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sweet-ann [11.9K]
2 years ago
9

If anyone could help me, it would be greatly appreciated!

Mathematics
1 answer:
Sav [38]2 years ago
7 0

Answer: x=65^{\circ}, y=65^{\circ}, z=65^{\circ}

Step-by-step explanation:

All radii of a circle are congruent, so by the base angles theorem

  • z = y = (180-50)/2 = 65.

Also, angles x and y are inscribed in the same arc, and they are thus congruent, meaning x = 65.

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Which expression has a value of 8, using only four 4s and any of the following: + , – , • , ÷, exponents, and/or parentheses?
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D. 4(4+4)-4=4(8)-4=32-4=28, not 8 incorrect


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Given that p²,q² are two roots of x²-x+16=0. <br>Form another equation with roots 1/p,1/q.
statuscvo [17]

Answer:

  x² -3/4x +1/4 = 0

Step-by-step explanation:

Consider the two equations in factored and expanded forms:

  (x -p²)(x -q²) = x² -(p²+q²)x +p²q² = 0   ⇒   p²+q² = 1, p²q² = 16

and

  (x -1/p)(x -1/q) = x² -(1/p+1/q)x +1/(pq) = 0

Consider the squares of the sum and product of roots:

  constant term: (1/(pq))² = 1/(p²q²) = 1/16   ⇒   1/(pq) = √(1/16) = 1/4

  x-term: (1/p +1/q)² = (p +q)²/(pq)² = (p² +q² +2pq)/(p²q²)

  = (p² +q²)/(p²q²) +2/(pq)

  = 1/16 +2/√16 = 9/16   ⇒   (1/p +1/q) = √(9/16) = 3/4

Then the equation with roots 1/p and 1/q is ...

  x² -3/4x +1/4 = 0

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