homework 4 4 answer key

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4.1 Linear Functions

m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; decreasing because m < 0. m < 0.

y = − 7 x + 3 y = − 7 x + 3

H ( x ) = 0.5 x + 12.5 H ( x ) = 0.5 x + 12.5

Possible answers include ( − 3 , 7 ) , ( − 3 , 7 ) , ( − 6 , 9 ) , ( − 6 , 9 ) , or ( − 9 , 11 ) . ( − 9 , 11 ) .

( 16 , 0 ) ( 16 , 0 )

• ⓐ f ( x ) = 2 x ; f ( x ) = 2 x ;
• ⓑ g ( x ) = − 1 2 x g ( x ) = − 1 2 x

y = – 1 3 x + 6 y = – 1 3 x + 6

4.2 Modeling with Linear Functions

ⓐ C ( x ) = 0.25 x + 25 , 000 C ( x ) = 0.25 x + 25 , 000 ⓑ The y -intercept is ( 0 , 25 , 000 ) ( 0 , 25 , 000 ) . If the company does not produce a single doughnut, they still incur a cost of $25,000.

ⓐ 41,100 ⓑ 2020

21.57 miles

4.3 Fitting Linear Models to Data

54 ° F 54 ° F

150.871 billion gallons; extrapolation

4.1 Section Exercises

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

d ( t ) = 100 − 10 t d ( t ) = 100 − 10 t

The point of intersection is ( a , a ) . ( a , a ) . This is because for the horizontal line, all of the y y coordinates are a a and for the vertical line, all of the x x coordinates are a . a . The point of intersection is on both lines and therefore will have these two characteristics.

y = 3 5 x − 1 y = 3 5 x − 1

y = 3 x − 2 y = 3 x − 2

y = − 1 3 x + 11 3 y = − 1 3 x + 11 3

y = − 1.5 x − 3 y = − 1.5 x − 3

perpendicular

f ( 0 ) = − ( 0 ) + 2 f ( 0 ) = 2 y − int : ( 0 , 2 ) 0 = − x + 2 x − int : ( 2 , 0 ) f ( 0 ) = − ( 0 ) + 2 f ( 0 ) = 2 y − int : ( 0 , 2 ) 0 = − x + 2 x − int : ( 2 , 0 )

h ( 0 ) = 3 ( 0 ) − 5 h ( 0 ) = − 5 y − int : ( 0 , − 5 ) 0 = 3 x − 5 x − int : ( 5 3 , 0 ) h ( 0 ) = 3 ( 0 ) − 5 h ( 0 ) = − 5 y − int : ( 0 , − 5 ) 0 = 3 x − 5 x − int : ( 5 3 , 0 )

− 2 x + 5 y = 20 − 2 ( 0 ) + 5 y = 20 5 y = 20 y = 4 y − int : ( 0 , 4 ) − 2 x + 5 ( 0 ) = 20 x = − 10 x − int : ( − 10 , 0 ) − 2 x + 5 y = 20 − 2 ( 0 ) + 5 y = 20 5 y = 20 y = 4 y − int : ( 0 , 4 ) − 2 x + 5 ( 0 ) = 20 x = − 10 x − int : ( − 10 , 0 )

Line 1: m = –10 Line 2: m = –10 Parallel

Line 1: m = –2 Line 2: m = 1 Neither

Line 1 :   m = – 2       Line 2 :   m = – 2       Parallel Line 1 :   m = – 2       Line 2 :   m = – 2       Parallel

y = 3 x − 3 y = 3 x − 3

y = − 1 3 t + 2 y = − 1 3 t + 2

y = − 5 4 x + 5 y = − 5 4 x + 5

y = 3 x − 1 y = 3 x − 1

y = − 2.5 y = − 2.5

y = 3 y = 3

x = − 3 x = − 3

Linear, g ( x ) = − 3 x + 5 g ( x ) = − 3 x + 5

Linear, f ( x ) = 5 x − 5 f ( x ) = 5 x − 5

Linear, g ( x ) = − 25 2 x + 6 g ( x ) = − 25 2 x + 6

Linear, f ( x ) = 10 x − 24 f ( x ) = 10 x − 24

f ( x ) = − 58 x + 17.3 f ( x ) = − 58 x + 17.3

• ⓐ a = 11,900 , b = 1000.1 a = 11,900 , b = 1000.1
• ⓑ q ( p ) = 1000 p – 100 q ( p ) = 1000 p – 100

y = − 16 3 y = − 16 3

x = a x = a

y = d c – a x – a d c – a y = d c – a x – a d c – a

y = 100 x – 98 y = 100 x – 98

x < 1999 201 , x > 1999 201 x < 1999 201 , x > 1999 201

$45 per training session.

