Tina described four triangles as shown below: triangle a: all sides have length 12 cm. triangle b: two sides have length 10 cm, and the included angle measures 60°. triangle c: base has length 15 cm, and base angles measure 40°. triangle d: all angles measure 60°. which triangle is not a unique triangle?

  D: All angles measure 60°. Which triangle is not a unique triangle?

Step-by-step explanation:

A triangle is uniquely specified if any of the following sets of information are known:

  where S = side, A = angle, H = hypotenuse, L = leg

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That is, all three sides, or at least one side and one angle must be specified, along with another side or angle.

If two sides and an angle are given, the angle must either be between the two sides, or opposite the longest side. (This latter condition is not generally recognized as describing a unique triangle, because the condition relating the angle and the sides is not easily summarized in an abbreviation like SSA. For a right triangle, the abbreviation is HA.)

In the HL and LL cases, we say "specific sides" because we need to know whether the given sides are both legs, or one is the hypotenuse.

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For this question, option D gives only three angles, and no sides, so no unique triangle is specified.

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The other options give unique triangles by ...

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

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step-by-step explanation: