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Phantasy [73]
3 years ago
7

A system of equations is graphed on a coordinate plane. Which coordinates are the best estimate of the solution to the system of

equations? (2, 3) (1, 2) (2, 2) (2, 4)

Mathematics
2 answers:
Keith_Richards [23]3 years ago
6 0

we have

5x-y=9 ---> equation A

2x+6y=13 ---> equation B

we know that

The solution of the system of linear equations is the intersection point both graphs

Multiply the equation A by 6 both sides

6(5x-y)=6*9

30x-6y=54 ------> equation C

Adds equation B and equation C

2x+6y=13\\30x-6y=54\\------- \\2x+30x=13+54 \\32x=67 \\x=67/32 \\x=2.09

Find the value of y

substitute in the equation A

5*2.09-y=9

y=10.47-9=1.47

therefore

the answer is

The best estimate of the solution to the system of equations is the point (2,2)

weqwewe [10]3 years ago
4 0
A solution for a system of equations graph wise, is where they equations intersect or meet.  check the picture below.

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A blind man wanders under a door into an empty room. After running into the walls repeatedly for a while, it stops to think and
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From the side where the man is located in the 10' by 12' rectangular room, we have;

A) 0.046

B) The average time to escape in first attempt is approximately 605.02 seconds

<h3>Which concept can be used to find the odds and time of escape?</h3>

A) From The given diagram, we have;

Width of the door = 10 - 6 - 2 = 2

Therefore, the door is 2 feet wide

Distance, d1, from the man to the side of the door closer to him is given by Pythagorean theorem as follows;

  • d1 = √(6² + 7²) = √(85)

From the furthest side of the door to the man, we have;

  • d2 = √(7² + 8²) = √(113)

According to the law of cosines, we have;

2² = 85+113 - 2×√(85)×√(113) cos(A)

Where angle <em>A </em>is the angle formed by the lines from the man to the closer and farther sides of the door.

2×√(85)×√(113) cos(A) = 85+113 - 2²

A = arccos((85+113 - 2²)/(2×√(85)×√(113)))

A = arccos (194/(2×√(9605)) ≈ 8.213°

The angle of the possible directions in which the man can turn is 180°.

Therefore;

The probability, <em>P(</em><em>E)</em>, of escaping in the first move is therefore;

  • P(E) = 8.213°/180° ≈ 0.046

B) Given that the man escapes in the first move, the shortest and longest distances the man moves are;

d1 = √(85) and d2 = √(113)

Speed of the man, <em>v </em>= 0.5 cm/sec

Therefore by unit conversion function of a graphing calculator;

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The times taken are;

t1 = √(85)/(25/1524) ≈ 562.023

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Average time, <em>t </em>= (t1 + t2)/2

Which gives;

t = (562.023 + 648.014)/2 ≈ 605.02

The average time it takes the man to escape in first move is <em>t </em><em>≈</em> 605.02 seconds.

Learn more about Pythagorean theorem and probability here:

brainly.com/question/27180985

brainly.com/question/654982

brainly.com/question/24756209

#SPJ1

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