The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.

The slope is –400. this means for every year between 1960 and 1989, the population dropped by 400 per year in the city.

4.2 Section Exercises

Determine the independent variable. This is the variable upon which the output depends.

To determine the initial value, find the output when the input is equal to zero.

6 square units

20.01 square units

P ( t ) = 75 , 000 + 2500 t P ( t ) = 75 , 000 + 2500 t

(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.

Ten years after the model began

W ( t ) = 0.5 t + 7.5 W ( t ) = 0.5 t + 7.5

( − 15 , 0 ) ( − 15 , 0 ) : The x -intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. ( 0 , 7 . 5 ) ( 0 , 7 . 5 ) : The baby weighed 7.5 pounds at birth.

At age 5.8 months

C ( t ) = 12 , 025 − 205 t C ( t ) = 12 , 025 − 205 t

( 58 . 7 , 0 ) : ( 58 . 7 , 0 ) : In roughly 59 years, the number of people inflicted with the common cold would be 0. ( 0 , 12 , 0 25 ) ( 0 , 12 , 0 25 ) Initially there were 12,025 people afflicted by the common cold.

y = − 2 t +180 y = − 2 t +180

In 2070, the company’s profit will be zero.

y = 3 0 t − 3 00 y = 3 0 t − 3 00

(10, 0) In the year 1990, the company’s profits were zero

During the year 1933

• ⓐ 696 people
• ⓒ 174 people per year
• ⓓ 305 people
• ⓔ P(t) = 305 + 174t
• ⓕ 2,219 people
• ⓐ C(x) = 0.15x + 10
• ⓑ The flat monthly fee is $10 and there is a $0.15 fee for each additional minute used

P(t) = 190t + 4,360

• ⓐ R ( t ) = − 2 . 1 t   +   16 R ( t ) = − 2 . 1 t   +   16
• ⓑ 5.5 billion cubic feet
• ⓒ During the year 2017

More than 133 minutes

More than $42,857.14 worth of jewelry

More than $66,666.67 in sales

4.3 Section Exercises

When our model no longer applies, after some value in the domain, the model itself doesn’t hold.

We predict a value outside the domain and range of the data.

The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.

61.966 years

Interpolation. About 60 ° F . 60 ° F .

This value of r indicates a strong negative correlation or slope, so C This value of r indicates a strong negative correlation or slope, so C

This value of r indicates a weak negative correlation, so B This value of r indicates a weak negative correlation, so B

Yes, trend appears linear because r = 0. 985 r = 0. 985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

y = 1 . 64 0 x + 13 . 8 00 , y = 1 . 64 0 x + 13 . 8 00 , r = 0. 987 r = 0. 987

y = − 0.962 x + 26.86 ,       r = − 0.965 y = − 0.962 x + 26.86 ,       r = − 0.965

y = − 1 . 981 x + 6 0. 197; y = − 1 . 981 x + 6 0. 197; r = − 0. 998 r = − 0. 998

y = 0. 121 x − 38.841 , r = 0.998 y = 0. 121 x − 38.841 , r = 0.998

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; ( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; Yes, the function is a good fit.

( 189 .8 , 0 ) ( 189 .8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.

y = 0.00587 x + 1985 .4 1 y = 0.00587 x + 1985 .4 1

y = 2 0. 25 x − 671 . 5 y = 2 0. 25 x − 671 . 5

y = − 1 0. 75 x + 742 . 5 0 y = − 1 0. 75 x + 742 . 5 0

Review Exercises

y = − 3 x + 26 y = − 3 x + 26

y = 2 x − 2 y = 2 x − 2

Not linear.

