recall that the radius is the distance from the center of a circle to any point on the circle.
we know the center is at -16,-14, and we know that -8,-8 is a point on the circle, so the distance between both must be the radius.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-8-(-16)]^2+[-8-(-14)]^2} \\\\\\ r=\sqrt{(-8+16)^2+(-8+14)^2}\implies r=\sqrt{8^2+6^2} \\\\\\ r=\sqrt{100}\implies \boxed{r=10} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0A%28%5Cstackrel%7Bx_1%7D%7B-16%7D~%2C~%5Cstackrel%7By_1%7D%7B-14%7D%29%5Cqquad%0A%28%5Cstackrel%7Bx_2%7D%7B-8%7D~%2C~%5Cstackrel%7By_2%7D%7B-8%7D%29%5Cqquad%20%5Cqquad%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7Bradius%7D%7Br%7D%3D%5Csqrt%7B%5B-8-%28-16%29%5D%5E2%2B%5B-8-%28-14%29%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B%28-8%2B16%29%5E2%2B%28-8%2B14%29%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B8%5E2%2B6%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B100%7D%5Cimplies%20%5Cboxed%7Br%3D10%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-16}{ h},\stackrel{-14}{ k})\qquad \qquad radius=\stackrel{10}{ r} \\\\\\\ [x-(-16)]^2+[y-(-14)]^2=10^2\implies \blacktriangleright (x+16)^2+(y+14)^2=100 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%0A%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%0A%5Cqquad%0Acenter~~%28%5Cstackrel%7B-16%7D%7B%20h%7D%2C%5Cstackrel%7B-14%7D%7B%20k%7D%29%5Cqquad%20%5Cqquad%0Aradius%3D%5Cstackrel%7B10%7D%7B%20r%7D%0A%5C%5C%5C%5C%5C%5C%5C%0A%5Bx-%28-16%29%5D%5E2%2B%5By-%28-14%29%5D%5E2%3D10%5E2%5Cimplies%20%5Cblacktriangleright%20%28x%2B16%29%5E2%2B%28y%2B14%29%5E2%3D100%20%5Cblacktriangleleft)
Let's solve your equation step-by-step.<span><span><span>4<span>(<span>x+1</span>)</span></span>+8</span>=24</span>
<span />Step 1: Simplify both sides of the equation. <span><span><span>4<span>(<span>x+1</span>)</span></span>+8</span>=24</span>
<span /><span>Simplify: (Show steps) </span><span><span><span><span><span>(4)</span><span>(x)</span></span>+<span><span>(4)</span><span>(1)</span></span></span>+8</span>=24</span> (Distribute)<span><span><span><span> 4x</span>+4</span>+8</span>=24</span><span><span><span>(<span>4x</span>)</span>+<span>(<span>4+8</span>)</span></span>=24</span>(Combine Like Terms)<span><span><span> 4x</span>+12</span>=24</span><span><span><span>4x</span>+12</span>=24</span>
<span />Step 2: Subtract 12 from both sides. <span><span><span><span>4x</span>+12</span>−12</span>=<span>24−12</span></span><span><span>4 x</span>=12</span>
<span />Step 3: Divide both sides by 4.<span><span><span><span><span>4x</span>4</span></span></span>=<span><span><span>124 </span></span></span></span><span>x=<span>3</span></span>
Answer:
the corner is not 90 degrees
Step-by-step explanation:
To confirm if the corner is 90 degrees, we would use Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
16² + 20² =
256 + 400 =656
find the square root of 656
= 25.6 feet
If the corner was 90 degrees the diagonal should be 25.6 feet and not 29 feet
To calculate the range of the given function we first need to calculate for the inverse of the function;
y=sqrt(x)-5
this can be written as:
y+5=sqrt(x)
From the above equation we can conclude that we can get the squaring of all values of x such that:
x≥-5
otherwise we won't get any square root since the square roots of negative numbers will complex numbers;
thus we conclude that the range of the function is {y∈R: y≥-5}
since -4 is included in this set, then our answer is option [A]
