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We have  the  equation

y = (-3/7)x  +  13                     

To  find  the x intercept , set  y  =  0   and  solve  for x

0   =   (-3/7)x  + 13

-13  = (-3/7) x

(-13)  /( -3/7)  = x   

13  *  7  / 3    =  x

91/3   =   x intercept

thank you so much! that's correct 

Strictly  by   inspection

2^1  + 2^3  +  2^5   =

2     +     8  +    32   = 

       42

So

1/2  +   1/3   +  1/5  =

15/30  +  10/30   +  6/30   =

31  / 30

I know  everything except for  f  and  g

a. domain =  0- 10  inclusive

b. range =     2 - 8   inclusive

c .  It is a  function .....any  vertical line drawn  will cut  the  graph only once

d .   Increasing on   (0,2)   and   (5,7)

e. Decreasing on  (4,5)  and (7,8)

h.   x intercept.....there  aren't  any

i. y intercept =     2

Assuming the  first digit isn't  0  .......

Number of  5  digit integers =    (99999  - 10000 + 1)  =  90000

P( remembering)    =    1  / 90000

Incorrect   .......the  answer  should  be

10  * 9  *  8  *  7   * 6     =   30,240       

P (remembering  )   =    1 /30240

THX to EP  for pointing out my silly  error   ( he assumes  that  the combo CAN start with 0  )

Set  the equations     =

-x^2   -x  +  1  =   2x^2   -3x        rearrange as

3x^2  - 2x  -  1     =   0              factor  as

(3x  + 1)  ( x - 1)    =   0

Setting both factors to 0  and solving  for  x  produces

 x =  a =  -1/3           x  =   c   =  1

So

c   -  a    =

1 - ( -1/3)   =

4 / 3

57 hair   and   14 nails   is a possibility      71 appts total

  or maybe 46 hair and  32 nails          78 appts

             or maybe   35 hair      50 nails        85 appts

                  etc ......

Need more info for a specific answer

Rewrite as

2x^2  +  10x   +  2y^2  - 6y   =    180                divide   through  by 2

x^2  +  5x   +  y^2   -  3y  =   90              complete  the square on  x and y

x^2  + 5x  +  25/4   +  y^2  - 3y  + 9/4   =  90  +  25/4  +  9/4

(x  + 5/2)^2  +  ( y  - 3/2)^2   =  90  +  17/2

(x + 5/2)^2  +  ( y - 3/2)^2   =  98.5                       {   98.5  = r^2    }

So....the  area  =

98.5 pi

Very nice, Bginner   !!!!

Here's  my attempt  :

Total  five -digit  integers =    (99999 - 10000  + 1)  =  90000

The ones  that   DON'T   contain  any of these  digits =

(6) (7) (7) (7) (7)   =  14406

Total  that DO contain    at least  one 2 or one 3 or one 4   among their  digits  =

90000  -  14406  =

75594

Note that $\sqrt{x^2}$ is equivalent to $|x|$ so the question asks how many real $x$ makes $\sqrt{1200-|x|}$ an integer.  Each such $x$ satisfies $1200 - |x| \ge 0$, and $1200-|x|$ must be a square number.  Since $34^2 = 1156$ and $35^2  = 1225$, the possible values of $1200-|x|$ are $0^2, 1^2, 2^2, \ldots, 34^2$.  Each of these square numbers gives exactly 2 values for $x$, one positive and one negative.   E.g.
$$0=1200-|1200|=1200-|-1200|$$
and
$$34^2=1200-|44|=1200-|-44|.$$
So the answer is $35*2=70$.

Since median and mode are both forms of average, I'm assuming that where you used the word average you were referring to the mean. In which case:

Thank you, CPhill !

THX, catmg   !!!

are you sure? 

The path must contain 8 rights, and 2 ups in some order. 

10!/8!/2! = 45

=^._.^=

Very nice , heureka   !!!!!

Edit:

My bad, I read all equations as x + y + z. :((

CPhill did a great job answering. :))

=^._.^=

https://web2.0calc.com/questions/i-am-following-ep-s-suggestion

....with slightly different angle ....

(2x + 10)  ( x + 3)   <  (3x + 9)(x + 5)        simplify

2x^2 + 16x   +  30  <  3x^2 + 24x  + 45    rewrite  as

x^2  + 8x  + 15  >  0         factor

(x + 3) ( x + 5)  >   0

This  will be  true  when   x <   -5     and   x >  - 3

So  the solution is

(inf, -5)  U  ( -3, inf)   

Find the value of $a_2 + a_4 + \ldots + a_{98}$

if $a_1, a_2, a_3, \ldots$ is an arithmetic progression with common difference 1

and $a_1 + a_2 + ... + a_{98} = 99$.

$\begin{array}{|rcll|} \hline a_1 + a_2 + ... + a_{98} &=& 99 \\\\ \left(\dfrac{a_1 + a_{98}}{2}\right)*98 &=& 99 \\ \mathbf{a_1 + a_{98}} &=& \mathbf{\dfrac{ 2*99 }{98} } \\ \hline \end{array}$

$\text{Let $x=a_2 + a_4 + \ldots + a_{98}$}\\ \begin{array}{|rcll|} \hline x &=& a_2 + a_4 + \ldots + a_{98} \\\\\ x &=& \left(\dfrac{a_2 + a_{98}}{2}\right)*\dfrac{98}{2} \quad | \quad a_2 = a_1 +1 \\\\ x &=& \left(\dfrac{1 + a_1 + a_{98}}{2}\right)*\dfrac{98}{2} \\\\ x &=& (1 + a_1 + a_{98})*\dfrac{98}{4} \\\\ x &=& \dfrac{98}{4} + (a_1 + a_{98})*\dfrac{98}{4} \quad | \quad \mathbf{a_1 + a_{98}=\dfrac{ 2*99 }{98} } \\\\ x &=& \dfrac{98}{4} + \dfrac{ 2*99 }{98}*\dfrac{98}{4} \\\\ x &=& \dfrac{98}{4} + \dfrac{ 2*99 }{4} \\\\ x &=& \dfrac{98+2*99}{4} \\\\ \mathbf{x} &=& \mathbf{74} \\ \hline \end{array}$

$a_2 + a_4 + \ldots + a_{98} = \mathbf{74}$

On Monday, there would be 24/3*4 adult cats which is 32 adult cats. 

Therefore, the difference between 34 and 32 is 2

Well, you know that distance = rate/time so rate = distance/time so therefore, 

201/3 = 67

w + x + y = -2    ⇒  x + y =  -2 - w      (1)

w + x + z = 4     ⇒  x +  z  = 4  - w     (2)

w + y + z = 29   ⇒  y + z  = 29 - w      (3)

x + y + z = 22   ⇒  2x  + 2y + 2z  =  44  (4)

Add (1)  , (2) , (3)

2x  + 2y  + 2z  =  31  - 3w      (5)

Sub (5)  into (4)

31  - 3w   =  44

-3w =  44 - 31

-3w  =   13

w  = -13/3

And  using (1)

x + y  =   -2 - (-13/3)   =   7/3

x + y +  z  =  22

(7/3) + z  =  22

z = 22 - 7/3  =  59/3

So

xz +  yz  =

(x + y)z  =

(7/3) (59/3)   =  

413 /  9