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3 years ago

true or false any point that belongs to the angle bisector of a given angle is equident to the sides of that angle

Mathematics

1 answer:

Roman55 [17]3 years ago

4 0

Answer:

True

Step-by-step explanation:

You can show this using the HA congruence theorem for right triangles. The distance of interest is the perpendicular distance from the point to the side of the angle. The distance from the point to the vertex is the same for both triangles (reflexive property), and the vertex angles are the same (definition of angle bisector). Hence the conditions required for HA congruence are met.

The distances from the point to the sides are then corresponding parts of congruent triangles, so are congruent. That is, the distance is the same, so the point is equidistant from the sides.

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PLEASE HELP THANK YOU!!!

Paul [167]

Answer:

Only C is a function

Step-by-step explanation:

To test whether a graph is a function you use the vertical line test.

If you can place a vertical line anywhere on the plane (in the domain of the "function" to be tested) and it intersects the curve at more than one point, the curve is not a function.

We see with A, wherever we put the vertical line it intersects twice.

With B, it intersects infinitely many times.

C is a function because wherever we put the vertical line, it only intersects once.

D is a function because it intersects twice providing we do not put it on the "tip" of the parabola.

The mathematical reasoning behind this is that a function must be well-defined, that is it must send every x-value to one specific y-value. There can be no confusion about where the function's input is going. If you look at graph B and I ask you what is f(3)? Is it 1? 2? 3? ... Who knows, it's not well-defined and so it's not a function. However if I ask you about C, whichever input value for x I give you, you can tell me to which y-value it gets mapped/sent to.

7 0

3 years ago

Solve the inequality for x 3^(6x+18)<27^(3x)

Lera25 [3.4K]

Answer:

$\displaystyle x > 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Equality Properties

Multiplication Property of Equality
Division Property of Equality
Addition Property of Equality
Subtraction Property of Equality

Algebra I

Terms/Coefficients
Factoring

Algebra II

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$
Solving exponential equations

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle 3^{6x + 18} < 27^{3x}$

Step 2: Solve for x

Rewrite: $\displaystyle 3^{6x + 18} < 3^{3(3x)}$
Set: $\displaystyle 6x + 18 < 3(3x)$
Factor: $\displaystyle 3(2x + 6) < 3(3x)$
[Division Property of Equality] Divide 3 on both sides: $\displaystyle 2x + 6 < 3x$
[Subtraction Property of Equality] Subtract 3x on both sides: $\displaystyle -x + 6 < 0$
[Subtraction Property of Equality] Subtract 6 on both sides: $\displaystyle -x < -6$
[Division Property of Equality] Divide -1 on both sides: $\displaystyle x > 6$

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Answer:

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