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3 years ago

Which set of ordered pairs has point symmetry with respect to the origin (0, 0)?

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

7 0

The answer is the second option, which is: $(9, 2), (-9, -2)$

The explanation for this answer is shown below:

By definition, a set of ordered pairs that has point symmetry with respect to the origin $(0,0)$ , has the following form: (a,b), (-a,-b). Therefore, as you can see in the options shown in the problem, the only set of ordered pair that has the form mentioned before is: $(9,2), (-9,-2)$

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Use decimals and fractions in the same equation showing the Commutative Property. Repeat for the Associative Property.

Anna71 [15]

For Commutative Property of Addition

Let us take a decimal number $2.14$ and a fraction $\frac{5}{20}$

Now, according to the Commutative property of Addition:

For any two numbers $a$ and $b$ :

$a+b = b+a$

So, for $2.14$ and $\frac{5}{20}$

Let us add

$2.14+\frac{5}{20} = \frac{214}{100} +\frac{5}{20}$

$=\frac{214}{100} + \frac{5 \times 5}{20 \times 5} \\ \\=\frac{214}{100} + \frac{25}{100} \\ \\= 2.14 + 0.25 \\ \\ = 2.39$

Also,

$\frac{5}{20} + 2.14 = \frac{5}{20} + \frac{214}{100}$

$= \frac{5 \times 5}{20 \times 5} +\frac{214}{100} \\ \\= \frac{25}{100} + \frac{214}{100} \\ \\= 0.25 + 2.14 \\ \\ = 2.39$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Commutative Property of Addition is satisfied.

For Associated Property of Addition

Let us take two same decimal numbers $2.14$ , $7.25$ and a fraction $\frac{5}{20}$

Now, according to the Associated property of Addition:

For any three numbers $a$ , $b$ and $c$

$a + (b+c) =(a+b) + c$

So, for $2.14$ , $7.25$ and $\frac{5}{20}$

The Left hand side:

$a + (b+c)$

$2.14 + (7.25 + \frac{5}{20}) = 2.14 + (\frac{725}{100} + \frac{5 \times 5}{20\times 5})$

$= 2.14 + (\frac{725}{100} + \frac{25 }{100})$

$= 2.14 + (\frac{750}{100} )$

$= \frac{214}{100} + \frac{750}{100}$

$= \frac{964}{100}$

$=9.64$

The Right hand side:

$(a + b )+c$

$(2.14 + 7.25 )+ \frac{5}{20}= ( 9.39 ) + \frac{5 }{20}$

$= 9.39 + \frac{5 \times 5 }{20 \times 5}$

$= 9.39 + \frac{25}{100}$

$= 9.39 + 0.25$

$= 9.64$

Thus,

$(2.14 + (7.25 + \frac{5}{20} )= (2.14 + 7.25 )+ \frac{5}{20}$

Therefore, $2.14+\frac{5}{20} = \frac{5}{20} + 2.14$

Hence, Associative Property of Addition is satisfied.

8 0

3 years ago

What is the combined lenght of all buttons longer than 1 inch?

HACTEHA [7]

Answer:

2 12 1/2 inches

Step-by-step explanation:

1: 1 1/4 + 1 1/4

2: 1+1 = 2; 1/4 + 1/4 = 2/4

3: 2 2/4

Answer: 2 2/4

<em><u>Hope this helps.</u></em>

7 0

3 years ago

Karen claps her hand and hears the echo from a distant wall 0.113 s later. How far away is the wall? The speed of sound in air i

insens350 [35]

Answer:

19.3795 m

Step-by-step explanation:

If sound travels at 343 m/s and it took Karen 0.113 s to hear the echo from the wall, the distance travelled by the sound is:

$D=343\frac{m}{s} *0.113\ s\\D= 38.759\ m$

Note that the distance calculated above is the distance travelled from Karen to the wall and then back from the wall to Karen. Therefore, the distance between Karen and the wall is:

$d=\frac{38.759}{2}\\d=19.3795\ m$

The wall is 19.3795 m away from Karen.

3 0

3 years ago

There are 10 members on the school Hungry Hungry Hippos club. They meet Thursdays to play Pokemon. Each member wants to play fou

andreev551 [17]

Answer:

40 games will be played in total.

Step-by-step explanation:

3 0

2 years ago

What is the volume of the solid?

Evgen [1.6K]

9514 1404 393

Answer:

(9√3 -3π/2) ft^3 ≈ 10.88 ft^3

Step-by-step explanation:

The area of the hexagon is given by the formula ...

A = (3/2)√3·s^2 . . . . for side length s

The area of the hexagonal face of this solid is ...

A = (3/2)√3·(2 ft)^2 = 6√3 ft^2

The area of the circular hole in the hexagonal face is ...

A = πr^2

The radius is half the diameter, so is r = (2 ft)/2 = 1 ft.

A = π(1 ft)^2 = π ft^2

Then the area of the "solid" part of the face of the figure is ...

A = (6√3 -π) ft^2

The volume is ...

V = Bh . . . . . where B is the area of the base of the prism, and h is its height

V = ((6√3 -π) ft^2)(3/2 ft) = (9√3 -3π/2) ft^3 ≈ 10.88 ft^3

8 0

3 years ago