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mamaluj [8]
3 years ago
14

Please help me with this stuff, thanks.

Mathematics
1 answer:
zysi [14]3 years ago
4 0
This is really ominous
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Can someone please help me out?
Tema [17]
6.) D (x+7)(x+1)
7.) B (x-9)(x+8)
8.) D
9.) A
10.)A
8 0
3 years ago
In how many ways can we seat 3 pairs of siblings in a row of 7 chairs, so that nobody sits next to their sibling
monitta

Answer:

1,968

Step-by-step explanation:

Let x₁ and x₂, y₁ and y₂, and z₁ and z₂ represent the 3 pairs of siblings, and let;

Set X represent the set where the siblings x₁ and x₂ sit together

Set Y represent the set where the siblings y₁ and y₂ sit together

Set Z represent the set where the siblings z₁ and z₂ sit together

We have;

Where the three siblings don't sit together given as X^c∩Y^c∩Z^c

By set theory, we have;

\left | X^c \cap Y^c \cap Z^c  \right | = \left | X^c \cup Y^c \cup Z^c  \right | =  \left | U  \right | - \left | X \cup Y \cup Z  \right |

\left | U  \right | - \left | X \cup Y \cup Z  \right | = \left | U  \right | - \left (\left | X \right | +  \left | Y\right | +  \left | Z\right | -  \left | X \cap Y\right | -  \left | X \cap Z\right | -  \left | Y\cap Z\right | +  \left | X \cap Y \cap Z\right | \right)

Therefore;

\left | X^c \cap Y^c \cap Z^c  \right | = \left | U  \right | - \left (\left | X \right | +  \left | Y\right | +  \left | Z\right | -  \left | X \cap Y\right | -  \left | X \cap Z\right | -  \left | Y\cap Z\right | +  \left | X \cap Y \cap Z\right | \right)

Where;

\left | U\right | = The number of ways the 3 pairs of siblings can sit on the 7 chairs = 7!

\left | X\right | = The number of ways x₁ and x₂ can sit together on the 7 chairs = 2 × 6!

\left | Y\right | = The number of ways y₁ and y₂ can sit together on the 7 chairs = 2 × 6!

\left | Z\right | = The number of ways z₁ and z₂ can sit together on the 7 chairs = 2 × 6!

\left | X \cap Y\right | = The number of ways x₁ and x₂ and y₁ and y₂ can sit together on the 7 chairs = 2 × 2 × 5!

\left | X \cap Z\right | = The number of ways x₁ and x₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\left | Y \cap Z\right | = The number of ways y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 5!

\left | X \cap Y \cap Z\right | = The number of ways x₁ and x₂,  y₁ and y₂ and z₁ and z₂ can sit together on the 7 chairs = 2 × 2 × 2 × 4!

Therefore, we get;

\left | X^c \cap Y^c \cap Z^c  \right | = 7! - (2×6! + 2×6! + 2×6! - 2 × 2 × 5! - 2 × 2 × 5! - 2 × 2 × 5! + 2 × 2 × 2 × 4!)

\left | X^c \cap Y^c \cap Z^c  \right | = 5,040 - 3072 = 1,968

The number of ways where the three siblings don't sit together given as \left | X^c \cap Y^c \cap Z^c  \right |  = 1,968

5 0
3 years ago
The points
const2013 [10]

Answer:

A

Step-by-step explanation:

The points

The points

A (3, 8),

B (6, 8),

C (6, 3),

D (5, 3)

need to be transformed to points

A'' (–3, 1),

B'' (–6, 1),

C'' (–6, –4),

D'' (–5, –4).

What transformations are made to make Building 4?

7 0
3 years ago
The equation of a line is y=-5/8x
Lesechka [4]

Answer:

B)  slope of the line   \frac{-5}{8}  ;Y- intercept is none

slope of the line   m = \frac{-5}{8}

Y- intercept is none

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given equation of the line   y = \frac{-5}{8} x

The equation of the straight line in slope - intercept form

                        y = m x + c

                        y = \frac{-5}{8} x+0

slope of the line   m = \frac{-5}{8}

Y- intercept is none

6 0
2 years ago
Classify Angle 1 &amp; Angle 2 by choosing the correct term from the choices below.
r-ruslan [8.4K]

Answer:

vertical

Step-by-step explanation:

did the test

5 0
2 years ago
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