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3 years ago

The definition of theorem?

Mathematics

1 answer:

charle [14.2K]3 years ago

5 0

Answer:

In mathematics, a theorem is a non-self-evident statement that has been proven to be true, either on the basis of generally accepted statements such as axioms or on the basis of previously established statements such as other theorems. A theorem is hence a logical consequence of the axioms, with a proof of the theorem being a logical argument which establishes its truth through the inference rules of a deductive system. As a result, the proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.

Step-by-step explanation:

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lana66690 [7]

Answer:

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3 years ago

Cuál es el resultado de |-15| x (-5)

notka56 [123]

Answer:

$\frac{15}{x^5}$

Step-by-step explanation:

$\left|-15\right|x^{-5}$

Step 1: Apply exponent rule: $\:a^{-b}=\frac{1}{a^b}$

$=\left|-15\right|\frac{1}{x^5}$

Step 2: Multiply fractions: $a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{1\cdot \left|-15\right|}{x^5}$

Step 3: Simplify

$=\frac{15}{x^5}$

The result is $=\frac{15}{x^5}$

Spanish/Espanól

Respuesta:

$\frac{15}{x^5}$

Explicación paso a paso:

$\left|-15\right|x^{-5}$

Paso 1: aplique la regla del exponente: $\:a^{-b}=\frac{1}{a^b}$

$=\left|-15\right|\frac{1}{x^5}$

Paso 2: multiplica fracciones: $a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=\frac{1\cdot \left|-15\right|}{x^5}$

Paso 3: simplifica

$=\frac{15}{x^5}$

El resultado es $=\frac{15}{x^5}$

7 0

3 years ago

Which of the following best completes the proof showing that ΔWXZ ~ ΔXYZ?

skelet666 [1.2K]

Angles formed by the segment $\overline{XZ}$ in the triangles ΔWXZ, and ΔXYZ, are equal and the given corresponding sides are proportional.

The option that best completes the proof showing that ΔWXZ ~ ΔXYZ is; 16 over 12 equals 12 over 9

Reasons:

The proof showing that ΔWXZ ~ ΔXYZ is presented as follows;

Segment $\overline{XZ}$ is perpendicular to segment $\overline{WY}$

∠WZX and ∠XZY are right angles by definition of $\overline{XZ}$ perpendicular to $\overline{WY}$

∠WZX in ΔWXZ = ∠XZY in ΔXYZ = 90° (definition)

$\displaystyle \frac{WZ}{XZ} = \frac{16}{12} = \mathbf{ \frac{4}{3}}$

$\displaystyle \mathbf{ \frac{XZ}{ZY}} = \frac{12}{9} = \frac{4}{3}$

Therefore;

$\displaystyle \frac{16}{12} = \frac{12}{9}$ , which gives, $\displaystyle \mathbf{\frac{WZ}{XZ} }= \frac{XZ}{ZY}$

Given that two sides of ΔWXZ are proportional to two sides of ΔXYZ, and

that the included angles between the two sides, ∠WZX and ∠XZY are

congruent, the two triangles, ΔWXZ and ΔXYZ are similar by Side-Angle-

Side, SAS, similarity postulate.

The option that best completes the proof is therefore;

$\displaystyle \frac{16}{12} = \frac{12}{9}$ which is; 16 over 12 equals 12 over 9

Learn more about the SAS similarity postulate here:

brainly.com/question/11923416

4 0

3 years ago

In the drawing below, label the distances given for the peak you chose

earnstyle [38]

Notice the larger triangle is a right-triangle, and the small one is also a right-triangle. Also notice the "angle tickmark" on each. So both angles have a pair of angles that are equal on each.

the triangles are similar by AA.

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3 years ago

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Sophie [7]

Answer:

Step-by-step explanation:

Each month your hair grows .5 inches

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The definition of theorem? ​

The definition of theorem?