CPhill

(1)    5x

(2)    7x

(3)   30

(4)   7x

(5)   35

(6)    5 

Remainder  = 5

Second one

x^3  - 4x^2  + x  + 6   =  0

Note  that.....using  the Rational Zeros  Theorem that  2  is a root    (a zero)

So   using synthetic division to find the remaing polynomial  we have that

2  [  1     -  4       1        6  ]

                2       -4       -6

      ___________________

       1     -2       -3        0

The remaining polynomial  is     x^2  - 2x  - 3

Set to 0   and we have that

x^2 - 2x  - 3  =  0      factor

(x - 3) ( x + 1)  = 0

Set each factor to 0 and solve for x and the other two zeros are   3   and -1

So....the zeros  are

-1 , 2  and  3

Top shelf  =  (1/3)* 12 + 10   =  4 + 10  =   14 books

Wow, Geno!!!.....that's a very nice proof of this!!!....impressive  !!!!

A "Best Answer" fer shure    !!!!!

1.

Using the Remainder Theorem   we have the following system

a(1)^3  - 6(1)^2  + b(1)  - 5  =  -5  ⇒    a - 6 + b = 0  ⇒    a + b  = 6   (1)

And

a(-2)^3  - 6(-2)^2  + b(-2)  - 5  = -53  ⇒  -8a - 24 - 2b - 5  = -53  ⇒  -8a - 2b  = -24 ⇒

-4a - b = -12    (2)

Add (1)  and (2)  and we have that

-3a = -6

a = 2

And  a + b  = 6   so  b =  4

So

(a, b)  = ( 2 , 4)

See here :

https://web2.0calc.com/questions/anyone-help_3

All sacks of sugar have the same weight. All sacks of flour also have the same weight, but not necessarily the same as the weight of the sacks of sugar. Suppose that two sacks of sugar together with three sacks of flour weigh no more than 40 pounds, and that the weight of a sack of flour is no more than 5 pounds more than the weight of two sacks of sugar. What is the largest possible weight (in pounds) of a sack of flour?

Let the weight of  a sack of sugar  =  W

Let the weight of  a sack of flour  =  2W + 5

And we have that

2W  + 3 (2W + 5)  ≤ 40       simplify

2W  + 6W + 15 ≤  40

8W ≤  25      divide  both sides by  8

W ≤  25 / 8  =   3.125  lbs

So....the max weight for a sack of flour  =  8.125 lbs

6 = -4/9t^2 + 14t  - 0.4     rearrange as

4.9t^2 - 14t + 6.4  = 0       multiply through by 10

49t^2  - 140t + 64  =  0      factor

(7t  - 4) ( 7t - 16)  = 0

Set  each factor to 0  and solve for t  and we have that

t = 4/7  sec    and  t  = 16/7 sec

So.....the time it is above 6 m  is

(16/7) - (4/7)  = 

12/ 7    sec

At 2:00 P.M. a train A leaves a station traveling at 100 mi/hr. At 4:30 P.M. train B leaves the station on a parallel route and traveling at 150 mi/hr. How far away from the station will the second train overtake the first train?

Let  H  be the number  of hours  that  train B travels

And the number of hours that train A travels = 2.5 + H

And   Rate * Time  = Distance Traveled

And when B catches A they will have traveled the same distance....so.....

100 (2.5 + H)  = 150 (H)    simplify

250 + 100H  = 150H          subtract 100H from both 

250  = 50H             divide both sides by  50

5   = H

So.....train B catches A at  4:30 PM + 5 hrs  =    9:30 PM

A fruit basket contains the same number of apples and pears. If Eric eats 5 apples and 1 pear, there will be twice as many pears as apples. How many pears remain in the basket?

Let x be the equal number of apples and pears....so

x - 1         2

____  =   ___              cross-multiply

x  - 5        1

1 ( x - 1)  = 2 ( x - 5)    simplify

x - 1 =  2x  - 10        add 10 to both sides, subtract x from both  sides

9  = x

The number of remaining pears =   x - 1  =  9  - 1   =  8

There are 40 pigs and chickens in a farmyard. Joseph counted 100 legs in all. How many pigs and how many chickens are there?

Let  x  be the number of chickens

Then 40 - x  =  the number of pigs

So

Legs per chicken * number of chickens  +  Legs per p*g * number of pigs  =  100

2x + 4(40 - x)  =  100   simplify

-2x + 160  = 100       subtract 160 from both sides

-2x = -60         divide both sides by -2

x = 30  = number of chickens