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)
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.
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?
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.
For each function, what is the output of the given input?
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.
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
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."
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.