geno3141

Make a vertical cut, dividing the object into a taller left section (12 x 5 x 6  =  360)

and a shorter right section (10 x 8 x 6  =  480)

and add these two volumes together.

64  =  8 x 8

64  =  4 x 4 x 4

As the second guest states:  the answer is 9.6.

Here is an explanation:  XY · XY  =  XB · XA   (This is the correct example of "power of a point".)

                                            9 · 9  =  XB · 15

                                                81  =  15·XB

                                                XB  =  5.4

Since   XB + BA  =  XA

            5.4 + BA  =  15

                     BA  =  9.6

-4(x + 4)  >=  x + 7

 -4x - 16  >=  x + 7                     distribute

 -5x - 16  >= 7                            subtract x

        -5x  >=  23                         add 16

          x  <=  -23/5                      divide by -5; change sense of inequality because you divided by a negative

            ( - infinity, -23/5 ]

To find the percentage decrease:

1)  Subtract the new from the original:  75 - 60  =  15

2)  Divide by the original:  15 / 75  =  0.20

3)  Turn into a decimal by multiplying by 100:  0.20 x 100  =  20.0%

In triangle(ABC),  D is the midpoint of AC,  E is the midpoint of AB,  and   F is the midpoint of BC.

Construct DE, DF, and EF.

There are 4 congruent triangles:  triangle(AED), triangle(EBF), triangle(DFC), and triangle(FDE).

Since all congruent triangles have equal areas, the area of triangle(ABC) is one-third the area of trapezoid(BCDE).

If you are using real numbers, this is impossible.

If you are using complex numbers, this is possible.

Let the three interior angles of the triangle be A', B', and C'

Then, A  =  360^o - 90^o - 90^o - A'  =  180^o - A'.

          B  =  360^o - 90^o - 90^o - B'  =  180^o - B'.

          C  =  360^o - 90^o - 90^o - C'  =  180^o - C'.

A + B + C  =  ( 180^o - A' ) + ( 180^o - B' ) + ( 180^o - C' )  =  540^o - A' - B' - C'  =  540^o - ( A' + B' + C' )

                  =  540^o - 180^o  =  360^o

The midsegment is the line segmnet MN where M is the midpoint of (1,1) and (2,8) and N is the midpoint of (5,1) and (4,8).

M = (1.5, 4.5)  and  N = (4.5, 4.5).

Now, use the slope formula.

Using the graphing equation:  y  =  a(x - h)² + k     where  (h, k) is the vertex.

The vertex of this parabola occurs at  (2, 1)     --->     y  =  a(x - 2)² + 1

It rises, so that the value of a is positive.

It has no stretching or contracting so the value of a is 1.

The equation is:  y  =  1(x - 2)² + 1     or     y  =  (x - 2)² + 1.

Now, multiply this out and simplify ...