1.1. Which statement explains why the two systems of equations below have the same solution?
A(6x + 8y = -10
2x - 5y = 12
B
8x + 3y = 2
12x + 16y = - 20
A. The first equation in B is the sum of the equations in A, while the other is obtained
by multiplying the second equation in A by 6.
B. The first equation in B is the sum of the equations in A, while the other is obtained
by multiplying the first equation in A by 2.
C. The equations in A are increased by 12 and -32 to get the equations in
D. The equations in A are multiplied by 2 and 4 to get the equations in B.

Correct Answer is B. The first equation in B is the sum of the equations in A, while the other is obtained  by multiplying the first equation in A by 2.

Step-by-step explanation:

As given,

A : 6x + 8y = -10     equation (1)

     2x - 5y = 12      equation (2)

B : 8x + 3y = 2         equation (1)

  12x + 16y = - 20    equation (1)

Correct Answer is B. The first equation in B is the sum of the equations in A, while the other is obtained  by multiplying the first equation in A by 2.

Proof :

The first part says that ,

Sum of equation (1) of A and equation (2) of A = Equation (1) of B

Firstly , find the Sum of equation (1) of A and equation (2) of A

⇒6x + 8y + 2x - 5y = -10 + 12

⇒8x + 3y = 2

this is same as equation (1) of B

So, it satisfies the first part

The second part says that,

The equation (2) of B is obtained by multiplying the first equation in A by 2.

It means , if the equation (1) is multiplied by 2 = equation (2) of B

Firstly , if the equation (1) is multiplied by 2 , we get

2 ( 6x + 8y = -10 )

⇒ 2 ( 6x + 8y ) = 2 ( -10)

⇒ 12x + 16y = -20

this is same as equation (2) of B

So, it satisfies the second part.

no not all of them.

step-by-step explanation:

some of them have a square base.

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: