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77julia77 [94]
3 years ago
8

Classify the triangle based on angle measures.

Mathematics
1 answer:
ki77a [65]3 years ago
7 0

<u>Let's name these angles</u>.

∠ A = 72°

∠ B = 54°

∠ C = 54°

Now, in this triangle, two angles, i.e., ∠ B and ∠ C are same.

According to the properties of triangle, sides opposite to two equal angles in a triangle are also equal, which means the two sides opposite to 54° in the figure will be equal.

=> <u>AB = AC</u>

Now, if there are two equal sides in a triangle then the triangle is called <u>Isosceles Triangle.</u>

So, the above triangle is an <u>Isosceles Triangle</u>.

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QUESTION TWO Determine whether or not a constant function can be
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<h3>Answers:</h3>
  • (a) It is <u>never</u> one-to-one
  • (b) It is <u>never</u> onto

=========================================================

Explanation:

The graph of any constant function is a horizontal flat line. The output is the same regardless of whatever input you select. Recall that a one-to-one function must pass the horizontal line test. Horizontal lines themselves fail this test. So this is sufficient to show we don't have a one-to-one function here.

Put another way: Let f(x) be a constant function. Let's say its output is 5. So f(x) = 5 no matter what you pick for x. We can then show that f(a) = f(b) = 5 where a,b are different values. This criteria is enough to show that f(x) is not one-to-one. A one-to-one function must have f(a) = f(b) lead directly to a = b. We cannot have a,b as different values.

----------------------------

The term "onto" in math, specifically when it concerns functions, refers to the idea of the entire range being accessible. If the range is the set of all real numbers, then we consider the function be onto. There's a bit more nuance, but this is the general idea.

With constant functions, we can only reach one output value (in that example above, it was the output 5). We fall very short of the goal of reaching all real numbers in the range. Therefore, this constant function and any constant function can never be onto.

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