Answer:
120°
Step-by-step explanation:
Set up a proportion of the circle circumference and angle to the arc length and central angle x:
![\frac{18}{360} = \frac{6}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B18%7D%7B360%7D%20%3D%20%5Cfrac%7B6%7D%7Bx%7D)
Solve for x:
![18x = 2160](https://tex.z-dn.net/?f=18x%20%3D%202160)
![x = 120](https://tex.z-dn.net/?f=x%20%3D%20120)
Measurement of the central angle of the arc is 120°
Answer:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
Step-by-step explanation:
The vertex form of a parabola is given by:
, where V(h,k) is the vertex of the parabola.
The given parabola has vertex (1,1).
This implies that:
.
Put these values into the vertex form equation.
![\implies y=a(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3Da%28x-1%29%5E2%2B1)
The y-intercept of this parabola is: (0,-3).
This point lies on the parabola hence it must satisfy its equation.
![\implies -3=a(0-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%280-1%29%5E2%2B1)
![\implies -3=a(-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%28-1%29%5E2%2B1)
![\implies -3=a(1)+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%281%29%2B1)
![\implies -3=a+1](https://tex.z-dn.net/?f=%5Cimplies%20-3%3Da%2B1)
![\implies -3-1=a](https://tex.z-dn.net/?f=%5Cimplies%20-3-1%3Da)
![\implies -4=a](https://tex.z-dn.net/?f=%5Cimplies%20-4%3Da)
The equation now becomes
![\implies y=-4(x-1)^2+1](https://tex.z-dn.net/?f=%5Cimplies%20y%3D-4%28x-1%29%5E2%2B1)
To find the x-intercept, put y=0 into the equation:
![\implies -4(x-1)^2+1=0](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%2B1%3D0)
![\implies -4(x-1)^2=-1](https://tex.z-dn.net/?f=%5Cimplies%20-4%28x-1%29%5E2%3D-1)
Divide through by -4.
![\implies \frac{-4(x-1)^2}{-4}=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7B-4%28x-1%29%5E2%7D%7B-4%7D%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{-1}{-4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B-1%7D%7B-4%7D)
![\implies (x-1)^2=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cimplies%20%28x-1%29%5E2%3D%5Cfrac%7B1%7D%7B4%7D)
Take plus or minus square root of both sides.
![\implies x-1=\pm \sqrt{\frac{1}{4}}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%7D)
![\implies x-1=\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x-1%3D%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
![\implies x=1\pm \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%5Cpm%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1+ \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%2B%20%5Cfrac%7B1%7D%7B2%7D)
or ![\implies x=1 \frac{1}{2}](https://tex.z-dn.net/?f=%5Cimplies%20x%3D1%20%5Cfrac%7B1%7D%7B2%7D)
Therefore the x-intercepts are:
![(\frac{1}{2},0),(\frac{3}{2},0)](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C0%29%2C%28%5Cfrac%7B3%7D%7B2%7D%2C0%29)
To the nearest hundredth, we have ![0.50,0),(1.50,0)](https://tex.z-dn.net/?f=0.50%2C0%29%2C%281.50%2C0%29)
The correct answer is D.) |−14.6 − (−5.2)|
This is the case because we are first subtracting the value of the two numbers from each other. Then we're taking the absolute value so we can find distance, which is always expressed in a positive number.
Answer:50-55
According to the trend
Step-by-step explanation:
The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the <span>difference</span> of the corresponding numbers. So the answer is B.