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KIM [24]
3 years ago
13

Based only on the information given in the diagram, which congruence

Mathematics
2 answers:
ad-work [718]3 years ago
4 0

Answer:

asa, ha, aas

Step-by-step explanation:

Wewaii [24]3 years ago
3 0

Answer:

Option B

Option E

Step-by-step explanation:

By the use of following postulates we can prove the two right triangles to be congruent.

1). HA - [Equal hypotenuse and an cute angles]

2). LL - [Two legs should be equal]

3). LA - [One leg and one angle must be equal]

4). ASA - [Two angles and the side containing these angles should be equal]

In the given right triangles,

1). OJ ≅ IL

2). ∠O ≅ ∠I

3). ∠J ≅ ∠L

Therefore, two postulates HA, ASA will be applicable for the congruence of the two triangles given.

Options A and E will be the answer.

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Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.
blagie [28]
A.
5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0

B.
3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\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} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  |\hbox{add 12 to both sides} \\
x=11
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I need help with this question
Svetlanka [38]

Answer:

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Step-by-step explanation:

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