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f (g(x))   is just putting  g(x) in for the 'x' if  f(x)

             =  (x-3)^2 + 1

f ( g(x)) =  x^2 -6x  + 10

SW....please provide explanations rather than just posting answers...... no one learns anything when you just puke up answers !    

Please explain how you got that answer........

This function is a concave down parabola so just find the maximum point.

hint: the x value is   -b/(2a)    then sub that in to get the P value

sin $\theta$ = 4/5

cos $\theta$ = 3/5

tan $\theta$ = 4/3

csc $\theta$ = 5/4

sec $\theta$ = 5/3

cot $\theta$ = 3/4

Use pythag theorem to find the hypotenuse  = 15

S O H C A H T O A   

sin = opp / hyp =  12/15

cos = adj / hyp =    9/15

tan = opp/adj = 12/ 9                 can you do the rest ?      

g(x) must be of  degree 7 also to cancel out the f(x) degree 7   ....   like this

-7x⁷ + 3x^3 ......        +         7x⁷  +   5x⁵            =     5x^5  + 3x^3

there are 12 choose 5 = 792 possible ways of getting to point (5,7) from (0,0), and there are 7 choose 3=35 possible ways of getting to point (4,3) from (0,0), so the number of ways to get to (5,7) from (0,0) are

 792-35=$\boxed{757}$

Yes, that is correct.   

The symbol for the determinant is a triangle.

Backslash triangle.  

 \(\triangle \)

re -arrange the given line into y = mx+ b form      m is slope       perpindicular is - 1/m

3x + 2y = 6

2y =  -3x+6

y = -3/2 x  + 3          can you take it from here?

thanks 

XY = 11/2.

h = heather price for a consumer grade mask

r = rosa price = 4 + h

5(4+h) = 7 h

20 + 5h = 7h

h = 10    dollars per consumer grade mask       $ 14 for professional grade mask             

y = ab^x      sub in 0,4

4 = ab⁰

4= a

Now use the second point

324 = 4 b²

b = 9

y = 4 * 9^x

Thanks so much!!!!!!!!!!!!! :)

its 12-p

100*72+2*72

7200+144=$7344$

The standard form for quadratic is $ax^2+bx+c=y$

if $f(-4)=-22, a*(-4)^2+b*(-4)+c=-22$

if $f(-1)=2, a*(-1)^2+b*(-1)+c=2$

if $f(2)=-1, a*(2)^2+b*(-1)+c=-1$

we have a system of three equations, after solving (which you can check), i get

$a=-1, b=3, c=6$

$(-x^2+3x+6)^(16)$
here is the polynomial: 

f(f(x))=(f(x))^2+2f(x)=x^4+4x^3+6x^2+4x

we want to find all numbers where

x^2+2x=x^4+4x^3+6x^2+4x

 or where

x^4+4x^3+5x^2+2x=0=x(x^3+4x^2+5x+2)

we can divide both sides by x, and get

x^3+4x^2+5x+2=0

we can then write

(x^3+3x^2+2x)+1(x^2+3x+2)=x(x^2+3x^2+2x)+1(x^2+3x+2)=(x+1)(x+2)(x+1)

and we know that 0 is also a solution, so all the real numbers possible are

$\boxed{-2,-1,0}$

sigh* keep making those sloppy mistakes ;-;

y+5=1/3 x-4/3

y=1/3 x - 19/3

slope:$\boxed{\frac13}$

point on vertical line: $\boxed{0, -\frac{19}3}$

when x = 0,

y = 1/3 (0)-19/3= -19/3

point on horizontal line: $\boxed{19,0}$

when y=0,

0 = 1/3 x - 19/3

0 = x - 19

x = 19

im just speculating, but if you draw a sector of 90 degrees, won't the answer just be 90-70 =20

tell me if im right or wrong please

We can substitute $x$ for $\frac{18+2y}{5}$. So we have $y=2(\frac{18+2y}{5} -7.$ That simplifies to $y=\frac{36+4y}{5}-7$, or $y+7=\frac{36+4y}{5}.$ We don't like fractions, so therefore, we can multiply the whole equation by $5$, to get $35+5y=36+4y$, or $y=\boxed{1}.$ To solve for $x$, we can substitute: $$x=\frac{18+2y}{5}=\frac{18+2}{5} = \frac{20}{5}=\boxed{4},$$ so $(x,y)=(4,1).$