To determine if y varies directly with x, we can check if the ratio of y to x remains constant.
First, let's calculate the ratio of y to x for each data point:
For the first data point: 6.4/4 = 1.6
For the second data point: 11.2/7 = 1.6
For the third data point: 16/10 = 1.6
For the fourth data point: 20.8/13 = 1.6
Since the ratio of y to x is constant (1.6) for all data points, we can conclude that y varies directly with x.
To find the constant of variation k, we can choose any data point and divide y by x:
Using the first data point: k = 6.4/4 = 1.6
Therefore, the equation for the direct variation is y = 1.6x.
x y
4 6.4
7 11.2
10 16
13 20.8
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
(3 points)
27 answers
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Find the value of y for a given value of x, if y varies directly with x.
If y=−252
when x = 84, what is y when x = 74?
Find the value of y for a given value of x, if y varies directly with x.
If y=−252
when x = 84, what is y when x = 74?
To find the value of y when x = 74, we can use the equation for direct variation.
We know that y varies directly with x, so we can write the equation as:
y = kx
To find the value of k, we can use the given information when x = 84 and y = -252.
-252 = k * 84
To solve for k, divide both sides by 84:
-252/84 = k
k = -3
Now that we know the value of k, we can substitute it into the equation:
y = -3x
To find y when x = 74, substitute x = 74 into the equation:
y = -3 * 74
y = -222
Therefore, when x = 74, y = -222.
We know that y varies directly with x, so we can write the equation as:
y = kx
To find the value of k, we can use the given information when x = 84 and y = -252.
-252 = k * 84
To solve for k, divide both sides by 84:
-252/84 = k
k = -3
Now that we know the value of k, we can substitute it into the equation:
y = -3x
To find y when x = 74, substitute x = 74 into the equation:
y = -3 * 74
y = -222
Therefore, when x = 74, y = -222.
For each function, what is the output of the given input?
For f(x)=4x+7
, find f(4)
(2 points)
For f(x)=4x+7
, find f(4)
(2 points)
To find f(4), we need to substitute the input x = 4 into the function f(x) = 4x + 7.
f(4) = 4(4) + 7
= 16 + 7
= 23
Therefore, when the input is 4, the output of the function f(x) = 4x + 7 is 23.
f(4) = 4(4) + 7
= 16 + 7
= 23
Therefore, when the input is 4, the output of the function f(x) = 4x + 7 is 23.
Identify the two houses of the United States Congress.(1 point)
The two houses of the United States Congress are:
1. The House of Representatives
2. The Senate
1. The House of Representatives
2. The Senate
Which statement best summarizes the role of Congress as outlined in Article I of the Constitution?(1 point)
The statement that best summarizes the role of Congress as outlined in Article I of the Constitution is:
"To make laws and represent the people of the United States."
"To make laws and represent the people of the United States."
Which statement best summarizes the role of Congress as outlined in Article I of the Constitution?(1 point)
Responses
Congress is a democratic governing body responsible for ratifying treaties that are negotiated by the president.
Congress is a democratic governing body responsible for ratifying treaties that are negotiated by the president.
Congress is a democratic governing body responsible for levying taxes and interpreting laws.
Congress is a democratic governing body responsible for levying taxes and interpreting laws.
Congress is a democratic governing body with impeachment power and the ability to enforce laws.
Congress is a democratic governing body with impeachment power and the ability to enforce laws.
Congress is a democratic governing body responsible for creating a federal budget and making national laws.
Congress is a democratic governing body responsible for creating a federal budget and making national laws.
Responses
Congress is a democratic governing body responsible for ratifying treaties that are negotiated by the president.
Congress is a democratic governing body responsible for ratifying treaties that are negotiated by the president.
Congress is a democratic governing body responsible for levying taxes and interpreting laws.
Congress is a democratic governing body responsible for levying taxes and interpreting laws.
Congress is a democratic governing body with impeachment power and the ability to enforce laws.
Congress is a democratic governing body with impeachment power and the ability to enforce laws.
Congress is a democratic governing body responsible for creating a federal budget and making national laws.
Congress is a democratic governing body responsible for creating a federal budget and making national laws.
The statement that best summarizes the role of Congress as outlined in Article I of the Constitution is:
"Congress is a democratic governing body responsible for creating a federal budget and making national laws."
"Congress is a democratic governing body responsible for creating a federal budget and making national laws."
