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1st graph:odd function

2nd graph:odd function

3rd graph:even function

9)        Part a.   A triangle has integer length sides. If two sides of the triangle are 16 and 21, how many possible lengths are there for the third side?

Either  

Unknown Side +  16 > 21

Unknown Side >  5

or

16 + 21  > Unknown Side

37 > Unknown Side   ⇒    Unknown Side  <  37

So.....the possible integer lengths range from     6 -  36  =   36 - 6 + 1   =  31 possible lengths

If we have only one solution  ...the discriminant will = 0

So    a  =  3 ,  b  =  4    and  c  =  ???

The discriminant is  given by :

b^2  - 4ac          so.... plugging in, we have that

4^2  - 4(3)(c)  =  0

16 -  12c  = 0

16  =  12c       divide both sides by 12

16/12   = c  =    4/3

Here's the graph that confirms one solution :

 https://www.desmos.com/calculator/1ldxjsdqjn

7 - See the answer to this one here:

https://web2.0calc.com/questions/the-distance-from-capital-city-to-little-village-is-660-miles-from-capital-city-to-mytown-is-310-miles-from-mytown-to-yourtown-is-200-miles-and-from

Avg rate of change  7 to 9   =  (5760 - 1920 ) / ( 9 - 7 )  =  1920

Avg  rate of change  from  (945 - 105 )  / ( 6 - 4)  =  420

1920 / 420  ≈   4.57 times as great

All whole numbers  [ there is a possibility that nothing is purchased ]

f(x)  =  -2x^4  + 3x^2

If we just have even powers on a function [ and posssibly, a constant term ] it will always be even

Proof...if even  f(x)  =  f(-x)

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

Nice job, lynx  !!!

1. What is (f−g)(x)?

f(x)=x^4−x^2+9

g(x)=x^3+3x^2+12

f - g   =   [ x^4 - x^2 + 9 ]  - [ x^3 + 3x^2 + 12 ]  =

x^4  -- x^3  - x^2 + 3x^2  + 9  -  12   =

x^4 - x^3   +  2x^2  -  3 

2. What is (f⋅g)(x)?

f(x)=x^2+2x−6

g(x)=x^4+3

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

         x^2  +  2x  + 6        multiply each term on top by 3  and then by x^4      

x                 x^4  + 3

       ____________

         3x^2  + 6x + 18

+    x^6  + 2x^5 + 6x^4

     ________________

x^6  + 2x^5 + 6x^4  + 3x^2 + 6x + 18  

3. What is (f+g)(x)?

f(x)=x^3−x

g(x)=x^3+2x^2−10   

f +  g   =   [ x^3 - x ]  +  [ x^3 + 2x^2  - 10  ]  =   2x^3 + 2x^2 - x  - 10

Do you mean this ???

ax^2 + 8x + c   =  0    ???   if so

If we have only one solution, the discriminant will = 0   .....so.....

8^2  - 4ac  = 0            and      a + c  =  10   ⇒    c  =  10 - a

So....substituting, we have

8^2 - 4a(10 - a)   = 0

8^2  - 40a + 4a^2  =  0

4a^2 - 40a +  64  =  0         divide through by 4

a^2  - 10a  + 16   =  0      factor

(a - 8) ( a - 2)  =  0

The solutions are a  = 8    or a  = 2

Note that if a  = 8, then c  = 2     or

If a  = 2  then c  = 8

But a > c  so     (a, c)   =   (  8, 2 )

Check the ggraph here that only one zero exists  at  x  = -1/2 :

https://www.desmos.com/calculator/idsuikzats

Probability that she walks  = 0.65

Probability that she cycles  = 0.35

Probability that  she is not late when she walks  = ( 1 - 0.4)  =  0.6

Probability  that she is not late when she cycles  = ( 1 - 0.1)  = 0.9

Probability that she is not late  =

(.65) (.6)  + (.35)(.9)   =   .705  =  70.5%

The diagonal of the square will be its greatest dimension....itf this is less than the diameter of the circle, it will fit

The sides of the square are the legs of a right triangle....so...by Pythagoras

Diagonal  = √ [ 5^2 + 5^2 ]  =  √50  ≈   7.07 units

So...it fits  !!!!

We can write this form, first

Since   x = 2  and x  = 4 are zeroes we know that it will factor as

y  =  a ( x - 2) (x - 4)     so.....when x  = 3  , y = 6    and we can solve for "a"

6 = a(3 - 2) ( 3 - 4)

6  = -1 a   ⇒     a = -6

So.....the fumction is

y  = -6 ( x - 2)(x - 4)

y  =  -6 (x^2 - 6x  + 8)

y = -6x^2 +36x - 48

Here's a graph to confirm this :

https://www.desmos.com/calculator/q6hbimtgh1

We need to find AC...it will be the hypotenuse of right triangle ABC

So we have

AC  =  √ [ AB^2 + BC^2  ] =  √ [ 5^2 + 9^2  ] =  √ [ 25 + 81  ] = √ 106

So....the area of the square is just the square of this  = 106 units^2

practice algebra qusetions on websites like:

corbettmaths

mathsgenie

practice algebra the day before your test so your brain functions quickly and does not go blank.

practice past papers on algebra

0.004444444.........etc.    Take the reciprocal of of it:

225 = 1/225

1.If it is outside the brackets then shift it down. f(x)-4

If it is inside the brackets then shift it right. f(x-4)

0.14242424242........etc.  Take the reciprocal of it:

7.021276595744680851063829787234 - 7 Take the reciprocal of the fraction:

47 - This is the numerator.

47 x 7.021276595744680851063829787234

330 - This is the denominator: So the fraction is:

47 / 330

See ya later

i think you have to have a account for that 

.004444......      = x

100x  = .4444....

1000x     =  4.444.....

1000x - 100x  = 4.0

900x = 4.0

x = 4/900 = 1 /225

Surface area of a sphere:  4 pi  r^2

64 pi  cm^2  =  4 pi r^2

Yields  r=  4

Volume of a sphere  4/3 pi r^3

    4/3 pi 4^3  = 268.08 cm^3

The chicken crossed the road to get to the ugly ogres house

knock knock

Whos there?

The chicken!!!!!

SA=64π

64π/4π=16

√16=4

r=4

v=4/3πr³

v=4/3π*4³

v=4/3π*64

v=85.3πcm³