( –9 , 0 ) ; ( 0 , –7 ) ( –9 , 0 ) ; ( 0 , –7 )

Line 1: m = − 2 ; m = − 2 ; Line 2: m = − 2 ; m = − 2 ; Parallel

y = − 0.2 x + 21 y = − 0.2 x + 21

More than 250

y = − 3 00 x + 11 , 5 00 y = − 3 00 x + 11 , 5 00

• ⓑ 100 students per year
• ⓒ P ( t ) = 1 00 t + 17 00 P ( t ) = 1 00 t + 17 00

Extrapolation

y = − 1.294 x + 49.412 ;   r = − 0.974 y = − 1.294 x + 49.412 ;   r = − 0.974

Practice Test

y = −1.5x − 6

y = −2x − 1

Perpendicular

(−7, 0); (0, −2)

y = −0.25x + 12

Slope = −1 and y-intercept = 6

y = 875x + 10,625

• ⓑ dropped an average of 46.875, or about 47 people per year
• ⓒ y = −46.875t + 1250

In early 2018

y = 0.00455x + 1979.5

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Eureka Math Grade 4 Module 4 Lesson 6 Answer Key

Engage ny eureka math 4th grade module 4 lesson 6 answer key, eureka math grade 4 module 4 lesson 6 practice sheet answer key.

Explanation: In the above image, we can see that the angle D is less than 90°. So the angle D will be the acute angle. And we can see that angle C is less than 90°. So the angle D will be the acute angle. And we can see that angle E is greater than 90°, so the angle is an obtuse angle.

Eureka Math Grade 4 Module 4 Lesson 6 Problem Set Answer Key

Explanation: By measuring the angle with protractor we will get the angle as 36° and it is an acute angle as the angle is less than 90°.

Explanation: By measuring the angle with protractor we will get the angle as 90° and it is a right angle as the angle is  90°.

Explanation: By measuring the angle with protractor we will get the angle as 155° and it is an obtuse angle as the angle is greater than 90°.

Explanation: By measuring the angle with protractor we will get the angle as 150° and it is an obtuse angle as the angle is greater than 90°.

Explanation: By using three different protractors we have got the same angle measurement, which is 29°.

b. What do you notice about the measurement of the above angle using each of the protractors? Answer: We have noticed that the measure of the angle is the same using each of the protractors.

Eureka Math Grade 4 Module 4 Lesson 6 Exit Ticket Answer Key

Use any protractor to measure the angles, and then record the measurements in degrees.

Explanation: By measuring the angle with protractor we will get the angle as 105° and it is an obtuse angle as the angle is greater than 90°.

Eureka Math Grade 4 Module 4 Lesson 6 Homework Answer Key

Explanation: In the above image, we can see that the angle is less than 90°. So the angle would be 60° or above but less 90° and the angle is called as acute angle.

Explanation: In the above image, we can see that the angle is greater than 90°. So the angle would be above 90° and the angle is called as obtuse angle.

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Federal criminal investigation opened into Key Bridge crash

The FBI has opened a criminal investigation focusing on the massive container ship that brought down the Francis Scott Key Bridge in Baltimore last month — a probe that will look at least in part at whether the crew left the port knowing the vessel had serious system problems, according to two U.S. officials familiar with the matter.

Authorities are reviewing the events leading up to the moment when the Dali, a 985-foot Singapore-flagged ship, lost power while leaving the Port of Baltimore and slammed into one of the bridge’s support pillars, said the officials, speaking on the condition of anonymity to discuss the ongoing probe.

Just after dawn Monday, dozens of law enforcement officials dressed in all black began arriving at the Dali — where the crew has remained since the crash — pulling up to the ship’s bow in numerous boats and climbing aboard using a ladder. The FBI later confirmed that agents were on board, and the Justice Department said authorities were conducting a “court-approved search.”

Baltimore bridge collapse

The news of the criminal investigation, which one official said is being handled by the U.S. attorney’s office in Maryland, came the same day that multiple private law firms separately announced that they had been retained to represent the Baltimore mayor’s office and some of the men who were working construction on the bridge when it collapsed. The moves signal an escalating effort to seek accountability and determine what caused the crash that left six of the eight men dead, a question that both the independent National Transportation Safety Board and the Coast Guard’s Marine Board of Investigation have been working to answer in separate inquiries since the collapse March 26.

Jennifer Gabris, an NTSB spokeswoman, said that the board’s investigation would continue and that a preliminary report was expected in early May.

The Coast Guard’s Marine Board of Investigation will pause evidence collection, but it will still be able to analyze evidence it has already gathered to inform safety efforts such as new regulations or inspection campaigns, according to a Coast Guard official who spoke on the condition of anonymity because of the ongoing investigations.

