Carol is planning a trip to south africa. she plans to spend ten nights there, so she is investigating her options for lodging. she has made arrangements to stay at least part of the time at a hostel, which is her cheapest option. however, she would like to spend as many nights as she can in a private hotel. the hostel costs r 34 (34 rands) per night, and the hotel costs r 55. if carol has a budget of 430 rands for lodging, how many nights can she afford to stay in the private hotel? a. six b. five c. four d. three

Step by step explanation:

The total number of nights to be spent are = 10

Let the number of nights to be spent in hostel be = h

So, nights to be spent in a hotel will be = 10-h

Given is , Carol has a budget of 430 rands for lodging, and hostel costs R34 per night and hotel costs R55 per night, so equation becomes.

Now checking the number of days by putting in equation:

If hostel = 5 nights and hotel = 5 nights

34(5) + 55(5) ≤ 430

170 + 275 ≤ 430

445 ≤ 430 (this is not possible.)

If hostel = 6 nights and hotel = 4 nights

34(6) + 55(4) ≤ 430

204 + 220 ≤ 430

424 ≤ 430  (This is correct)

Hence, Carol can spend a maximum of 4 nights in the private hotel.

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0