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Inga [223]
3 years ago
12

a line segment has end points (-5, 7) and (4,-3) find the inverse of the line segment and graph both the segment and its inverse

.

Mathematics
1 answer:
Romashka-Z-Leto [24]3 years ago
5 0
Answer

See graph

Step-by-step explanation

The given line segment passes through the point (-5,7) and  (4,-3).

We plot this points and draw a straight line to them to obtain the blue line as shown in the

attachment.

The slope of this line segment is given by the formula

m=\frac{y_2-y_1}{x_2-x_1}

This implies that,

m=\frac{7--3}{-5-4}

m=-\frac{10}{9}

The equation of this line is given by the formula,

y-y_1=m(x-x_1)

y+3=-\frac{10}{9}(x-4)

9y+27=-10(x-4)

9y+27=-10x+40

9y=-10x+13

We now find the inverse by interchanging x and y.

9x=-10y+13

We now make y the subject,

9x-13=-10y

y=-\frac{9}{10}x+\frac{13}{10}

We now plot some points.

When

x=7

y=-\frac{9}{10}\times 7+\frac{13}{10}

y=-\frac{50}{10}=-5

This gives the ordered pair

(7,-5)

Also when

x=-3

y=-\frac{9}{10}\times -3+\frac{13}{10}

y=\frac{40}{10}=4

This gives the ordered pairs,

(-3,4)

We plot these points too and draw a straight line through them to get the red line in the attachment.

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A test has 50 questions. each right answer is worth 2 points; each wrong answer deducts 0.5 points; blank answers are not counte
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ANSWER: There are 2 blank answers

 

EXPLANATION

 

Let

The number of right answers be ‘r’

The number of wrong answers be ‘w’

The number of blank answers be ‘b’

 

r + w + b = 50

This means r + w ≤ 50

 

Then we know,

Right answers = 2 marks

Wrong answers = -0.5 mark

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2r – 0.5w = 88.5

2r = 88.5 + 0.5w                               … (Equation I)                   

 

Since the score as .5, we know that there is at least one wrong answer, and the number of wrong answers is an odd number.

 

Since the score is 88.5, and each right answer gives 2 marks

There are at more than 44 (i.e. 88/2) right answers

 

Since r + w ≤ 50, and possible values of w are odd numbers

If r = 45, Possible values of w are 1, 3, and 5

If r = 46, Possible values of w are 1, 3

If r = 47, Possible values of w are 1, 3

If r = 48, The only possible value of w is 1

If r = 49,The only possible value of w is 1

 

 

Since 2r = 88.5 + 0.5w  (Equation I)

We test for possible values:

 

If r = 45

2r = 88.5 + 0.5w  

2(45) = 88.5 + 0.5w  

90 = 88.5 + 0.5w

0.5w = 90 – 88.5

0.5w = 1.5

w = 3

 

So,

If there are 45 right answers

There are 3 wrong answers

r + w + b = 50

45 + 3 + b = 50

48 + b = 50

b = 50 – 48

b = 2

Then, there are 2 blank answers.

 

If r = 46

2r = 88.5 + 0.5w

2(46) = 88.5 + 0.5w

92 = 88.5 + 0.5w

0.5w = 92 – 88.5

0.5w = 3.5

w = 7

 

So,

If there are 46 right answers

There are 7 wrong answers

We know that r + w ≤ 50

46 + 7 = 53

So 46 and higher numbers are not possible solutions.

 

The only possible solution is:

There are 45 right answers

There are 3 wrong answers

<span>There are 2 blank answers</span>

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2x = 4

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x = 2

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