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3 years ago

draw an array to show how to arrange 20 chairs into 5 equal rows. Explain what each part of the array represents.

1 answer:

6 0

<span>Since there are 20 chairs and should be arrange into 5 equal rows. So the number of chairs in each row is equal to 20 / 5 which equal to 4. so let x represent a chair in the array. so the drawing should be like:
x x x x
x x x x
x x x x
x x x x
x x x x </span>

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Factorize this expression completely <br>using (a-b)² formula<br>3a²- 36a + 108

Novosadov [1.4K]

Answer:

$3a^2 - 36a + 108 = (\sqrt{3}a - 6\sqrt{3} )^2$

Step-by-step explanation:

$3a^2 = (\sqrt{3} a)^2\\108 = 9 \times 4 \times 3= 3^2 \times 2^2 \times 3 = (3\times2 \sqrt{3} )^2 = (6\sqrt{3})^2$

$so, a = \sqrt{3} a \ , \ b = 6\sqrt{3} \\\\(a - b)^2 = a^2 -2ab + b^2\\\\-36a = -2ab\\\\-36a = -2 \times \sqrt{3} a \times 6\sqrt{3}$

Therefore ,

$3a^2 - 36a + 108 = (\sqrt{3}a )^2 - 2(\sqrt{3}a \times 6\sqrt{3} ) + (6\sqrt{3} )^2 = (\sqrt{3}a - 6\sqrt{3} )^2$

6 0

3 years ago

Standard issue passenger license plates in Ohio consist of three letters followed by four numbers. How many standard issue licen

dezoksy [38]

Answer:

The standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 175760000

Step-by-step explanation:

If there are no restrictions, all numbers and letters are available to be used then. And with no restrictions, every number or letter can appear more than once.

There are 7 spaces available; 3 spaces for letters, 4 spaces for numbers

The different combination of letters and numbers then becomes,

26 × 26 × 26 × 10 × 10 × 10 × 10

This is because, all 26 letters (A to Z) can occupy the first space, the second space and the third space. And all 10 digits (0 to 9) can occupy the fourth space, the fifth space, the sixth space and the seventh space.

So, the standard issue license plates that can be produced if there are no restrictions on the letters and numbers = 26 × 26 × 26 × 10 × 10 × 10 × 10 = 175760000 different standard issue license plates.

8 0

3 years ago

A drawer contains 6 white socks and 10 black socks. If 2 socks are chosen at random, what is the probability that they will have

SpyIntel [72]

$|\Omega|=C(16,2)=\dfrac{16!}{2!14!}=\dfrac{15\cdot16}{2}=120\\|A|=C(6,2)+C(10,2)=\dfrac{6!}{2!4!}+\dfrac{10!}{2!8!}=\dfrac{5\cdot6}{2}+\dfrac{9\cdot10}{2}=15+45=60\\\\P(A)=\dfrac{60}{120}=\dfrac{1}{2}=50\%$

3 0

4 years ago

Read 2 more answers

A graph displays point A (5, 3, 4) and point B (−4, 2, 6). Calculate the approximate distance each point is from the origin. Rou

SIZIF [17.4K]

Distance from the origin to the points ≈ 0.41.

<h3>What is the distance between two points ( p,q) and (x,y)?</h3>

The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:

D = √[(x-p)² + (y-q)²]

Point A (5, 3, 4) and point B (−4, 2, 6) are located away from the origin (0,0,0), and the points from the origin to this points are expressed as OB - OA where;

Let OB is the distance from the origin to the point B

Let OA is the distance from the origin to the point A

Using the formula for calculating the distance between two points;

OA = √(z2-z1)²+(y2-y1)²+(x2-x1)²

OA = √(4-0)²+(3-0)²+(5-0)²

OA = √(16)+(9)+(25)

OA = √50

OA = 7.071

Similarly;

OB = √(6-0)²+(2-0)²+(-4-0)²

OB = √(6)²+(2)²+(-4)²

OB = √36+4+16

OB = √56

OB = 7.4833

Distance from the origin to the points = 7.4833 - 7.071= 0.4123

Distance from the origin to the points ≈ 0.41

Learn more about distance between two points here:

brainly.com/question/16410393

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5 0

2 years ago

If anyone could help that would be great / right answer gets brainilest

Keith_Richards [23]

2.69 cm would be the answer

7 0

3 years ago

Read 2 more answers