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Not too difficult....we just need to know what function to use

f (x) = f(-10)

So x must be -10

Notice that the first function is the one to use if x ≤  -4

f(-10) =   l -10 + 6 l  =  l - 4 l   =   4

So....graph the point (-10, 4)

Second one...it looks hard....but isn't

If x  ≥5....then the output  is -5

So f(444)....x = 444.....and this is  ≥ 5

So....f(444) = -5

Graph the point  (444, -5)    (you need a larger graph  !!!)

Last one

f(-1)

x = -1     so....the second function because this value falls between  -4 and 5

So  we use  x + 2

(-1) + 2  =   1

So graph the point (-1, 1)

[13t^2 - 34t + 12]   / [ 3t - 2]   + 5t  = 6t - 1       subtract 5t from both sides

[ 13t^2 - 34t + 12 ] / [ 3t - 2 ]  = t - 1            multiply both sides by  3t - 2

13t^2 - 34t + 12  =  (3t - 2) ( t - 1)

13t^2 - 34t + 12 = 3 t^2 - 5t + 2      rearrange as

10t^2 - 29t + 10  =  0

(2t - 5) ( 5t - 2)  = 0

Set both factors to 0  and solve for t  and we have that

t = 5/2      or     t =  2/5

So....t = 5/2 is the max value of t

Thank you!

In the form  Ax + By = -C

The slope of the line = -A/B

So

A = 2   B = 4

And  the slope is

- A / B =  -2 /4 = - 1/2

If we inscribed the hexagonal bsse in a circle, AD would be a diameter of 8  and the  radius of this circle = side of the hexagon = half of this  = 4  units

The height   of the pryramid  can be found as

sqrt (8^2 - 4^2) =  sqrt (64 - 16) = sqrt (48) = 4sqrt (3)

The area of the base is just the area of the hexagon =   area of 6 equilateral triangles with sides of 4

So the base area =

6(1/2) (4)^2 sqrt (3) / 2  =    

24sqrt (3) units ^2

So...the volume of the pyramid =

(1/3) base area * height  =

(1/3) (24 sqrt (3) ) * (4 sqrt (3))  =

(1/3) (96) (3) =

96 units^3

Solve for t:
5 t + (13 t^2 - 34 t + 12)/(3 t - 2) = 6 t - 1

Bring 5 t + (13 t^2 - 34 t + 12)/(3 t - 2) together using the common denominator 3 t - 2:
(4 (7 t^2 - 11 t + 3))/(3 t - 2) = 6 t - 1

Multiply both sides by 3 t - 2:
4 (7 t^2 - 11 t + 3) = 2 - 3 t + 6 t (3 t - 2)

Expand out terms of the left hand side:
28 t^2 - 44 t + 12 = 2 - 3 t + 6 t (3 t - 2)

Expand out terms of the right hand side:
28 t^2 - 44 t + 12 = 18 t^2 - 15 t + 2

Subtract 18 t^2 - 15 t + 2 from both sides:
10 t^2 - 29 t + 10 = 0

The left hand side factors into a product with two terms:
(2 t - 5) (5 t - 2) = 0

Split into two equations:
2 t - 5 = 0 or 5 t - 2 = 0

Add 5 to both sides:
2 t = 5 or 5 t - 2 = 0

Divide both sides by 2:
t = 5/2 or 5 t - 2 = 0

Add 2 to both sides:
t = 5/2 or 5 t = 2

Divide both sides by 5:
t = 5/2                         or                           t = 2/5

its is -1/2

THANK YOU SO MUCH! 
U SAVED MY HOMEWORK THX

umm...if u did not care u did not have to anwser so rudely 

idc!

t=97

Second one

Note that the angle supplemental to the 78°  angle is 180 - 78  =  102°

Now....we can applty the Tangent-Chord Theorem that says that

An Angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc

In simple terms :

The measure of the of the angle that measures 102°  = (1/2) (23x - 3)°

So we have

102 = (1/2) (23x - 3)    multiply both sides by 2

204  = 23x - 3

207 = 23x

9 = x

First one  ....this is using the Intercepting Chords Theorem

It says that.....

The measure of the angle inside the circle = (1/2)(sum of the two arcs)

So we have

(5x - 7) = (1/2)(119 + 27)    multiply through by 2

2 (5x - 7) = 146    simplify

10x - 14  =  146       add 14 to both sides

10x =  160

 x =  16

This is all very true!

No prob....easy to make mistakes on here.....

Hint:  Use the expansion of  \((x+\frac{1}{x})^3\)

Then it will all fall out.  If it doesn't at first then you may need to think a little harder.

Please no one answer over me, this should be a teaching site, which includes hints.   

(this site should not be a cheat site)

Yes, thank you! 

Tertre probably just made a typo...it should be

6! / (2! * 3! ) =    720 / (2 * 6)  =  720 / 12  =    60  ways

For some reason it says that #1 is wrong? 

Thanks, EW....here's a way of obtaining his answer

% decrease =   [ original price - sales price ] / original price X 100% =

[225 - 195 ] 225  x 100%

[ 30 ] / 225 x 100%

[ 30 * 100 / 225]   %  =

3000/225 % ≈  13.33% =  13% decrease

1. 2 B's and 2 C's repeat, so the total number of possible ways to arrange it is \(\frac{6!}{2!*3!}=\boxed{60}.\)

2. I think the answer is \(\binom{5}{1}*\binom{6}{1}*\binom{7}{2}=\boxed{630}. \)