Step-by-step explanation:
4a(a-x)+x(a-x)
[4a]2-4ax+ax-(x)2
(4a)2-3ax-(x)2
Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Cerrena [4.2K]
Answer:
5.
Step-by-step explanation:
There are 5 numbers in the data you have listed that are in between the numbers 15-20.
Cost of the spa treatment = $42
Percentage of sales tax = 6%
Percentage of tips = 20%
Normally the tips amount is calculated before adding sales tax.
Then
Amount of tips given = (20/100) * 42
= (1/5) * 42
= 8.40 dollars
Amount of sales tax taken = (6/100) * 42
= 252/100
= 2.52 dollars
Then
The total amount spent for spa treatment = (42 + 8.40 + 2.52) dollars
= 52.92 dollars
So we can see that $52.92 has been spent in total for spa treatment and this amount includes a sales tax of $2.52 and a tip of $8.40.
The coordinate of the circumcenter of a triangle is (1,3).
Here we have to find the coordinates of the circumcenter of a triangle.
Given data:
The vertices of the triangle are:
A = (0,1)
B = ( 2,1)
C= ( 2,5)
The formula to find the distance between the two points:
Distance = ![\sqrt{(x2 - x1)^{2} + (y2-y1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%28x2%20-%20x1%29%5E%7B2%7D%20%2B%20%28y2-y1%29%5E%7B2%7D%20%7D)
In the same manner distance between AB, BC, and AC are:
AB = ![\sqrt{(2-0)^{2} + (1-1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%282-0%29%5E%7B2%7D%20%2B%20%281-1%29%5E%7B2%7D%20%20%7D)
= 2
BC = ![\sqrt{(2-2)^{2} + (5-1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%282-2%29%5E%7B2%7D%20%2B%20%285-1%29%5E%7B2%7D%20%20%7D)
= 4
AC = ![\sqrt{(2-0)^{2} + (5-1)^{2} }](https://tex.z-dn.net/?f=%5Csqrt%7B%282-0%29%5E%7B2%7D%20%2B%20%285-1%29%5E%7B2%7D%20%7D)
= 2√5
So by the Pythagoras, we get to know that the triangle is a right-angle triangle.
The circumcenter of a right-angle triangle is the midpoint of the hypotenuse.
Midpoint of AC = (0+2)/2 , (1+5)/2
= 2/2, 6/2
= 1,3
Therefore the coordinate of the circumcenter is (1,3).
To know more about the circumcenter refer to the link given below:
brainly.com/question/21299234
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