Find the vertex for the function

(-3, -34)

Step-by-step explanation:

I'm assuming g(x) is supposed to by g(x) = 2x² + 12x - 16

The general form for a quadratic function is f(x) = ax² + bx + c

For our equation, a = 2, b = 12 and c = -16

The formula for the x coordinate of the vertex is

x = -b/(2a)

Plug in our values and simplify...

x = -12/(2*2) = -12/4 = -3

Plug that value into g(x) to find the y coordinate of the vertex:

g(-3) = 2(-3)² + 12(-3) - 16

  g(-3) = 2(9) - 36 - 16

     g(-3) = -34

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,