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Semmy [17]
3 years ago
14

Question 1

Mathematics
1 answer:
Ahat [919]3 years ago
5 0

Answer: x = 22


Explanation:


1) Corresponding sides and correspoding angles of congruent triangles are equal.


2) When you name two congruent triangles the order of the vertices signal which sides and angles are congruents.


That triangle ABC is congruent to triangle DEF means that these are the corresponding parts, which are congruent to each other:


  • ∠A and ∠D are congruent
  • ∠B and ∠ E are congruent
  • ∠C and ∠F are congruent
  • Segment AB and segment DE are congruent
  • Segment BC and segment EF are congruent
  • Segment AC and segment  DF are congruent

In the figures, it is given that the segment DF measures (1/2)x  - 1 and the corresponding segment AC measures 10 units.


Hence, you set this equation: (1/2)x - 1 = 10


Solving for x:

  • (1/2)x = 10 + 1
  • (1/2)x = 11
  • x = 2(11)
  • x = 22 ← answer
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Step-by-step explanation:

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Answer:

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2 years ago
Solve by elimination:
Pie

Answer:

B (5, 13)

Step-by-step explanation:

9x + 4y = 97

9x + 6y = 123

To solve by elimination, we want to <em>eliminate</em> a variable. To do this, we must make one variable cancel out.

First, we can see that both equations have 9x. To cancel out x, we must make <em>one</em> of the 9x's <em>negative</em>. To do this, multiply <em>each term</em> in the equation by -1.

-1(9x + 6y = 123)

-9x - 6y = -123

This is one of your equations. Set it up with your other given equation.

9x + 4y = 97

-9x - 6y = -123

Imagine this is one equation. Since every term is negative, you will be subtracting each term.

9x + 4y = 97

-9x - 6y = -123

___________

0x -2y = -26

-2y = -26

To isolate y further, divide both sides by -2.

y = 13

Now, to find x, plug y back into one of the original equations.

9x + 4(13) = 97

Multiply.

9x + 52 = 97

Subtract.

9x = 45

Divide.

x = 5

Check your answer by plugging both variables into the equation you have not used yet.

-9(5) - 6(13) = -123

-45 - 78 = -123

-123 = -123

Your answer is correct!

(5, 13)

Hope this helps!

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3 years ago
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Answer:

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