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3 years ago

1. List the properties of a parallelogram

Mathematics

2 answers:

CaHeK987 [17]3 years ago

8 0

9514 1404 393

Answer:

see the list below
no
yes

Step-by-step explanation:

1. The dictionary definition of a parallelogram is ...

a quadrilateral with opposite sides parallel

As a consequence of this condition, a number of additional properties arise:

opposite sides are the same length
opposite angles are congruent
adjacent angles are supplementary
diagonals bisect each other

2. The dictionary definition of a trapezoid (US; trapezium, UK) is ...

a quadrilateral with one pair of parallel sides.

As a consequence of this condition, it is not possible for a trapezoid to be a parallelogram.

3. A rhombus is a special case of parallelogram in which all sides are the same length. A square is a special case of rhombus in which all angles are congruent (as are the diagonals). Yes, a rhombus may be a square.

Tcecarenko [31]3 years ago

8 0

$\displaystyle 2b.$ A rhombus can <em>never</em> be a square because although opposite interiour angles and all four sides are congruent, their interiour angles are not right angles.

$\displaystyle 2a.$ A trapezium is impossibly a parallelogram because a parallelogram has two pairs of parallel sides.

$\displaystyle 1.$ Convex polygon with two pairs of opposite sides that are parallel and congruent [equal in length (<em>see above picture</em>)]

I am joyous to assist you at any time.

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2. Four pieces of candy are drawn at random from a bag containing five orange pieces and seven brown pieces.

alexandr402 [8]

Answer:

a) $12C4 = \frac{12!}{4! (12-4)!}= \frac{12!}{4! 8!}=\frac{12*11*10*9*8!}{4! 8!}= 495$ ways

b) $5C2 = \frac{5!}{2! (5-2)!}= \frac{5!}{2! 3!}=\frac{5*4*3!}{2! 3!}= 10$ ways

c) $7C2 = \frac{7!}{2! (7-2)!}= \frac{7!}{2! 5!}=\frac{7*6*5!}{2! 5!}= 21$ ways

Step-by-step explanation:

Combinatory means combination or arrangement of different elements.

If we have n total elements and we want to find in how many ways we can select x we can use this general formula:

$nCx= \frac{n!}{x! (n-x)!}$

Where $n! = n *(n-1)!$

a. How many different ways can four pieces be selected from the 12 colored pieces?

For this case we have:

$12C4 = \frac{12!}{4! (12-4)!}= \frac{12!}{4! 8!}=\frac{12*11*10*9*8!}{4! 8!}= 495$ ways

b. How many different ways can two orange pieces be selected from five orange pieces?

For this case we have:

$5C2 = \frac{5!}{2! (5-2)!}= \frac{5!}{2! 3!}=\frac{5*4*3!}{2! 3!}= 10$ ways

c. How many different ways can two brown pieces be selected from seven brown pieces?

For this case we have:

$7C2 = \frac{7!}{2! (7-2)!}= \frac{7!}{2! 5!}=\frac{7*6*5!}{2! 5!}= 21$ ways

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4 years ago

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ladessa [460]

Answer: $h(x)=10(0.4)^x$

Step-by-step explanation:

The exponential function h, represented in the table, can be written as $h(x)=ab^x$

From table, at x=0, h(x) =10

Put theses values in equation,, we get

$10=a.b^0\\\\\Rightarrow\ 10= a (1)\\\\\Rightarrow\ a= 10$

Also, for x= 1 , h(x) = 4, so put these values and a=10 in the equation , we get

$4=10b^1\\\\\Rightarrow\ b=\dfrac{4}{10}\\\\\Rightarrow\ b= 0.4$

Put value of a and b in the equation ,

$h(x)=10(0.4)^x$ → Required equation.

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Mariulka [41]

Answer:

see explanation

Step-by-step explanation:

(9m + 4)² - (9m - 4)² ← expand both factors using FOIL

= 81m² + 72m + 16 - (81m² - 72m + 16) ← distribute parenthesis by - 1

= 81m² + 72m + 16 - 81m² + 72m - 16 ← collect like terms

= 144m

= 72(2m)

which is divisible by 72 for all m

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