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NARA [144]
3 years ago
6

Solve by substitution x-y=-11 y+7=-2x

Mathematics
1 answer:
Bess [88]3 years ago
4 0

x - y = - 11   .............( 1 )

y + 7 = - 2x ...............( 2 )

from equation ( 1 )

x - y = - 11

x   = -11 + y  ...........( 3)      

putting x in equation  ( 2 )

y + 7 = - 2 x  

y  + 7 = -2 ( -11 + y )             y + 7 = 22 - 2 y                       y + 2 y =22 - 7            

3 y = 15                  y = 15 / 3

putting value of y in equation 3

x   = -11+ ( 13 /5 )                       x = -33 /3 + 15 / 3         ( l.c.m)

x  = -17 / 5                      

check      

x = -11 + y

- 17 / 5 = -11 + 13 / 5

-17 /5   = -17 / 5

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Number of ways to choose colors = ^7C_3\times\ ^5C_2

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If RSTU is a rhombus, find the measure of angle RUT.
Schach [20]

<u>Finding x:</u>

We know that the diagonals of a rhombus bisect its angles

So, since US is a diagonal of the given rhombus:

∠RUS = ∠TUS

10x - 23 = 3x + 19                      [replacing the given values of the angles]

7x - 23 = 19                                [subtracting 3x from both sides]

7x = 42                                       [adding 23 on both sides]

x = 6                                           [dividing both sides by 7]

<u>Finding ∠RUT:</u>

We can see that:

∠RUT = ∠RUS + ∠TUS

<em>Since we are given the values of ∠RUS and ∠TUS:</em>

∠RUT = (10x - 23) + (3x + 19)

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<em>We know that x = 6:</em>

∠RUT = 13(6)-  4

∠RUT = 74°

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