Which type of visual aid would you construct to best explain the legislative process?(1 point)
Responses
a T-Chart showing the process of the passage of the bill in both houses and then moving on for the president’s approval
a T-Chart showing the process of the passage of the bill in both houses and then moving on for the president’s approval
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
a Venn diagram showing the process of the passage of the bill in both houses and then the president’s approval
a Venn diagram showing the process of the passage of the bill in both houses and then the president’s approval
a flowchart showing the passage of the bill in both houses and then moving on for the president’s approval
a flowchart showing the passage of the bill in both houses and then moving on for the president’s approval
Responses
a T-Chart showing the process of the passage of the bill in both houses and then moving on for the president’s approval
a T-Chart showing the process of the passage of the bill in both houses and then moving on for the president’s approval
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
a Venn diagram showing the process of the passage of the bill in both houses and then the president’s approval
a Venn diagram showing the process of the passage of the bill in both houses and then the president’s approval
a flowchart showing the passage of the bill in both houses and then moving on for the president’s approval
a flowchart showing the passage of the bill in both houses and then moving on for the president’s approval
The best type of visual aid to construct to explain the legislative process would be:
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
a flowchart showing the process of the passage of the bill in the House of Representatives and then the Senate
How can Congress override the president’s veto of a bill?(1 point)
Responses
with a two-thirds majority in both houses
with a two-thirds majority in both houses
with a two-thirds majority in conference committees
with a two-thirds majority in conference committees
with a simple majority in both houses
with a simple majority in both houses
by using the filibuster
Responses
with a two-thirds majority in both houses
with a two-thirds majority in both houses
with a two-thirds majority in conference committees
with a two-thirds majority in conference committees
with a simple majority in both houses
with a simple majority in both houses
by using the filibuster
To override the president's veto of a bill, Congress can do so with a two-thirds majority in both houses.
Which of the following statements best explains the importance of taxing by Congress?(1 point)
Responses
The importance of taxing is to eliminate personal consumer debt and loans.
The importance of taxing is to eliminate personal consumer debt and loans.
The importance of taxing is to raise revenue for the federal government.
The importance of taxing is to raise revenue for the federal government.
The importance of taxing is to help all citizens fund and pay for personal living expenses.
The importance of taxing is to help all citizens fund and pay for personal living expenses.
The importance of taxing is to decrease the national debt.
Responses
The importance of taxing is to eliminate personal consumer debt and loans.
The importance of taxing is to eliminate personal consumer debt and loans.
The importance of taxing is to raise revenue for the federal government.
The importance of taxing is to raise revenue for the federal government.
The importance of taxing is to help all citizens fund and pay for personal living expenses.
The importance of taxing is to help all citizens fund and pay for personal living expenses.
The importance of taxing is to decrease the national debt.
The statement that best explains the importance of taxing by Congress is:
"The importance of taxing is to raise revenue for the federal government."
"The importance of taxing is to raise revenue for the federal government."
Power of the House of Representatives Power of the Senate
A. Initiate revenue bills Choose the president if no majority in Electoral College
B. Impeach federal officials Confirm presidential appointments
C. Convict federal officials in impeachment trial Ratify treaties
D. Negotiate treaties Declare war
Use the chart to identify the correct powers of each congressional chamber as outlined in Article I of the Constitution.
A. Initiate revenue bills Choose the president if no majority in Electoral College
B. Impeach federal officials Confirm presidential appointments
C. Convict federal officials in impeachment trial Ratify treaties
D. Negotiate treaties Declare war
Use the chart to identify the correct powers of each congressional chamber as outlined in Article I of the Constitution.
According to the chart:
Power of the House of Representatives:
A. Initiate revenue bills
B. Impeach federal officials
Power of the Senate:
C. Convict federal officials in impeachment trial
D. Ratify treaties
The correct powers of each congressional chamber as outlined in Article I of the Constitution are:
House of Representatives:
A. Initiate revenue bills
B. Impeach federal officials
Senate:
C. Convict federal officials in impeachment trial
D. Ratify treaties
Power of the House of Representatives:
A. Initiate revenue bills
B. Impeach federal officials
Power of the Senate:
C. Convict federal officials in impeachment trial
D. Ratify treaties
The correct powers of each congressional chamber as outlined in Article I of the Constitution are:
House of Representatives:
A. Initiate revenue bills
B. Impeach federal officials
Senate:
C. Convict federal officials in impeachment trial
D. Ratify treaties
Which of the following statements best describes how the necessary and proper clause led to Congress’s implied powers?(1 point)
Responses
The necessary and proper clause states that the Constitution is the supreme law of the land, which allowed Congress to create implied powers.
The necessary and proper clause states that the Constitution is the supreme law of the land, which allowed Congress to create implied powers.
The necessary and proper clause limits Congress’s power relative to the states in the Constitution, which created implied powers.
