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EastWind [94]
2 years ago
7

The value of X in the figure ABCD witch is a rhombus

Mathematics
1 answer:
NeX [460]2 years ago
5 0

Answer:

  x = 10°

Step-by-step explanation:

The diagonals of a rhombus divide the figure into congruent right triangles. That means the two marked acute angles are complementary.

__

<h3>solve for x</h3>

Complementary angles total 90°, so the relation we can use to find x is ...

  (3x -13) +(8x -7) = 90

  11x = 110 . . . . . . . . . add 20

  x = 10 . . . . . . . . . divide by the coefficient of x

The value of x is 10°.

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5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;5x-4=-2 \times 3x-2 \times 2 \\&#10;5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\&#10;11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\&#10;11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\&#10;x=0

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3(2x-4)=5x-1 \\&#10;6x-12=5x-1 \\&#10;\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\&#10;11x=11 \\&#10;\boxed{x=11} \Leftarrow \hbox{the second mistake}

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\&#10;3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\&#10;x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\&#10;x=11
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2 years ago
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