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f(x)+x^2= (x+1)(x-2)(x+3)(x-4)

f(1)=2*(-1)*4*(-3)-1^2=23

JP

You're welcome. :))

As for the first one, try using mod 7. 

5, 25, 125, 625

5, 4, 6, 2, 3, 1, 5, 4, 6, 2, 3, 1...

So it repeats every 6. 

Can you take it from here?

=^._.^=

For  n ≥  1

5 ^(3*2n) mod  7 =   1

5^(3(2n + 1) )  mod 7  =  6

5^(3 * (2 * 166666 + 1) )  mod 7  =  6

5^ ( 3  * 333333)  mod 7  =  6

5^(999999)  mod 7   =  6

ohhh i didnt think of that! TYSMM

2.) A palindrome is a number that reads the same forward and backward. The largest possible 4-digit palindrome in base 3 can be expressed as a 3-digit palindrome in another base b>2. What is b?

The largest 4 digit palindrome in base 3 is 2222. 

Trying all the bases, in base 6, 2222 (base 3) = 212 (base 6). 

=^._.^=

\({1 \over 4}\)x + 24 = 38

solve for x

cos A  =  sqrt ( 4^2  -1^2) / 4  = sqrt (15)  / 4

sin (2A)  =  2sin A cos A  =   

2 (1/4) sqrt (15)  / 4  =

sqrt (15)  /  8

Key idea:

1) Slope of the perpendicular line is oposite recipocal slope to the other

line equation  y  = mx + b  ,

perpendicular line y = (- 1/m)x  + b.

or

[Formula:  oposite recipocal    m₁ * m₂ = -1].

2) The given line equation  y = (6/5)x -30 .....(1).

slope of the given line = 6/5

Then oposite recipocal to (6/5)  =  negative of *(5/6) = - (5/6)

3) Get the  perpendicuar line equation by using the given point ( x= -6,  y= -7)

4)  y = mx + b    ,  -7 = (-5/6)x +b .....(2)

5) Find the  b value :  where x = 0   in (2)   .  Then  b =  -7.

The perpendicular line y = (oposite recipocal slope) *x + b

Tranformation rule  =   ( 9, 5)

Scale factor  =   2

P  =   

( 3  +  (2/9) (-4 - 3)  ,   6  +  (2/9) ( 3 - 6)  )  =

(3  - 14/9  ,  6 -  6/9)  =

(  27/9 - 14/9 ,  18/3 - 2/3)  =

(13/9 , 16/3)

Glad I could help!

1 sale -> 1

2. sales -> 6

3. sales --> 12

4. sales -> 19

  +5 +6 +7 +8 + 9 + 10 + 11

 1, 6, 12, 19   27   36   46   57

look for a pattern

each increment is incremented by 1

So eight sales is 57 tokens

Oh, sorry!

In the card game Set, each card features a number of shapes, with four attributes:

Number: The number of shapes is 1, 2, or 3.
Color: Each shape is red, purple, or green.
Shape: Each shape is oval, diamond, or squiggle.
Shading: Each shape is hollow, shaded, or solid.

There is exactly one card for each possible combination of attributes.

Is this better?

Thank you!

 ⚡️

Pink area = 79.24483918 m²

I cannot access the file.

Slope of line: (32-17)/(6-3)=15/3=5

In point slope form: y-17=5(x-3)

                               y-17=5x-15

                               y=5x+2

                            f(x)=5x+2 (if you want function notation)

Is there more to this question?

The pic comes AFTER part b  So what are the instructions for part a and part b.

Nowhere does it say that you can only have 3 objects on a card.  Maybe you can have 20 objects or 50 etc

So could you determine the number of possible combinations?

Guest made assumptions when answering, and maybe those assumptions were as intended but mathematics should be precise and this question is pitiful.

z + (1/z) = 1

z^2 + 2 + 1/z^2 = 1^2

z^2 + 1/z^2 = -1

=^._.^=

(1520 - 950) ÷ 950 = 570 ÷ 950

                               = 0.6

                               = 60%

   2 1/2 * 1/2

= 5/2 * 1/2

= 5/4 = 1 1/4