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Mandarinka [93]
3 years ago
8

2. BT bisects ZABC. MZABT = 4x-16 and m CBT = 2x + 6 Find MZABT.

Mathematics
1 answer:
Paladinen [302]3 years ago
6 0

Answer:

The measure of angle ABT is 28°

Step-by-step explanation:

* Lets revise the bisector of a angle

- If a ray bisects and angle that mean the ray divide the angle into

 two equal parts in measure

- Ex: if the ray BD bisects angle ABC, then the measure of angle ABD is

 equal to the measure of angle CBD

* Lets solve the problem

∵ BT bisects ∠ABC

∴ m∠ABT = m∠CBT

∵ m∠ABT = 4x - 16

∵ m∠CBT = 2x + 6

- Equate the two values

∴ 4x - 16 = 2x + 6

- Lets solve the equation by subtracting 2x from both sides and

 adding 16 to both sides

∴ 4x - 2x = 6 + 16

∴ 2x = 22 ⇒ divide both sides by 2

∴ x = 11

- Lets find the measure of angle ABT

∵ m∠ABT = 4x - 16

- Substitute x by 11

∴ m∠ABT = 4(11) - 16 = 44 - 16 = 28°

* The measure of angle ABT is 28°

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Answer:

The ordered pairs in the <em>inverse of g = </em>{(-3, 5), (1, 4), (-2, 3), (0, 2)}

Step-by-step explanation:

Given that:

Relation <em>g</em> is given by the following table of values:

\begin{center}\begin{tabular}{ c c }x & y \\5 & -3 \\4 & 1\\3 & -2\\2 & 0\\\end{tabular}\end{center}

To find:

The ordered pairs in the inverse of relation <em>g.</em>

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First of all, let us learn about domain and range of a relation y=f(x).

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Range of a relation is the values of y\ or\ f(x) that come as the output of the relation.

When we take the inverse of any relation,

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Now, let us have a look at the domain of given relation <em>g.</em>

Domain of g = set of values of x = {5, 4, 3, 2}

Range of g = set of values of y = {-3, 1, -2, 0}

Ordered pairs will be like (x, y)

Ordered pairs in <em> g </em>are: {(5, -3), (4, 1), (3, -2), (2, 0)}

The ordered pairs in the <em>inverse of g = </em>{(-3, 5), (1, 4), (-2, 3), (0, 2)}

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