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3 years ago

What set of transformations is performed on LMNO to form L’ M’ N’ O’ ?

Mathematics

2 answers:

Zinaida [17]3 years ago

6 0

Answer:

its the third one

Sunny_sXe [5.5K]3 years ago

6 0

Answer:

A) A 90 degree counterclockwise rotation about the origin followed by a translation 1 unit to the left

Step-by-step explanation:

The formula to do a 90 degree counterclockwise rotation is (x, y) to (y, -x) so if the ordered pair is (5, 3) and you were to rotate it counterclockwise it would be (3, -5). Once you do this to all of the values, you are one unit to the right of what you should be, so then you would have to translate it 1 to the left in order to match up both of the trapezoids.

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The formula for the surface area of a rectangular prism with a square base is SA = 2s2 + 4sh. What is the surface area of this r

Harman [31]

Answer:

Step-by-step explanation:

Step 1: Given data

Side of the rectangular prism (s): 3

Height of the rectangular prism (h): 6

Step 2: Calculate the surface area (SA) of the base

We will use the following expression, replacing the values for s and h.

SA = 2 × s² + 4 × s × h

SA = 2 × 3² + 4 × 3 × 6 = 90

The units are not provided but the SA should have the same units as s and h, but raised to the power of 2.

7 0

2 years ago

Four universities - 1, 2, 3, and 4 - are participating in a holiday basketball tournament. In first round, 1 will play 2 and 3 w

tia_tia [17]

Answer:

Part A. {S} = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 4123, 4132, 4213, 4231}

Part B. {A} = {1324, 1342, 1423. 1432}

Part C. {B} = {2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

Part D.

(A∪B) = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

(A∩B) = ∅

{A'} = {2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 4123, 4132, 4213, 4231}

Step-by-step explanation:

A. All possible outcomes

There are four teams, each play a semi final where 1 and 2 plays against each other while 3 and 4 plays against each other. Winner of the first semi final can be either 1 or 2 therefore they both can not be in the championship game or in the losers game at the same time same goes for the other semi final.

Using this explanation (1324 denotes: 1 beats 2 and 3 beats 4 in first-round games and then 1 beats 3 and 2 beats 4), All possible outcomes are

{S} = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 4123, 4132, 4213, 4231}

B. Event A in which 1 wins the tournament

From {S} we only have to write the outcomes in which 1 is the first number in 4digit combinations given in part A

{A} = {1324, 1342, 1423. 1432}

C. Event B in which 2 gets into championship game

From {S} we only have to write the outcomes in which 2 is either the first or second digit in 4digit combinations given in part A

{B} = {2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

D. Outcomes in (A∪B), (A∩B) and A'

I. (A∪B)

(A∪B) means A union B therefore all we have to do is combine all the members of A and B

(A∪B) = {1324, 1342, 1423, 1432} ∪{2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

(A∪B) = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

II. (A∩B)

(A∩B) means A intersection B in which we have to find the common members of A and B. If there are no common members then the result of (A∩B) is a null set.

(A∩B) = {1324, 1342, 1423, 1432} ∩ {2314, 2341, 2413, 2431, 3214, 3241, 4213, 4231}

(A∩B) = ∅

III. {A'}

A' means A compliment, in other words it can be described as all the possible outcomes that are not part of A. So all we do is to subtract outcomes of A from the total possible outcomes S

{A'} = {S} - {A}

{A'} = {1324, 1342, 1423, 1432, 2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 4123, 4132, 4213, 4231} - {1324, 1342, 1423. 1432}

{A'} = {2314, 2341, 2413, 2431, 3124, 3142, 3214, 3241, 4123, 4132, 4213, 4231}

7 0

3 years ago

a rectangle has a length 3 meters more than three times the width. the area of the rectangle is less than 90 meters squared. wri

Natasha2012 [34]

Answer: -6<x<5

Step-by-step explanation:

Given

Length is 3 m more than three times the width

Suppose width is x