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The sum of all possible values of x is 108.

[7!/(5!*2!*2^7)] + [7!/(6!*1!*2^7)] + [7!/(0!*2^7)] =29 / 2^7 = 22.65625%

(a) See the graph below.

(b) g(x) = 1/3*f(2x + 2).

(c) We stretch the graph horiztonally by a factor of 2, then stretch the graph vertically by a factor of 3, then shift down 2 units.

x=1;p=0; y=1;z=1;n=lcm(x, y, z);m=gcd(x, y, z);if(n==630 and m==14, goto loop, goto next);loop:p=p+1;printp," =",x,y,z;next:x++;if(x<200, goto4,0);x=1;y++;if(y<200, goto4, 0);x=1;y=1;z++;if(z<200, goto4,0)

OUTPUT: x = 14,  y = 70,  z = 126. x + y + z =14 + 70 + 126 = 210

The smallest possible value of x + y + z is 162.

The sum of the first five numbers is 65.

343!= 2^337 * 3^169 * 5^83 * 7^57 * 11^33 * 13^28 * 17^21 * 19^18 * 23^14 * 29^11 * 31^11 * 37^9 * 41^8 * 43^7 * 47^7 * 53^6 * 59^5 * 61^5 * 67^5 * 71^4 * 73^4 * 79^4 * 83^4 * 89^3 * 97^3 * 101^3 * 103^3 * 107^3 * 109^3 * 113^3 * 127^2 * 131^2 * 137^2 * 139^2 * 149^2 * 151^2 * 157^2 * 163^2 * 167^2 * 173 * 179 * 181 * 191 * 193 * 197 * 199 * 211 * 223 * 227 * 229 * 233 * 239 * 241 * 251 * 257 * 263 * 269 * 271 * 277 * 281 * 283 * 293 * 307 * 311 * 313 * 317 * 331 * 337.

The largest k = 57 and [343! / 7^57] mod 7 = 6

(3x - 2)(8/x + 1) = 14

x = 3

You can take it from here.

The correct answer is A.

7 correct and 7 incorrect = 14 problems so far        and this is equal to 1/3 of her homework

3 * 14 = 42 problems in all

The points F, G, H, and I all lie on the same line segment, in that order, such that the ratio of FG : GH: HI is equal to 6:4: 1. If FI = 55, find GH.

               F------------------------G----------------H----I

                          ^{30 units                    20 units           5 units}

Ate 3/4 of the number....only 1/4 remains    and the remains = 7

1/4 x   = 7    multily both sides by 4

x = 28

Easy to write in point slope form and conver to requested form:

point 8,-2

y+2 = 3/4 ( x -8)

y+2 = 3/4x - 6

y - 3/4 x = -8      mult iply by 4

4y - 3x = -32

I'm sorry, but it says that's not correct. 

Take the cube root to get x^2y = 36.

x=6,

y=1

The answer is 6

Can I ask you a favor, can you delete some of my posts?

Happens all of the time..... I just leave them (if they are correct ) ....   or you can 'edit' them to say   *** deleted ***    or similar.......   

At 24 mins the will be together again at the starting line.....

   the slower runner will be beginning their 4th mile

     the faster runner will be a mile further and beginning their 5 th mile and will 'lap' the slower......

Maybe  LCM 6, 8 = 24

A face card is a Jack, Queen, or King card, since it has a "face" of a person on it in most decks, hence the name face card.
 

Edit: ElectricPavlov answered while I was typing, is there a way to delete my own posts?

A face card is a card with a 'face' on it ....   a   jack  a queen   a king    (of each suit)

Sub in the point given for x and y

1 - k (4) = -3(-3)

1 - 4k = 9

-4k = 8

k = -2

A = amount of type A                               cost = 4.3 A

B amount of type B =   177-A                  cost  = 5.7 (177-A)                 summed = 877.3

4.3A    +    5.7(177-A)        = 877.3      solve for A     then B = 177- A

Hmm, what's a face card? not too familiar with poker