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3 years ago

Suppose U= {1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P= {1, 2, 3, 4}. What is P?

1 answer:

4 0

Did you mean P' ? The letter P with a tick mark after it. If so, then start with set U and erase any number you find in set P

We start with
{1,2,3,4,5,6,7,8}
and we erase the following: 1,2,3,4
since those numbers are in set P

P = {1,2,3,4}
P ' = {5, 6, 7, 8}

The set P' is the complement of set P. It is, in a sense, the opposite of set P. It contains everything that P doesn't have.

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Geometry problem help! Please refer to the image below...

Vinil7 [7]

Answer:

A. 1/3

B. √10

C. -1, 1

D. √8, 6

E. congruent and opposite pairs parallel

F. perpendicular, not congruent

G. rhombus, explanation below

Step-by-step explanation:

Hey there! I'm happy to help!

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Slope is the rise over the run. Let's look at F to G.

We are going from -1 to 2 on our x-axis (run), so our run is 3 units.

Our rise is 1 unit as we go from 2 to 3 on the y-axis.

$slope=\frac{rise}{run} =\frac{1}{3}$

This slope is the same for all of the sides.

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We will use the distance formula (which is basically just the Pythagorean Theorem) to calculate the length of each side. Let's go between F and G again, but this distance is the same for all the sides.

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+1)^2+(3-2)^2 } \\\\\sqrt{(3)^2+(1)^2 }\\\\\sqrt{9+1 }\\\\\sqrt{10}$

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The diagonals are the lines that connect the non-adjacent vertices.

Our two diagonals are FH and GE.

-----------------------------

FH

We go from x-value -1 to 1 from F to H, so our run is 2.

We go from y-value 2 to 0. so our rise is -2.

$slope=\frac{rise}{run} =-\frac{2}{2} =-1$

-----------------------------

GE

We go from x-value -2 to 2 from E to G, so our run is 4.

We go from y-value -1 to 3. so our rise is 4.

$slope=\frac{rise}{run} =\frac{4}{4} =1$

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Let's use the distance formula on each of our diagonals.

-----------------------------

FH

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-1,2)\\\\(x_2,y_2)=(1,0)\\\\\\\sqrt{(1+1)^2+(0-2)^2 } \\\\\sqrt{(2)^2+(-2)^2 }\\\\\sqrt{4+4 }\\\\\sqrt{8}$

-----------------------------

GE

$\sqrt{(x_{2}-x_1)^2+(y_{2}-y_1)^2 } \\\\(x_1,y_1)=(-2,-1)\\\\(x_2,y_2)=(2,3)\\\\\\\sqrt{(2+2)^2+(3+1)^2 } \\\\\sqrt{(4)^2+(4)^2 }\\\\\sqrt{16+16 }\\\\\sqrt{36}\\\\6$

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They are congruent as they all have the same length (√10) and the opposite sides are parallel as they have the same slope (1/3)

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They are perpendicular diagonals as their slopes are negative reciprocals (1 and -1), and they are not congruent as they have different lengths (√8 and 6).

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Parallelogram- quadrilateral with opposite pairs of parallel sides.

Rhombus- a parallelogram with four equal sides

Square- a rhombus with four right angles

We can see that this is a parallelogram as we saw that the opposite sides are parallel due to having the same slope, and the perpendicular diagonals show that as well. This is also a rhombus because if we use that distance formula on all the sides, it will be the same. It is not a square though because it does not have four right angles, so this is a rhombus.

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Have a wonderful day and keep on learning!

8 0

3 years ago

How would 350 percent be written as a simplified fraction

Sauron [17]

Divide by 100. 350/100=3.5 which is 3 and 1/2

4 0

3 years ago

Read 2 more answers

You are given that claims are reported according to a homogeneous Poisson process. Starting from time zero, the expected waiting

maxonik [38]

Answer:

1.732

Step-by-step explanation:

You are given that claims are reported according to a homogeneous Poisson process

LetX be the waiting time from 0 to second claim

X is Poisson with averageof 3 hours.

We know in a Poisson distribution the mean = variance

Hence average waiting time = mean = 3

This will also be equal to var(x)

Var(x) = mean of Poisson distribution= 3

Hence standard deviation = square root of variance

= $\sqrt{3} \\=1.732$

7 0

3 years ago

Here is a picture of an older version of the flag of Great Britain. There is a rigid transformation that takes Triangle 1 to Tri

Akimi4 [234]

i just need so i’m not sure

7 0

3 years ago

In 16-19, use the equations to compete the tables. (Picture provided)

aalyn [17]

Answer:

16. 20, 25

17. 3, 4

18. 5, 7

19. 6.5, 5, 3.5, 2, 0.5

Step-by-step explanation:

The way you would solve this is by replacing the variable with an x-value, the answer would be the y-value.

8 0

2 years ago