.440
and therefore:
405.5 ÷ 12.5 = 32.440
Both calculated to 3 decimal places.
Eqt 1 = 4a-5b=7
eqt 2 = 4a+5b=17
eqt1+eqt2= 8a=24
a=3 then 4*3-5b=7
so b=1
The vertices of the original quadrilateral can be written in matrix form using the vertex matrix. The vertex matrix is

To find the coordinates of the endpoints or vertices of the image of the given coordinate points reflected about the y-axis, we just need to multiply the transformation matrix by the vertex matrix. The transformation matrix for this particular problem is

Multiplying the two matrices, we have

Therefore, the coordinates of the endpoints or vertices of the image are
(5,4), (1,-1), (3, -6) and (7, -3).
There may be more brilliant solution than the following, but here are my thoughts.
We make use of Euclid's algorithm to help us out.
Consider finding the hcf of A=2^(n+x)-1 and B=2^(n)-1.
If we repeated subtract B from A until the difference C is less than B (smaller number), the hcf between A and B is the same as the hcf between B and C.
For example, we would subtract 2^x times B from A, or
C=A-2^xB=2^(n+x)-2^x(2^n-1)=2^(n+x)-2^(n+x)+2^n-1=2^n-1
By the Euclidean algorithm,
hcf(A,B)=hcf(B,C)=hcf(2^n-1,2^x-1)
If n is a multiple of x, then by repetition, we will end up with
hcf(A,B)=hcf(2^x-1,2^x-1)=2^x-1
For the given example, n=100, x=20, so
HCF(2^120-1, 2^100-1)=2^(120-100)-1=2^20-1=1048575
(since n=6x, a multiple of x).