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Gre4nikov [31]
2 years ago
8

Drag the tiles to the correct boxes to complete the pairs. Match the systems of equations with their solutions.

Mathematics
1 answer:
Oksanka [162]2 years ago
4 0

Answer:

See explanation for matching pairs

Step-by-step explanation:

Equations

(1)

x - y = 25

2x + 3y = 180  

(2)

2x - 3y = -5

11x + y = 550  

(3)

x - y = 19

-12x + y = 168

Solutions

(-17,-36)

(47, 33)

(51, 26)

Required

Match equations with solutions

(1) x - y = 25 and 2x + 3y = 180

Make x the subject in: x - y = 25

x = 25 + y

Substitute x = 25 + y in 2x + 3y = 180

2(25 + y) + 3y = 180

50 + 2y + 3y = 180

50 + 5y = 180

Collect like terms

5y = 180-50

5y = 130

Solve for y

y =26

Recall that: x = 25 + y

x = 25 + 26

x = 51

So:

(x,y) = (51,26)

(2)  2x - 3y = -5 and 11x + y = 550

Make y the subject in 11x + y = 550

y = 550 - 11x

Substitute y = 550 - 11x in 2x - 3y = -5

2x - 3(550 - 11x) = -5

2x - 1650 + 33x = -5

Collect like terms

2x  + 33x = -5+1650

35x = 1645

Solve for x

x = 47

Solve for y in y = 550 - 11x

y = 550 - 11 * 47

y = 550 - 517

y = 33

So:

(x,y) = (47,33)

(3)

x - y = 19  and -12x + y = 168

Make y the subject in -12x + y = 168

y = 168 + 12x

Substitute y = 168 + 12x in x - y = 19

x - 168 - 12x = 19

Collect like terms

x -12x = 168 + 19

-11x = 187

Solve for x

x = -17

Solve for y in y = 168 + 12x

y =168-12 *17

y =-36

So:

(x,y) = (-17,-36)

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Answer:

The answer to your question is   Tree's height = 26.8 ft  

Step-by-step explanation:

Data

Person                         Tree

height = 6 ft                 height = x

shadow = 8.5 ft            shadow = 38 ft

Process

1.- Use the Thales' theorem to solve this problem

   Person's height/ Person's shadow = Tree´s height / Tree's shadow

Solve for Tree's height

   Tree's height = Person's height x Tree's shadow / Person's shadow

Substitution

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Simplification

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Result

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The population of Minnesota in thousands, t years since 2000 can be represented by P=37t+4934.
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Answer(A):

Given that the population of Minnesota in thousands, t years since 2000 can be represented by equation:

P=37t+4934

P-intercept means value of P when t=0

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Answer(B):

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divide by 37

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