Ask a New Question
Menu

The graph shows the number of gallons in a wading pool that is being drained. Using the points (1,160)

and (3,80)
as (x1,y1)
and (x2,y2)
, what is the rate of change in the number of gallons in the pool after each hour has passed?

(1 point)
Responses

−40
gal./hr.
negative 40 gal./hr.

40 gal./hr.

−140
gal./hr.
negative Start Fraction 1 over 40 End Fraction gal./hr.

140
gal./hr.
Start Fraction 1 over 40 End Fraction gal./hr.

11 answers

To find the rate of change in the number of gallons in the wading pool over the time period between the two points, you can use the formula for the slope of a line, which is:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Given the points \((x_1, y_1) = (1, 160)\) and \((x_2, y_2) = (3, 80)\), you can substitute the values into the formula:

\[ \text{slope} = \frac{80 - 160}{3 - 1} = \frac{-80}{2} = -40 \]

So, the rate of change in the number of gallons in the pool after each hour has passed is:

\[ \boxed{-40 \text{ gal./hr.}} \]

Which formula can be used to find the slope of a line from two points (x1,y1)
and (x2,y2)
?(1 point)
Responses

y2−y1x2−x1
Start Fraction y subscript 2 baseline minus y subscript 1 baseline over x subscript 2 baseline minus x subscript 1 baseline End Fraction

y2+y1x2+x1
Start Fraction y subscript 2 baseline plus y subscript 1 baseline over x subscript 2 baseline plus x subscript 1 baseline End Fraction

x2−x1y2−y1
Start Fraction x subscript 2 baseline minus x subscript 1 baseline over y subscript 2 baseline minus y subscript 1 baseline End Fraction

y2y1−x2x1
Start Fraction y subscript 2 baseline over y subscript 1 baseline End Fraction minus Start Fraction x subscript 2 baseline over x subscript 1 baseline End Fraction

The correct formula to find the slope of a line from two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

So, the corresponding response would be:

\[ \text{Start Fraction } y_2 - y_1 \text{ over } x_2 - x_1 \text{ End Fraction} \]

This represents the change in \(y\) (the vertical change) over the change in \(x\) (the horizontal change).

Which is true of the University of Georgia?
(1 point)
Responses

It was founded by the first President of the United States.
It was founded by the first President of the United States.

It was the first African American university in the country.
It was the first African American university in the country.

It was the first state-funded institution of higher education in the country.
It was the first state-funded institution of higher education in the country.

It provided education for the first three governors of the state of Georgia.
It provided education for the first three governors of the state of Georgia.

The correct statement about the University of Georgia is:

It was the first state-funded institution of higher education in the country.

The University of Georgia, founded in 1785, holds this distinction and is considered a pioneer in public higher education in the United States.

Which of the following statements best describes the event that became known as the Yazoo land fraud?
(1 point)
Responses

The governor of Georgia gave away much of Georgia’s unsettled land to personal friends.
The governor of Georgia gave away much of Georgia’s unsettled land to personal friends.

Several Georgia legislators were bribed into selling some of the state’s western lands for pennies an acre.
Several Georgia legislators were bribed into selling some of the state’s western lands for pennies an acre.

The judicial branch of Georgia was given favors in exchange for striking down a law limiting land sales.
The judicial branch of Georgia was given favors in exchange for striking down a law limiting land sales.

Several large land companies were selling land to Georgia settlers even though the companies did not own the land.

The statement that best describes the event known as the Yazoo land fraud is:

Several Georgia legislators were bribed into selling some of the state’s western lands for pennies an acre.

The Yazoo land fraud occurred in the late 18th century when Georgia legislators were involved in a scandal involving the sale of vast tracts of land in present-day Mississippi and Alabama to land companies at a very low price, allegedly due to bribery and corruption. This event led to significant controversy and was later repealed, resulting in legal battles and long-lasting effects on land ownership in Georgia.

Which of these describes the Headright System? (1 point)
Responses

Free land was given to white heads of households over 21
Free land was given to white heads of households over 21

Free land was given to white men and slaves who fought during the Civil War.
Free land was given to white men and slaves who fought during the Civil War.

A barter and trade system that was established for anyone with a family or for soldiers who wished to own land.
A barter and trade system that was established for anyone with a family or for soldiers who wished to own land.

Land was sold to heads of households who could pay a penny per acre.
Land was sold to heads of households who could pay a penny per acre.

The statement that best describes the Headright System is:

Free land was given to white heads of households over 21.

The Headright System was a land allocation system established in Georgia in the 18th century to encourage settlement by granting land to white male heads of households, typically over the age of 21. This system allowed individuals to acquire significant amounts of land, which was central to the expansion and settlement of the state.

Which methods did Georgia use to distribute land in the late 1700s and early 1800s?
(1 point)
Responses

collective bargaining and issuing bonds
collective bargaining and issuing bonds

speculation and sharecropping
speculation and sharecropping

the headright system and the land lottery
the headright system and the land lottery

the land-use plan and the embargo system

The methods that Georgia used to distribute land in the late 1700s and early 1800s were:

the headright system and the land lottery.

The Headright System allowed white male heads of households to receive land grants, while the Land Lottery system was introduced later as a way to distribute land more fairly and randomly among eligible white males, giving them the chance to win land parcels.