For Flight Distances A cross country coach recorded the
Math Practices and
Problem Solving
Lesson 12-4
Critique Reasoning
..
reams practice runs and made the line plot below.
The coach had each runner analyze the line plot
explain whether you think each runner's reasoning
and write an observation. Read the statements and
33
36
Feel
makes
sense,
I can...
September Practice Runs
critique the reasoning of others by
using what I know about line plots
and fractions
se How could you estimate
162 + 192
X
Mathematical Practices MP3. Also MR1,
MP2, MP4, MP
Content Standards 5.MD. B.2, 5. NFA 2
S. NF. B.6
1 lis 1 2 2 2 2 3
Distance (miles)
Multiplication
Natalie
The foam ron 8 diffcnt Times
each time for a different distance
Olivia
The distance we can the
ut of ten was 3 miles.
Michelle
The farm tan different distances
an affordays. We wually man
fr 2 miles or more
Thinking Habits
Be a good thinker!
These questions can help you.
• What questions can
I ask to understand
other people's thinking?
• Are there mistakes in
other people's thinking?
. Can I improve other
people's thinking?
Peter
16 X 6.5 = 104
20 X 6.75 = 135
Each day the team ran the
same distance or a little
for ther than the day before.
I’

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

3100

step-by-step explanation: