Cass -

secondary - student

if the graph of a equation is 2x^{2} - y^{2} = 8 passes through point (6,k), find the positive value of k.

if 5^{x2 - 2 x} = 1, find positive value of x

Hi Cass,
The statement about the graph, "the graph of 2x^{2} -y^{2} = 8 passes through point (6,k)" means the same as the statement about the expression, "the point (6,k) satisfies the expression 2x^{2} - y^{2} = 8". Thus the statement "the graph of 2x^{2} - y^{2} = 8 passes through point (6,k)" means that the expression is a true statement if you replace x by 6 and y by k. That is

2 (6^{2}) - k^{2} = 8
Hence to answer the question you need to solve this expression for k and choose the positive value you find.
For the second problem you need first to realize that if 5^{h} = 1 then h must be zero. Thus to solve this problem you need to find the positive value of x that satisfies x^{2} - 2 x = 0.

Cheers,

Penny