F(x)=x^2+6 and g(x)=2x-1 g[f(x)]= a.4x^2-4x+7 b.2x^2+11 c.2x^2+5

g( f(x) ) = 2x^2 + 11 (Answer choice B)

Step-by-step explanation:

g( f(x) ) involves using the function f(x) = x^2 + 6 as the input to g(x).

Here, g(x) = 2x - 1.  Replace the x in g(x) by "f(x)" and the x in 2x - 1 by x^2 + 6.  Then we have g( f(x) ) = 2[x^2 + 6] -1.  This can be simplified, as follows:

                                     = 2x^2 + 12 - 1, or 2x^2 + 11.  This is answer choice B.

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.