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Doss [256]
3 years ago
12

True or False? All angles with measures between 120 degrees and 180 degrees are obtuse.

Mathematics
2 answers:
lions [1.4K]3 years ago
8 0
True, any angle higher than 90° is obtuse, and any angle lower than 90 is acute <span />
enot [183]3 years ago
8 0
This is true.
Because 90 degrees, and 180 is a straight line, anything between that is obtuse.
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Answer:

You can proceed as follows:

Step-by-step explanation:

First solve the quadratic inequality x^{2}-5x+4\leq 0. To do that, factorize, then we have that (x-4)(x-1)\leq 0. This implies that

x-1\leq 0\, \text{and}\, x-4\geq 0

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x-1 \geq 0\, \text{and}\, x-4\leq 0

In the first case the solution is the empty set \emptyset. In the second case the solution is the interval 1\leq x \leq 4. Now we have that

A=[1,4]

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C=(3,4].

To show that A\cap B\subseteq C consider x\in A\cap B. Then 1\leq x \leq 4\, \text{and}\, 1, this implies that 3, then x\in C. Now, to show that C\subseteq A\cap B consider x\in C, then 3, then 1\leq x \leq 4\, \text{and}\, 3, then x\in [1,4] \, \text{and}\, x\in (3,5), this implies that x\in A\cap B.

Observe the image below.

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