Answer:
C
Step-by-step explanation:
To simplify this equation,
-x+10<2
-10 from both sides
-x<-8
Take out the negative
x<8
This means x is less than 8
For ≤ and ≥ , use a closed dot to indicate the number itself is part of the solution.
For < and >, use an open circle to indicate the number itself is not part of the solution.
In this case you use a open circle and becasue x is less than 8, the arrow pointing left is correct.
Answer:
Option C.
The distance from the point to the circle is 6 units
Step-by-step explanation:
we know that
The distance between the circle and the point will be the difference of the distance of the point from the center of circle and the radius of the circle
step 1
Find the center and radius of the circle
we have
![x^{2} +y^{2}-8y=0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2By%5E%7B2%7D-8y%3D0)
Convert to radius center form
Complete the square
![x^{2} +(y^{2}-8y+16)=0+16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28y%5E%7B2%7D-8y%2B16%29%3D0%2B16)
Rewrite as perfect squares
![x^{2} +(y-4)^{2}=16](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%28y-4%29%5E%7B2%7D%3D16)
so
The center is the point (0,4)
The radius is
![r^{2}=16\\r=4\ units](https://tex.z-dn.net/?f=r%5E%7B2%7D%3D16%5C%5Cr%3D4%5C%20units)
step 2
Find the distance of the point from the center of circle
the formula to calculate the distance between two points is equal to
![d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28y2-y1%29%5E%7B2%7D%2B%28x2-x1%29%5E%7B2%7D%7D)
we have
(6,-4) and (0,4)
substitute the values
![d=\sqrt{(4+4)^{2}+(0-6)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%284%2B4%29%5E%7B2%7D%2B%280-6%29%5E%7B2%7D%7D)
![d=\sqrt{(8)^{2}+(-6)^{2}}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%288%29%5E%7B2%7D%2B%28-6%29%5E%7B2%7D%7D)
![d=\sqrt{100}\ units](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B100%7D%5C%20units)
![d=10\ units](https://tex.z-dn.net/?f=d%3D10%5C%20units)
step 3
Find the difference of the distance of the point from the center of circle and the radius of the circle
![10\ units-4\ units=6\ units](https://tex.z-dn.net/?f=10%5C%20units-4%5C%20units%3D6%5C%20units)
therefore
The distance from the point to the circle is 6 units
see the attached figure to better understand the problem
It is all real numbers because when graphing it, it would go infinitely in both directions.
Answer:
you would weigh 140 lbs
Step-by-step explanation:
x= weeks in time
165-5x=y y being your final weight in lbs
◩ Hello! ◩
3x-5<u>></u>7
move all the numbers to the left:
3x≥7+5
3x≥12
Divide both sides by 3:
x≥4
<h3>Therefore, our answer is: 4</h3>
Hope it helps!
~Just a cheerful teen
#CarryOnLearning
Answered by
![-SilentNature-](https://tex.z-dn.net/?f=-SilentNature-)