Every jump a game piece makes measures 8/9 . The piece starts at point A = 3 and jumps to the right. As soon as the piece jumps over B = 60, it switches direction and jumps to the left. The piece then stops at point C = −21. How many jumps did the game piece take?

  157

Step-by-step explanation:

The number of jumps (p) in the positive direction will be the smallest integer value that satisfies ...

  3 + 8/9p ≥ 60

  8/9p ≥ 57 . . . . . . subtract 3

  p ≥ 57(9/8)

  p ≥ 64 1/8

The desired solution is p = 65. Then the final location in the positive direction is ...

  3 + 65(8/9) = 60 7/9

__

From there to the final position of -21 is a distance of ...

  60 7/9 -(-21) = 81 7/9

The number of moves in the negative direction (n) is then ...

  n = (81 7/9)/(8/9) = (736/9)/(8/9) = 736/8 = 92

So, the total number of moves is the number the positive direction added to the number in the negative direction:

  moves = p + n = 65 + 92 = 157

The game piece took 157 jumps.

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.  

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!