1. scientists estimate the rate of the wildebeest running at full speed to be 66 feet per second. write a function rule to describe the relationship between the time, t, and the distance ,d, a wildebeest travels when running at full speed.(1 point)

a. t = 66d
b. 66 = d • t
c. d = 66/t
d. d = 66t

2. identify the function rule shown in the table. (1 point)

n 3 4 5 6
y 2 1 0 -1

a. y = 2 + n
b. y = 5n
c. y = 5 - n
d. not enough information

3. rico made a function table to illustrate the rate he charges for mowing lawns. complete the table. then write a function rule for the function. (1 point) ( ) = blank

hours (h) 1 2 3 4 5
earnings (e) ( ) ( ) ( ) $22.00 $27.50

a. $5.75, $11.50, $17.25; e = 5.75h
b. $6.00, $12.00, $18.00; e = 6.00h
c. $5.25, $10.50, $15.75; e = 5.25h
d. $5.50, $11.00, $16.50; e = 5.50h

4. a dvd store charges $4.70 for each day, d, a dvd is rented. the store also gives you a dollar off if the dvd is returned before 5 days.

1. write a rule to represent the rental charges c.
2. how much will you pay if you return the dvd after 4 days? 7 days?

a. c = 4.70d; $18.00, $32.90
b. if d ≤ 5 then c = 4.70d, if d > 5 then c = 4.70d + 1; $17.80, $31.90
c. if d ≥ 5 then c = 4.70, if d < 5 then c = 4.70d - 1; $17.80, $32.90
d. if d ≤ then c = 4.70d, if d > 5 then c = 4.70d - 1; 18.80, $31.90

5. write a rule for the function represented by the table. (1 point)
input (x) 0 1 2 3 4
output (y) 3 6 9 12 15

a. y = 3x
b. y = 3x + 3
c. y = 5x + 1
d. y = x + 5

6. (i know the answer)

7. use the function rule to complete the table -10x + y = 4 (3 points)
( ) = blank

x -2 -1 0 1 2
y ( ) ( ) ( ) ( ) ( )

8. find the function rule. (2 points)

x -2 -1 0 1 2
y 9 4 -1 -6 -11

1. d. d = 66t

The maximum speed of the wildebeest is v=66 ft/s. Speed is defined as the ratio between the distance covered (d) and the time taken (t):

Re-arranging the formula, we get

And substituting v=66 ft/s, we find

2. c. y = 5 - n

In fact, we can check that this rule satisfies all the numbers of the sequence:

n=3 --> y = 5 - 3 = 2

n=4 --> y = 5 - 4 = 1

n=5 --> y = 5 - 5 = 0

n=6 --> y = 5 - 6 = -1

3. d. $5.50, $11.00, $16.50; E = 5.50h

In fact, if we use the rule E=5.50 h, we see that the table is completed as follows:

h=1 --> E=(5.50)(1 h)=5.50$

h=2 --> E=(5.50)(2 h)=11.00 $

h=3 --> E=(5.50)(3 h)=16.50$

h=4 --> E=(5.50)(4 h)=22.00$

h=5 --> E=(5.50)(5 h)=27.50$

4. c. if d ≥ 5 then C = 4.70d, if d < 5 then C = 4.70d - 1; $17.80, $32.90

If the number of days is more than 5, the cost is 4.70$ per day, therefore c=4.70d (where d is the number of days); if the number of days is less than 5, one dollar is returned, so the cost will be C=4.70d-1. By applying this rule, we can calculate the rental cost after d=4 days and d=7 days:

- d=4 --> c=4.70*4-1=17.80$

- d=7 --> c=4.70*7=32.90$

5. b. y = 3x + 3

In fact, we can check this is the correct rule by substituting the numbers:

x=0 --> y=3*0+3=3

x=1 --> y=3*1+3=6

x=2 --> y=3*2+3=9

x=3 --> y=3*3+3=12

x=4 --> y=3*4+3=15

7. x -2 -1 0 1 2

y (-16 ) (-6 ) (4 ) (14 ) (24 )

The rule we have to apply is:

-10x + y = 4

Re-arranging it, we can solve for y:

y = 10x + 4

So, let's substitute the different values of x:

x=-2 --> 10*(-2)+4=-20+4= -16

x=-1 --> 10*(-1)+4=-10+4= -6

x=0 --> 10*0+4= 4

x=1 --> 10*1+4=10+4= 14

x=2 --> 10*2 +4 =20+4 = 24

8. y = -5x - 1

In fact, if substitute the different values of x given by the problem, we find:

x = -2 --> y = -5*(-2) -1= 10 -1 = 9

x = -1 --> y = -5*(-1) -1 = 5 -1 = 4

x = 0 --> y = -5*0 -1 = -1

x = 1 --> y = -5*1 - 1 = -6

x = 2 --> y = -5*2 -1 = -11

1.4

2.3

step-by-step explanation:

the formula for the constant of variation is

y= kx

divide each side by x

y/x =kx/x

y/x =k

we know a and y

1.   y/x = k

4/1 =4

check the other values to make sure they are the same

8/2 = 4   12/3 =4   and 16/4 =4  

the constant of variation is 4

2.   y/x = k

3/1 =3

check the other values to make sure they are the same

6/2 = 3   9/3 =3   and 12/4 =3  

the constant of variation is 3

ye

step-by-step explanation: