(08.04 mc) christina bought a yoyo from a company that claims that, with each retraction, the string rolls up by 70% of the original length. she sets up a tape measure and throws the yoyo 3 times. her data are charted below. throw length of string (feet)
1 3
2 2.1
3 1.47

answers:

9.99
9.72
3.24
0.12

9.72

Step-by-step explanation: We can use the equation, a1 - a1(r^n)/1 - r

a1 = first term of sequence (3)

r = common ratio (0.70)

n = position of term in sequence (10)

1. 3 - 3(0.70)^10/1 - 0.70

2. 3 - 3(0.0282475)/0.30

3. 3 - 0.0847426/0.30

4. 2.91526/0.30

5. 9.72 is the sum of the lengths.

15 units use socratic

step-by-step explanation: 15 units

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3