Answer:
Unit rate
Step-by-step explanation:
unit rate: A rate is a ratio that is used to compare different kinds of quantities.
Answer:
![\large\boxed{(x-8)^2+(y-6)^2=6^2\to(x-8)^2+(y-6)^2=36}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%28x-8%29%5E2%2B%28y-6%29%5E2%3D6%5E2%5Cto%28x-8%29%5E2%2B%28y-6%29%5E2%3D36%7D)
Step-by-step explanation:
The standard form of an equation of a circle:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
<em>(h, k)</em><em> - center</em>
<em>r</em><em> - radius</em>
We have the center (8, 6) → h = 8, k = 6,
and endpoints of a radius (8, 6) & (8, 0).
The formula of a distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substitute:
![r=\sqrt{(0-6)^2+(8-8)^2}=\sqrt{(-6)^2+0^2}=\sqrt{36}=6](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%280-6%29%5E2%2B%288-8%29%5E2%7D%3D%5Csqrt%7B%28-6%29%5E2%2B0%5E2%7D%3D%5Csqrt%7B36%7D%3D6)
Finally:
![(x-8)^2+(y-6)^2=6^2](https://tex.z-dn.net/?f=%28x-8%29%5E2%2B%28y-6%29%5E2%3D6%5E2)
Answer:
Step-by-step explanation:
9514 1404 393
Answer:
x = 12
Step-by-step explanation:
Sides of similar figures are proportional, so ...
AB/FE = BC/EC
x/6 = 10/5
x = 6·(10/5) . . . multiply by 6
x = 12
18-carat gold is 75 percent pure, and gold ratings are proportional, you know that...
<span>18 / 75 = 24 / x </span>
<span>X needs to have the same relationship to 24 that 75 has to 18. </span>
To solve, simply cross-multiply (multiply the numerator in one fraction by the denominator in the opposite fraction, and vice versa). The resulting products will be equal. Then, simply divide away the remaining coefficient to solve for x.
<span>18 / 75 = 24 / x </span>
<span>18x = 24 * 75 = 1800 </span>
<span>x = 1800 / 18 = 100 </span>
<span>x = 100 </span>
<span>Therefore, the purity of 24 carat gold is 100%.</span>