Use the diagram to solve for the three variables so that the quadrilateral will be a rhombus. show all of your work for full credit.

Step-by-step explanation:

Each triangle is a right triangle, and all are congruent. So ...

  90 -m∠CAB = (1/2)m∠CDA

  90 -(4x +33) = (1/2)(12x +34)

  57 -4x = 6x +17 . . . . . . . eliminate parentheses

  40 = 10x . . . . . . . . . . . . .add 4x-17

  4 = x

We also have ...

  2m∠CAD = m∠BCD

  2(3z +28) = 10z +28

  6z +56 = 10z +28 . . . . . eliminate parentheses

  28 = 4z . . . . . . . . . . . . . .subtract 6z+28

  7 = z . . . . . . . . . . . . . . . . divide by 4

Since BC = CD ...

  x = y = 4

The values of the three variables are ...

  x = 4, y = 4, z = 7.

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.