Helpppo:) please

32

Step-by-step explanation:

Step 1: Define

f(x) = 3x² - 5x - 4

g(x) = -4x - 12

Step 2: Find f(g(x))

f(g(x)) = 3(-4x - 12)² - 5(-4x - 12) - 4

f(g(x)) = 3(16x² + 96x + 144) + 20x + 60 + 4

f(g(x)) = 48x² + 288x + 432 + 20x + 64

f(g(x)) = 48x² + 308x + 496

Step 3: Find f(g(-4))

f(g(-4)) = 48(-4)² + 308(-4) + 496

f(g(-4)) = 48(16) - 1232 + 496

f(g(-4)) = 768 - 736

f(g(-4)) = 32

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1