Ella’s geometry teacher asked each student to devise a problem and write out its solution. Here is Ella’s work:
2 answers:
Answer:
Ella’s procedure and conclusion are incorrect.
Step-by-step explanation:
The sum of the squares of the short sides can be compared to the square of the long side to see if the triangle is acute, right, or obtuse. The appropriate conclusions are ...
- a² +b² > c² -- acute triangle
- a² +b² = c² -- right triangle
- a² +b² < c² -- obtuse triangle
For Ella's side lengths, the appropriate "work" is ...
10² +11² ?? 15²
100 +121 < 225
The triangle is obtuse.
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Ella used an incorrect comparison and came to the wrong conclusion. Both her procedure and conclusion are incorrect.
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Answer:
Step-by-step explanation:
Given , substitute what is in the parentheses for
to find an output.
For , the term
is in the parentheses. Thus, substitute
into
to find
:
Answer:
3 a : 2 b = 6 : 1
Step-by-step explanation:
<em> =
</em>
<em>3 ( a + b) = 5 ( a - b) </em>
<em>3 a + 3 b = 5 a - 5 b </em>
<em>5 b + 3 b = 5 a - 3 a </em>
<em> 8 b = 2 a </em>
<em> 2 a = 8 b</em>
<em><u>a = 4 b</u></em>
<em>3 a = 3 × 4 b</em>
<em><u>3 a = 12 b</u></em>
<em>3 a: 2 b = 12 b : 2 b</em>
<em>3 a : 2 b = 6 : 1</em>