tertre

First...realize that 180-150=30 degrees, since it is a straight line. Since the angles in a triangle add up to 180, the angle in the topmost triangle is 180-30-45=105. Again, there is a straight line, so 180-105=95 degrees(one of the angles in the quadrilateral.)

Next, by opposite angle, the triangle to the leftmost has angles 30 degrees and 50 degrees, so the remaining measure is 180-30-50=100 degrees. And, 180-100=80 degrees.

Now, that we filled up the angles in the quadrilateral and trying to solve for x, we get 360-130-95-80=55 degrees.

I sometimes forget that, too! 

Thank you! 

Rearranging, we have 3x + 4y = x - 8y + 24= 3x-x=-12y+24.

Therefore, 2x=-12y+24 and \(x=-6y+12.\)

The perimeter of the semi-circle is half the circumference plus the diameter.

In this case, we have three as the radius, so the diameter is 6 inches long, and the perimeter around the arc is \(\frac{2\pi*3}{2}=3\pi.\) Thus, the answer is \(\boxed{3\pi+6}.\)

Part (b) is using \((x+b)^2.\)

Remember that \((x+b)^2=x^2+b^2+2xb.\)

Therefore, plugging in the values, we get \((-\frac{7}{2})^2=x^2+b^2+2(4).\)

Simplifying, \(\frac{49}{4}-8=x^2+b^2\), and that is equal to \(\frac{49}{4}-\frac{32}{4}=\boxed{\frac{17}{4}}.\)

Hope that helped,

tertre 

I think you mean -2.8.

Part (a) is just Vieta's.

The sum of the roots is -b/a, or in the quadratic equation, it is -7/2.

On the other hand, the product of the roots is c/a, so the answer is 8/2=4.

Hope that helped,

tertre 

Happy belated birthday, Alan!

Have fun! 

54-10x<20+7x

34<17x

17x>34

x>2

(C).

Lol!