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2 years ago

which of the following are among the five basic postulates of euclidean geometry? check all that apply

1 answer:

7 0

The five essential hypothesizes of Geometry, additionally alluded to as Euclid's proposes are the accompanying:
1.) A straight line section can be drawn joining any two focuses.
2.) Any straight line portion can be expanded uncertainly in a straight line.
3.) Given any straight line fragment, a circle can be drawn having the portion as a span and one endpoint as the inside.
4.) All correct points are harmonious.
5.) If two lines are drawn which meet a third such that the total of the internal points on one side is under two right edges (or 180 degrees), then the two lines unavoidably should converge each other on that side if reached out sufficiently far.

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Evaluate the expression 4ab, for a =2 and b = 5

yan [13]

Answer:

Step-by-step explanation:

4x2=8

8x5=40

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2 years ago

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There are 80 students enrolled in an introductory Statistics class; you are to select a sample of 5. How can you select an SRS o

VladimirAG [237]

Answer:

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Step-by-step explanation:

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2 years ago

(x-7)(x^2+3x-3) multiply the polynomials

Akimi4 [234]

Step-by-step explanation:

= (x - 7)(x² + 3x - 3)

= x³ - 7x² + 3x² - 21x - 3x + 21

= x³ - 4x² - 24x + 21

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2 years ago

You are in charge of erecting a radio telescope on a newly discovered planet. To minimize interference, you want to place it whe

strojnjashka [21]

Answer:

Step-by-step explanation:

$\text{The equation of the surface of the sphere whose radius is 6 can be represented as:}$

$x^2+y^2+z^2 = 36}$

$So , g(x,y,z) = x^2 + y^2 + z^2 - 36$

$\text{To minimize the function :} \\ \\ M(x,y,z0 = 6x - y^2 +xz + 60$

$\text{by applying lagrange multipliers }$

$\bigtriangledown M (x,y,z) = \lambda \bigtriangledown g(x,y,z)$

$\langle 6+zz,-2y,x \rangle = \lambda \langle 2x,2y,2z \rangle$

$6+z = 2\lambda x$

$-2y = 2 \lambda y$

$\text{from the second equation ;} (\lambda +1)y = 0, \text{so , it is either y =0 or }\lambda = -1$

$Suppose \ \lambda = -1 ; \text{other equation becomes x = -2z and 6+z = -2x}$

$\text{such that; 6+z =4z or z = 2}$

$\text{it implies that: x= -4 and }y = \pm \sqrt{36 - 4-16} = \pm 4$

$\text{Here; there exist two possible points}$

$\text{(-4,-4,2) and (-4,4,2)}$

$\text{In the scenario here y=0,} \lambda \text{ is unknown, then we remove it}$

$x = 2 \lambda z \\ \\ 6+z = 2 \lambda x \\ \\ 6+z = 4 \lambda ^2z \\ \\ 6 = (4 \lambda ^2 -1) z ---(1)$

$z = \dfrac{6}{4 \lambda ^2 -1}$

$x = \dfrac{12 \lambda }{4 \lambda ^2 -1 }$

$\text{recall that; it i possible to divide }4 \lambda ^2 -1 \text{since (1) shows that it cannot be equal to zero.} \\ \\ \text{hence, puttinf this into constraint, whereby y =0, Then:}$