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Rzqust [24]
4 years ago
9

explain step by step how to solve. please point out any similarities in the steps used for each question

Mathematics
1 answer:
Mamont248 [21]4 years ago
6 0
#1
m∠A=180 - 115 - 24 = 41°

By the law of sines:

b/sinB = a/sinA  ⇒  
b = (a*sinB)/sinA = (21*sin24°)/sin41° = (21*0.4067)/0.656 ≈ 13

c/sinC = a/sinA  ⇒  
c = (a*sinC)/sinA = (21*sin115°)/sin41° = (21*0.9063)/0.656 ≈ 29


#2
m∠C=180 - 119 - 27 = 34°

By the law of sines:

b/sinB = a/sinA  ⇒  
b = (a*sinB)/sinA = (13*sin119°)/sin27° = (13*0.8746)/0.454 ≈ 25

c/sinC = a/sinA  ⇒  
c = (a*sinC)/sinA = (13*sin34°)/sin27° = (13*0.5592)/0.454 ≈ 16


#3
m∠C=180 - 57 - 37 = 86°

By the law of sines:

c/sinC = a/sinA  ⇒  
c = (a*sinC)/sinA = (11*sin86°)/sin57° = (11*0.9976)/0.8387 ≈ 13.1
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sally is on a scavenger hunt. a clue tells her to walk 100 steps due south from the starting point and then walk west when she g
Sophie [7]

Answer:

She should take 112 steps west  

Step-by-step explanation:

* Lets explain the relation between the four directions

- North and South on the same line by in opposite directions

- East and West on the same line by in opposite directions

- East and West are perpendicular to the North and South

* Now lets study the situation i the problem

- Sally 100 steps due to South from the starting point

- Then she walk West when she gets the next clue

- The distance between her starting point and ending point is 150 steps

∵ The South is perpendicular to the West

- Lets consider her trip is a right angle triangle ABC, where AB

 her steps South and BC her steps West and AC the distance

 between her starting point and ending point

∵ AB = 100

∵ AC = 150

∵ m∠B = 90°

- By using Pythagoras theorem

∵ BC = √(AC² - AB²)

∴ BC = √(150² - 100²) = 50√5 = 111.8 steps

* She should take 112 steps west  

8 0
3 years ago
A car is 180 inches long. A truck is 75% longer than the car. How long is the truck?
nasty-shy [4]

Answer:

The answer is 315 inches

Step-by-step explanation:

180+75%

4 0
2 years ago
If m<BEG = (19x + 3)° and m<EGC = (m<GCB + 4x)°, which of the following statements is true about quadrilateral BEGC? Se
viktelen [127]

Answer:

The sum of all exterior angles of BEGC is equal to 360° ⇒ answer F only

Step-by-step explanation:

* Lets revise some facts about the quadrilateral

- Quadrilateral is a polygon of 4 sides

- The sum of measures of the interior angles of any quadrilateral is 360°

- The sum of measures of the exterior angles of any quadrilateral is 360°

* Lets solve the problem

- DEGC is a quadrilateral

∵ m∠BEG = (19x + 3)°

∵ m∠EGC = (m∠GCB + 4x)°

∵ The sum of the measures of its interior angles is 360°

∴ m∠BEG + m∠EGC + m∠GCB + m∠CBE = 360

∴ (19x + 3) + (m∠GCB + 4x) + m∠GCB + m∠CBE = 360 ⇒ add the like terms

∴ (19x + 4x) + (m∠GCB + m∠GCB) + m∠CBE + 3 = 360 ⇒ -3 from both sides

∴ 23x + 2m∠GCB + m∠CBE = 375

∵ The sum of measures of the exterior angles of any quadrilateral is 360°

∴ The statement in answer F is only true

3 0
3 years ago
What is the reciprocal of 1/x^3
Gennadij [26K]

Answer:

x^3

Step-by-step explanation:

reciprocal is 1/(given value)

1/(1/x^3)

=x^3

4 0
3 years ago
What is infinite ?<br> i want an extremely detailed answer for 100 points
Andru [333]

Answer:

infinite adjective

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in·​fi·​nite | \ ˈin-fə-nət  \

Definition of infinite (Entry 1 of 2)

1: extending indefinitely : ENDLESS

infinite space

2: immeasurably or inconceivably great or extensive : INEXHAUSTIBLE

infinite patience

3: subject to no limitation or external determination

4a: extending beyond, lying beyond, or being greater than any preassigned finite value however large

infinite number of positive numbers

b: extending to infinity

infinite plane surface

c: characterized by an infinite number of elements or terms

an infinite set

an infinite series

infinite noun

Definition of infinite (Entry 2 of 2)

: something that is infinite (as in extent, duration, or number)

Other Words from infinite

Synonyms & Antonyms

More Example Sentences

Learn More about infinite

Other Words from infinite

Adjective

infiniteness noun

Synonyms & Antonyms for infinite

Synonyms: Adjective

bottomless, boundless, endless, fathomless, horizonless, illimitable, immeasurable, immensurable, indefinite, limitless, measureless, unbounded, unfathomable, unlimited

Antonyms: Adjective

bounded, circumscribed, confined, definite, finite, limited, restricted

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Examples of infinite in a Sentence

Adjective

an infinite series of numbers

She has infinite patience when she's dealing with children.

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Recent Examples on the Web: Adjective

So that in that infinite potential of emptiness, the form falls away and the formless blossoms into this dance of the elements.

— New York Times, "The Topanga Tea Ceremony," 6 Dec. 2019

The numbers these researchers used global multithread computing to crack were 240 digits long, and there are infinite prime numbers for cryptographers to choose from for the entire future.

— Caroline Delbert, Popular Mechanics, "Scientists Crack Longest, Most Complex Encryption Key Ever," 6 Dec. 2019

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'infinite.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of infinite

Adjective

14th century, in the meaning defined at sense 1

Noun

15th century, in the meaning defined above

History and Etymology for infinite

Adjective

Middle English infynyt, borrowed from Anglo-French & Latin; Anglo-French infinit, borrowed from Latin infīnītus "indefinite, having no limit, endless," from in- IN- entry 1 + fīnītus "specific, definite, having bounds or limits" — more at FINITE

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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