<h3>
Answer: Choice C</h3>
Why isn't choice C a function? It's because we have the input x = 4 lead to more than one output at the same time (y = 5 and y = -5). A function must have all allowed inputs lead to exactly one output.
The diagram for choice C shows we have the points (4,5) and (4,-5). If we plotted those two points, then a vertical line forms, which will show this relation fails the vertical line test.
Choices A, B, and D do not have this happen where a certain input leads to multiple outputs at once; therefore, these are all functions. For the tables A and D, note there aren't any repeated x values. If you were to convert choice C into table form, then you would have the x value 4 repeat itself.
Answer:
1. 
2. 
3. The first one represents Dale's commission
Explanation:
1. The composition of the function
means that you first apply the function g(x) and then f(x) on the output of g(x).
That is:
- f(x) = 0.05x
- g(x) = x - 3000
2. The composition of the function
means that you first apply the function f(x) and then g(x) on the output of f(x).
That is:
3. Which one represents Dale's commission
To calculate Dales's commision you must subtract $3,000 from the sales, to find the sales over $3000. That is: x - 3,000, which is the function g(x).
Therefore, you first use g(x).
Then, you must multiply the output of g(x) by 0.05 to find the 5% of the sales over $3,000. That is: 0.05(g((x)) = 0.05(x - 3000) = 0.05x - 150.
Therefore, the composition that represents Dale's commission is the first one:
A <span>counterclockwise rotation of 270º about the origin is equivalent to a </span><span>clockwise rotation of 90º about the origin.
Given a point (4, 5), the x-value, i.e. 4 and the y-value, i.e. 5 are positive, hence the point is in the 1st quadrant of the xy-plane.
A clockwise rotation of </span><span>90º about the origin of a point in the first quadrant of the xy-plane will have its image in the fourth quadrant of the xy-plane. Thus the x-value of the image remains positive but the y-value of the image changes to negative.
Also the x-value and the y-value of the original figure is interchanged.
For example, given a point (a, b) in the first quadrant of the xy-plane, </span><span>a counterclockwise rotation of 270º about the origin which is equivalent to a <span>clockwise rotation of 90º about the origin will result in an image with the coordinate of (b, -a)</span>
Therefore, a </span><span>counterclockwise rotation of 270º about the origin </span><span>of the point (4, 5) will result in an image with the coordinate of (5, -4)</span> (option C)
Answer:
Henry has $19, Dan has $57, and Melissa has $11
Step-by-step explanation:
Let x represent how much money Henry has
Since Dan has 3 times what Henry has, his amount is 3x
Since Melissa has $8 less than Henry, her amount is x - 8
Create an equation that sets these 3 values equal to 87, then solve for x
(x) + (3x) + (x - 8) = 87
5x - 8 = 87
5x = 95
x = 19
So, Henry has $19
Find how much Dan has by multiplying 19 by 3
19(3)
= 57
Find how much Melissa has by subtracting 8 from 19
19 - 8
= 11
So, Henry has $19, Dan has $57, and Melissa has $11
