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3 years ago

Which of the following value pairs can be used as m and n to factor the expression 2003-16-04-00-00_files/i0100000.jpg?

Mathematics

1 answer:

iris [78.8K]3 years ago

4 0

23,164 it is the answer

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Prove that P (P) = (QA ~ Q)] is a tautology.

alekssr [168]

Answer:

The statement $P \leftrightarrow [(\lnot P) \rightarrow (Q \land \lnot Q)]$ is a tautology.

Step-by-step explanation:

A tautology is a formula which is "always true" that is, it is true for every assignment of truth values to its simple components.

To show that this statement is a tautology we are going to use a table of logical equivalences:

$P \leftrightarrow [(\lnot P) \rightarrow (Q \land \lnot Q)] \equiv$

$\equiv (P \land [(\lnot P)\rightarrow (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [(\lnot P)\rightarrow (Q \land \lnot Q)])$ by the logical equivalences involving bi-conditional statements

$\equiv (P \land [\lnot(\lnot P)\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [\lnot(\lnot P)\lor (Q \land \lnot Q)])$ by the logical equivalences involving conditional statements

$\equiv (P \land [P\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot [ P\lor (Q \land \lnot Q)])$ by the Double negation law

$\equiv (P \land [P\lor (Q \land \lnot Q)]) \lor(\lnot P \land \lnot P\land \lnot(Q \land \lnot Q))$ by De Morgan's law

$\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot(Q \land \lnot Q))$ by the Negation law

$\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot Q \lor \lnot(\lnot Q))$ by De Morgan's law

$\equiv (P \land [P\lor F]) \lor(\lnot P \land \lnot P\land \lnot Q \lor Q)$ by the Double negation law

$\equiv (P \land P) \lor(\lnot P \land \lnot P\land \lnot Q \lor Q)$ by the Identity law

$\equiv (P) \lor(\lnot P \land \lnot P\land \lnot Q \lor Q)$ by the Idempotent law

$\equiv (P) \lor(\lnot P \land \lnot P\land (Q\lor \lnot Q))$ by the Commutative law

$\equiv (P) \lor(\lnot P \land \lnot P\land T)$ by the Negation law

$\equiv (P) \lor(\lnot (P \lor P)\land T)$ by De Morgan's law

$\equiv (P) \lor(\lnot (P)\land T)$ by the Idempotent law

$\equiv (P \lor\lnot P) \land(P \lor T)$ by the Distributive law

$\equiv (T) \land(P \lor T)$ by the Negation law

$\equiv (T) \land(T)$ by the Domination law

$\equiv T$

8 0

3 years ago

What would the value of 0 represent in her data?

ozzi

Answer:My family hates me

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

(6, - 3, 1) and (8,9,-11) find the angle between the vector

Svetllana [295]

Answer:

The angle between the two vectors is 84.813°.

Step-by-step explanation:

Statement is incomplete. Complete form is presented below:

Let be (6,-3, 1) and (8, 9, -11) vector with same origin. Find the angle between the two vectors.

Let $\vec u = \langle 6, -3, 1 \rangle$ and $\vec v = \langle 8,9,-11 \rangle$ , the angle between the two vectors is determined from definition of dot product:

$\theta = \cos^{-1} \left(\frac{\vec u \,\bullet \,\vec v}{\|\vec u\|\cdot \|\vec v\|} \right)$ (1)

Where:

$\vec u$ , $\vec v$ - Vectors.

$\|\vec u\|$ , $\|\vec v\|$ - Norms of each vector.

Note: The norm of a vector in rectangular form can be determined by either the Pythagorean Theorem or definition of Dot Product.

If we know that $\vec u = \langle 6,-3,1 \rangle$ and $\vec v = \langle 8, 9,-11 \rangle$ , then the angle between the two vectors is:

$\theta = \cos^{-1}\left[\frac{(6)\cdot (8) + (-3)\cdot (9) + (1)\cdot (-11)}{\sqrt{6^{2}+(-3)^{2}+1^{2}}\cdot \sqrt{8^{2}+9^{2}+(-11)^{2}}} \right]$

$\theta \approx 84.813^{\circ}$

The angle between the two vectors is 84.813°.

6 0

2 years ago

What's the answer please help

boyakko [2]

You don't need the apothem if the side length is known, the area can be expressed as:

A(n,s)=ns^2/(4tan(180/n)), n=number of sides and s=side length so

A(7,28)=(7*28^2)/(4tan(180/7))

A≈2848.987 ft^2

A≈2849 ft^2 (to the nearest tenth of a square foot)

6 0

3 years ago

7x + 6(-3 + 4x) = 199 what does x equal?

tresset_1 [31]

Simplify. Note the equal sign. What you do to one side, you do to the other. Follow PEMDAS.

Isolate the x.

First, distribute 6 to all terms within the parenthesis

6(-3) = -18

6(4x) = 24x

7x - 18 + 24x = 199

Simplify. Combine like terms

31x - 18 = 199

Isolate the x. Add 18 to both sides

31x - 18 (+18) = 199 (+18)

31x = 199 + 18

31x = 217

Isolate the x. Divide 31 from both sides

31x/31 = 217/31

x = 217/31

x = 7

7 is your answer for x

hope this helps

8 0

3 years ago