The necessary and proper clause limits Congress’s power relative to the states in the Constitution, which created implied powers.
The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive.
The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive.
The necessary and proper clause allows Congress to limit states’ rights, which led to Congress’s implied powers.
Responses
The necessary and proper clause states that the Constitution is the supreme law of the land, which allowed Congress to create implied powers.
The necessary and proper clause states that the Constitution is the supreme law of the land, which allowed Congress to create implied powers.
The necessary and proper clause limits Congress’s power relative to the states in the Constitution, which created implied powers.
The necessary and proper clause limits Congress’s power relative to the states in the Constitution, which created implied powers.
The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive.
The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive.
The necessary and proper clause allows Congress to limit states’ rights, which led to Congress’s implied powers.
The statement that best describes how the necessary and proper clause led to Congress's implied powers is:
"The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive."
"The necessary and proper clause allows Congress to expand upon the powers stated in the Constitution, from which implied powers derive."
How did McCulloch v. Maryland establish the implied powers doctrine?(1 point)
Responses
It allowed Congress to declare war even though it was not expressed in the Constitution.
It allowed Congress to declare war even though it was not expressed in the Constitution.
It allowed Congress to collect taxes even though it was not expressed in the Constitution.
It allowed Congress to collect taxes even though it was not expressed in the Constitution.
It allowed Congress to create a national bank even though it was not expressed in the Constitution.
It allowed Congress to create a national bank even though it was not expressed in the Constitution.
It allowed Congress to establish a post office even though it was not expressed in the Constitution.
Responses
It allowed Congress to declare war even though it was not expressed in the Constitution.
It allowed Congress to declare war even though it was not expressed in the Constitution.
It allowed Congress to collect taxes even though it was not expressed in the Constitution.
It allowed Congress to collect taxes even though it was not expressed in the Constitution.
It allowed Congress to create a national bank even though it was not expressed in the Constitution.
It allowed Congress to create a national bank even though it was not expressed in the Constitution.
It allowed Congress to establish a post office even though it was not expressed in the Constitution.
The statement that best describes how McCulloch v. Maryland established the implied powers doctrine is:
"It allowed Congress to create a national bank even though it was not expressed in the Constitution."
"It allowed Congress to create a national bank even though it was not expressed in the Constitution."
Which of the following statements best hypothesizes why the Constitution provides for expressed powers?(1 point)
Responses
Congress needed sufficient power to govern, but not unlimited power.
Congress needed sufficient power to govern, but not unlimited power.
Congress needed the power to pass laws involving taxation.
Congress needed the power to pass laws involving taxation.
Congress needed unlimited power, so the Framers provided for that.
Congress needed unlimited power, so the Framers provided for that.
Congress needed the power to add amendments to the Constitution in the future.
Congress needed the power to add amendments to the Constitution in the future.
Responses
Congress needed sufficient power to govern, but not unlimited power.
Congress needed sufficient power to govern, but not unlimited power.
Congress needed the power to pass laws involving taxation.
Congress needed the power to pass laws involving taxation.
Congress needed unlimited power, so the Framers provided for that.
Congress needed unlimited power, so the Framers provided for that.
Congress needed the power to add amendments to the Constitution in the future.
Congress needed the power to add amendments to the Constitution in the future.
The statement that best hypothesizes why the Constitution provides for expressed powers is:
"Congress needed sufficient power to govern, but not unlimited power."
"Congress needed sufficient power to govern, but not unlimited power."
Which of the following best summarizes this quote from Federalist, no. 33?
(1 point)
Responses
Allowing for implied powers by adding the elastic clause could potentially take power away from the executive branch.
Allowing for implied powers by adding the elastic clause could potentially take power away from the executive branch.
The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness.
The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness.
Expressed powers are necessary for a government to function because Congress needs a certain amount of power.
Expressed powers are necessary for a government to function because Congress needs a certain amount of power.
The elastic clause would create a tyrannical government and should not be part of the Constitution.
(1 point)
Responses
Allowing for implied powers by adding the elastic clause could potentially take power away from the executive branch.
Allowing for implied powers by adding the elastic clause could potentially take power away from the executive branch.
The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness.
The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness.
Expressed powers are necessary for a government to function because Congress needs a certain amount of power.
Expressed powers are necessary for a government to function because Congress needs a certain amount of power.
The elastic clause would create a tyrannical government and should not be part of the Constitution.
The statement that best summarizes this quote from Federalist, no. 33 is:
"The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness."
"The elastic clause would not create a tyrannical government, but enable the government to perform basic functions crucial for its effectiveness."