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3 years ago

The following graph represents an inequality.

Mathematics

1 answer:

Len [333]3 years ago

5 0

Answer:

x < −6 or x ≥ 3

Step-by-step explanation:

Whenever they are split apart, we will be using "or". Second, you see how the left side of the number line is graphed? All x-values go up to -6 with an open circle, therefore it is less than, NOT less than or equal to [circle NOT closed]. The right side of the number line, however, does have a closed circle starting from 3, therefore it is greater than or equal to, NOT greater than [circle NOT open].

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Find the general solution of <img src="https://tex.z-dn.net/?f=2cos%282x%20%2B%20%5Cfrac%7B%5Cpi%20%7D%7B4%7D%20%29%20%3D%20%5Cs

Aleks04 [339]

Answer:

$\large\boxed{x=-\dfrac{\pi}{4}+k\pi\ \text{or}\ x=k\pi\ \text{for}\ k\in\mathbb{Z}}$

Step-by-step explanation:

$2\cos\left(2x+\dfrac{\pi}{4}\right)=\sqrt2\qquad\text{divide both sides by 2}\\\\\cos\left(2x+\dfrac{\pi}{4}\right)=\dfrac{\sqrt2}{2}\to2x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+2k\pi\\\\2x+\dfrac{\pi}{4}=-\dfrac{\pi}{4}+2k\pi\ \vee\ 2x+\dfrac{\pi}{4}=\dfrac{\pi}{4}+2k\pi\qquad\text{subtract}\ \dfrac{\pi}{4}\ \text{from all sides}\\\\2x=-\dfrac{2\pi}{4}+2k\pi\ \vee\ 2x=2k\pi\qquad\text{divide all sides by 2}\\\\x=-\dfrac{\pi}{4}+k\pi\ \vee\ x=k\pi\ \text{for}\ k\in\mathbb{Z}$

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4 years ago

What is the relationship between a conjecture, a theorem, and a two-column proof?

lidiya [134]

In mathematics, a proof is a deductive argument for a mathematical statement. In the argument, proven statements such as theorems, can be used. In principle, a proof can be traced back to self-evident or assumed statements, known as axioms. the two column proof uses data and theorems to carry out thorough proving.

4 0

3 years ago

Read 2 more answers

One formula for measuring the magnitude of an earthquake is by using the Richter scale. It is a logarithmic scale created by the

lubasha [3.4K]

Answer:

Richter scale is a good way to talk about how strong an earthquake is. It is also easy to compare two earthquakes using the Richter scale.

Generally, earthquakes are estimated to be under

on the Richter scale.

Below is the formula for comparing two earthquakes.

M2-M1=log(I2-I1)

You can check out how this formula is derived.

Compute the magnitude of an earthquake

Given the intensity of two earthquakes and the magnitude of one of them, we can find the magnitude of the other earthquake. For example:

Earthquake

times stronger than earthquake

. Earthquake

is estimated to be

2.3

on the Richter scale. What is Earthquake

on the Richter scale?

M_A-M_B=log(I_A/I_B)

M_A-2.3=log(15)

M_A=log(15)+3.5

M_A=3.5

How much stronger is this earthquake comparing to that?

When given the magnitudes of

earthquakes, we can figure out how much stronger one earthquake is comparing to the other one. For example:

On the Richter scale, earthquake

is estimated to be

and earthquake

is estimated to be

1.5

How much stronger is earthquake

times

Step-by-step explanation:

The picture is the explanation......

And please comment if it helps you

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3 years ago

Use truth tables to show that the following statements are logically equivalent. ∼ P ⇔ Q = (P ⇒∼ Q)∧(∼ Q ⇒ P)

Alina [70]

Answer: The given logical equivalence is proved below.

Step-by-step explanation: We are given to use truth tables to show the following logical equivalence :

∼ P ⇔ Q ≡ (P ⇒∼ Q)∧(∼ Q ⇒ P)

We know that

two compound propositions are said to be logically equivalent if they have same corresponding truth values in the truth table.

The truth table is as follows :

P Q ∼ P ∼Q ∼ P⇔ Q P ⇒∼ Q ∼ Q ⇒ P (P ⇒∼ Q)∧(∼ Q ⇒ P)

T T F F F F T F

T F F T T T T T

F T T F T T T T

F F T T F T F F

Since the corresponding truth vales for ∼ P ⇔ Q and (P ⇒∼ Q)∧(∼ Q ⇒ P) are same, so the given propositions are logically equivalent.

Thus, ∼ P ⇔ Q ≡ (P ⇒∼ Q)∧(∼ Q ⇒ P).

8 0

3 years ago

Line segment C X is an altitude in triangle ABC. Triangle A B C is shown. Angle A C B is a right angle. An altitude is drawn fro

ira [324]

Answer:

i. ΔAXC ~ ΔCXB

ii. ΔBCX Is-congruent-to ΔACX

Step-by-step explanation:

From the given ΔABC, CX is the altitude of ΔABC; and also an angle bisector of <ACB.

So that:

m<AXC = m<BXC (right angle property)

m<ACX = m<BCX (congruent property)

m<ACX + m<AXC + m<CAX = $180^{o}$ (sum of angles in a triangle)

m<BCX + m<BXC + m<CBX = $180^{o}$ (sum of angles in a triangle)

Therefore, from the figure it can be deduced that;

i. ΔAXC ~ ΔCXB (Angle-Angle-Side, AAS, property)

ii. ΔBCX Is-congruent-to ΔACX (Angle-Angle-Side, AAS, property)

7 0

4 years ago

Read 2 more answers