Archers shoot down (domain) the "range"
domain is where they shoot from, range is where they shoot
Answer: 63 She finds her average resting heart rate to be 62 after 5 days. That means, average of the 5 heart rate pulse=62 If the last day was 58 and all the other days were the same.
Step-by-step explanation
5 would be an answer.<span />
To find the length of the missing side, you can use the Pythagorean Theorem, which you can only use for right triangles.
Pythagorean Theorem: a² + b² = c²
[ c is the hypotenuse or the longest side of the triangle, and a and b are the other sides, I think it doesn't matter which side ]
Plug in what you know:
b = 8
c = 14
a² + b² = c²
a² + (8)² = (14)²
a² + 64 = 196 Subtract 64 on both sides
a² = 132 Square root both sides to get "a" by itself
![\sqrt{a^2} =\sqrt{132}](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E2%7D%20%3D%5Csqrt%7B132%7D)
a =
inches
If you need to simplify more, you need to find two numbers that multiply to = 132 where one of them can be square rooted, to do so you can list the greatest common factors of 132
132: 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The only number that can be square rooted is 4, so you can do:
![a=\sqrt{4*33}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B4%2A33%7D)
![a=\sqrt{4} *\sqrt{33}](https://tex.z-dn.net/?f=a%3D%5Csqrt%7B4%7D%20%2A%5Csqrt%7B33%7D)
![a=2\sqrt{33}](https://tex.z-dn.net/?f=a%3D2%5Csqrt%7B33%7D)
With this question, it is incredibly essential that you consider each transformation separately to prevent confusion.
First, the negative on the top of the fraction indicates that there is a reflection. This means that you will be filling in quadrants II and IV rather than I and III prior to the other transformations.
Dilation is indicated by the 3 in the numerator of the fraction and will actually affect the main points marked on the graph. For the parent function y= 1/x, the coordinate (1,1) is the main point in the first quadrant and the coordinate (-1,-1) is the main point in the third quadrant. When a dilation occurs, it dilates the x value for one of the coordinates and the y-value in the other. Since a reflection has also occurred, our initial points are (-1,1) and (1,-1) so the points in the second quadrant will be (-1,3) and (-3,1) as compared to the asymptotes (multiple translations have also occurred) and the points in the fourth quadrant will be (1,-3) and (3,-1) as compared to the asymptotes.
Lastly, let's consider translations: a horizontal translation involves the addition or subtraction of a number from x in the denominator of the fraction whereas a vertical translation involves the addition or subtraction of a number from (1/x), completely separate from the fraction. Therefore, the -2 is part of a horizontal translation and the +4 is part of a vertical translation. I always tell my students that the direction of the vertical translation(up or down) will be what you would assume, but the direction of the horizontal translation (right or left) will be the exact opposite of your assumption. For this reason, the -2 would indicate a shift to the right 2 units and the +4 would indicate a shift upwards 4 units. This would result in a shift of the vertical asymptote to the right 2 units and a shift in the horizontal asymptote upwards 4 units. The horizontal asymptote is written as y = 4 and the vertical is written as x=2