An attorney representing Grace Ocean Private Ltd., which owns the Dali, and Synergy Marine Pte Ltd., the ship’s manager, did not respond to a request for comment.

President Biden and Maryland Gov. Wes Moore (D) have both previously said that they intend to hold accountable any parties deemed potentially liable for the destruction of the bridge, but they have yet to announce any legal action. Baltimore Mayor Brandon M. Scott said the city has hired DiCello Levitt and Saltz Mongeluzzi Bendesky Trial Lawyers to work with the city’s own legal team to take “decisive action” against the owner, charter, operator and manufacturer of the Dali and “any other potentially liable third parties.”

Erek L. Barron, the U.S. Attorney for Maryland, said his office does not comment on criminal investigations but asserted in a statement that “the public should know, whether it’s gun violence, civil rights abuse, financial fraud, or any other threat to public safety or property we will seek accountability for anyone who may be responsible.”

His office did not respond to questions about what issues the Dali may have experienced before its port departure and how the actions of the crew might be criminal.

Systems issues on vessels such as the Dali can become the basis for criminal charges if they are discovered by those responsible for the ship but not properly remedied before a ship departs, said Todd Lochner, an Annapolis-based admiralty attorney. Lochner said investigators could be trying to weight the legal standard of whether the Dali was “reasonably fit for the intended voyage” when it left the Port of Baltimore en route to Sri Lanka.

“You may not send a vessel to sea in a known unseaworthy condition,” Lochner said, though what exactly constitutes as “unseaworthy” in this case would probably be debated in court.

“There are all kinds of things that can lead to an unseaworthy condition,” he said.

On Capitol Hill last week, NTSB Chair Jennifer Homendy said her investigators were focusing on the Dali’s electrical issues, adding that her team believes there may be a connection between the ship’s lights going out and the power loss to its engines in the moments before the crash.

Homendy said Hyundai, the South Korea-based company that manufactured the engine-room equipment used on the Dali, sent experts to the United States to download electrical data from the ship and look at its circuit breakers.

Attorneys from Stewart Miller Simmons Trial Attorneys and Kreindler & Kreindler said Monday they will be conducting their own independent investigation into the Key Bridge collapse on behalf of the victims they are representing: Alejandro Hernandez Fuentes, José López and Julio Adrian Cervantes Suarez. Fuentes and López died after they fell into the Patapsco River when the bridge collapsed. Cervantes, who also fell into the frigid waters, is the only person to survive the fall.

The attorneys said they intend to fight the petition filed in federal court on April 1 by the Dali’s owner and manager, asking a judge to cap how much money responsible parties could be asked to pay in liabilities. One of the attorneys, Justin Miller, said their probe is intended to complement those conducted by the NTSB, the Coast Guard and the FBI. “The details that we need are not the details that they need,” he said.

L. Chris Stewart, another lawyer for the three victims, said that in past cases, the existence of a federal criminal investigation has proved “very effective” in the pursuit of civil accountability. “It leaves no stone unturned,” Stewart said.

The victims’ lawyers said they take issue with the Dali’s owner and operator seeking to limit their liability to about $43.6 million.

“Imagine telling that to grieving families,” Stewart said, “that while they are planning a funeral, the owner of the boat is in court trying to stop the city, state and victims from filing claims.”

In the three weeks since the Dali crashed into the Key Bridge, dive teams have been able to recover four of the six people who died in the collapse, including Maynor Suazo Sandoval , Dorlian Castillo Cabrera and Fuentes. A fourth person was recovered over the weekend, officials with Unified Command announced Monday, but he was not identified per the request of his family.

Authorities had previously identified the three other missing members of the construction crew as López and two other men, Miguel Luna and Carlos Hernandez, all of whom are presumed dead.

The recovery mission was paused after days of searching the Patapsco River’s cold and murky waters. Officials have said they are now focusing on clearing the river of debris and relocating the Dali to shore, but at still looking for those who died among the wreckage.

James Harkness, chief engineer for the Maryland Transportation Authority and a member of the Unified Command, said Monday the cleanup is proceeding on the timetable laid out in recent weeks.

He said officials plan to have a 35-foot deep temporary channel open in the coming weeks and clear the entire shipping channel by the end of May. Harkness said crews have removed 1,000 tons of debris from the river. He said 31 ships have used two small temporary channels to get into and out of the Port of Baltimore.

Justin Jouvenal and Ian Duncan contributed to this report.