HELP ASAP!! 100 POINTS!! describe how you would plot the point (-4, 3)
2 answers:
Answer:
Step-by-step explanation:
in a coordinate pair (x,y) the first point is x
it goes on the horizontal axis ( left to right)
if it is positive it goes to the right of the (0,0) point or the origin
if it is negative it goes to the left of the origin
since x=-4 it will go 4 units to the left
now we look at the y coordinate, we will move up or down from the -4 point
if it is positive, we will move up
if it is negative, we will move down
since y= 3 is positive, we will move up 3 units
draw a dot and label it (-4,3)
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<h2>SOLVING</h2>
Find the point-slope equation of the line, with the info given
Formula used,
| result
A geometry program can show you the total displacement is about 10.14 miles.
_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°
_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest
Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.
Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles
_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°
_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest
Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.
Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles
Answer: A. 85.7
Step-by-step explanation:
Given : Two sections of a class took the same quiz.
Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90.
We know that ,
Then , for section A :
Similarly in Section B,
Total scores = Sum of scores in sec A+Sum of scores in sec B
=1200+1800=3000
Total students = Students in sec A +Students in sec B
=15+20=35
Now , the mean score for all of the students on the quiz =
Hence, the approximate mean score for all of the students on the quiz = 85.7
Thus , the correct answer is option A. 85.7.