Answer:
![\sqrt[n]{x}=x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
Step-by-step explanation:
The index of a radical is the denominator of a fractional exponent, and vice versa. If you think about the rules of exponents, you know this must be so.
For example, consider the cube root:
![\sqrt[3]{x}\cdot \sqrt[3]{x}\cdot \sqrt[3]{x}=(\sqrt[3]{x})^3=x\\\\(x^{\frac{1}{3}})^3=x^{\frac{3}{3}}=x^1=x](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D%3D%28%5Csqrt%5B3%5D%7Bx%7D%29%5E3%3Dx%5C%5C%5C%5C%28x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5E3%3Dx%5E%7B%5Cfrac%7B3%7D%7B3%7D%7D%3Dx%5E1%3Dx)
That is ...
![\sqrt[3]{x}=x^{\frac{1}{3}} \quad\text{radical index = fraction denominator}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%7D%3Dx%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%5Cquad%5Ctext%7Bradical%20index%20%3D%20fraction%20denominator%7D)
It's an isosceles triangle so both sides are the same. The missing side is 30
So
100%=original
25% discount
100-25=75
it is 180 sale
75%=180
find 100%
a hack is to recognize that 75/3 times 4=100 so
75%=180
divide 3
25%=60
times 4
100%=240
the real way is proportions
75:180 =100:x
75/180=100/x
multiply both sides by 180x
75x=18000
divide 75
x=240
origitnal price=$240
Answer:
<u>Properties of a rhombus used to solve the following </u>
- <em>Opposite angles are congruent</em>
- <em>Diagonals are angle bisectors</em>
- <em>Diagonals are perpendicular to each other</em>
- <em>Adjacent angles are supplementary</em>
(30)
- ∠2 = ∠3 = ∠5 = 27°
- ∠1 = ∠4 = 180° - (2*27°) = 126°
(31)
- ∠4 = 70°
- ∠1 = ∠2 = ∠3 = ∠5 = 1/2(180° - 70°) = 1/2(110°) = 55°
(32)
- ∠1 = ∠2 = ∠5 = 90° - 26° = 64°
- ∠3 = 26°
- ∠4 = 90°
bearing in mind that a <u>circle</u> means the round thing, so only the points on the round thing are ON the circle, others like the RC chord or the PQ diameter or the point C are NOT ON the circle.
