Which is equivalent to the expression? x2 + 6x + 4 a) (x + 3)2 + 5 b) (x + 3)2 − 5 c) (x − 3)2 + 5 d) (x − 3)2 − 5

Step-by-step explanation:

(x + 3)² − 5   because :

(x + 3)² − 5 = x² +6x+9 -5 =x²+6x+4

B)

Step-by-step explanation:

the equation is:

we have an equation of the form

where

and we must complete the square to obtain a perfect square binomial,

we must add and substract the following:

which is:

and then the equation becomes:

where the terms are the components of the perfect square binomial:

and thus, the equation now is:

the answer is: B)

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.

isaiah walks 3 miles due north, turns and then 5 miles due east. how far is he from his starting point?

a^2 + b^2 = c^2

let c = distance from starting point.

(3)^2 + (5)^2 = c^2

9 + 25 = c^2

34 = c^2

sqrt{34} = sqrt{c^2}

sqrt{34} = c