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2 years ago

6. If xy = 6 and x = 2, then x + y =

Mathematics

1 answer:

ANTONII [103]2 years ago

6 0

Xy = 6
x = 2

2y = 6

y = 6÷2

y = 3

x + y = (2) + (3) = 5

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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

$\equiv T$

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3 years ago

Find the standard equation for the ellipse, using the given characteristic or characteristics. vertices:(0,+-7) foci: (0,+-√33)

Alexxx [7]

Answer:

$=\frac{x^2}{16} +\frac{y^2}{49}=1$

Step-by-step explanation:

The equation of this ellipse is

$\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1$

for a vertical oriented ellipse where;

(h,k) is the center

c=distance from center to the foci

a=distance from center to the vertices

b=distance from center to the co-vertices

You know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipse

Given that

a= distance between the center and the vertices, a=7

c=distance between the center and the foci, c=√33

Then find b

$a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16$

The equation for the ellipse will be

$\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1$

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2 years ago

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ValentinkaMS [17]

180 (and then whatever the units of measure are)

to find the perimeter you have to add all four sides together to get your total. (3y+2)+(3y+2)+(5y+8)+(5y+8)

y=180

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2 years ago

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Which statement is true about figures ABCD and A'B'C'D? (1 point)

Vlad [161]

A.statement . They are congruent

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3 years ago

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18) What value of x makes R(x) = 10

Illusion [34]

<h3>Two Answers: <u>x = 2 and x = 10</u></h3>

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Explanation:

Draw a horizontal line through 10 on the y axis. This is because R(x) = 10 is the same as y = 10. The output of the function is the y value.

See the diagram below.

The horizontal line crosses the parabola at two locations. From those points, draw a vertical line straight down to the x axis. Note how we land at x = 2 and x = 10. This means that R(2) = 10 and R(10) = 10.

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3 years ago

6. If xy = 6 and x = 2, then x + y = ​

6. If xy = 6 and x = 2, then x + y =