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The center is  (1, - 3)

The major axis is along yand is 26 units long  .......the major vertices are correct  !!!!

The minor axis is along x and is 14 units long .....the minor vertices are

(1 - 7, -3)  = ( -6, -3)     and    ( 1 + 7, -3)  = (8, -3)

The focal length from the center  =  sqrt [ 169 - 49 ]  = sqrt [ 120 ]  = 2sqrt30) units

So....the foci  =  ( 1, -3 +2sqrt(30) )   and ( 1, - 3 - 2sqrt (30) )

Here's a graph :  https://www.desmos.com/calculator/gojbznlt3x

a. (4, -3)

c.  (5, 2)

These two points - along with the given ones - form a rectangle

See the graph here : https://www.desmos.com/calculator/vgumnvzzia

Second one      x^2 + y  =  25      y = x+3

Using the same idea.....

x^2 + (x + 3) = 25

x^2 + x + 3  = 25       subtract 25 from both sides

x^2 + x - 22 = 0         add 22 to both sides

x^2 + x  = 22          complete the square on x

x^2 + x + 1/4  = 22 + 1/4

(x + 1/2)^2  =  89/4   take both roots

x + 1/2  = ±√89 / 2      subtract 1/2 from both sides

x = ±√89 / 2 - 1/2

And y  =   x + 3  =   ±√89 / 2 - 1/2 + 3   =   ±√89 / 2 - 1/2 + 6/2  =   ±√89 / 2 + 5/2

So  (x , y)  =   (  ±√89 / 2 - 1/2 , ±√89 / 2 + 5/2 )

OK...first one     x^2 - y^2  = 12      and  y = x - 2

Put the secnd into the first for y  and we have

x^2 - ( x - 2)^2  = 12

x^2 - (x^2 - 4x + 4)  = 12

x^2 - x^2 + 4x - 4  = 12

4x - 4  = 12      add 4 to both sides

4x = 16    divide both sides by 4

x =  4

And y  =   x - 2  =   (4) - 2  =   2

So   (x, y)  = (4, 2)

EDIT TO CORRECT A PREVIOUS ERROR>>>>>thanks, heureka  !!!

Thank you so much for your help! I truly appreciate it!!

Second  one.....we have the points  (-2, - 2)    (-1, 3) (2, 2)

Distance between   (-2, -2)  and (-1, 3)  =  sqrt [ ( -2 - - 1)^2 + (-2 - 3)^2 ] = sqrt [ (-1)^2 + (-5)^2 ] =

sqrt [ 1 + 25]  =  sqrt (26)

Distance between (-2, -2)  and (2, 2)  = sqrt [ ( -2 - 2)^2 + (-2 - 2)^2 ]  = sqrt [ (-4)^2 + (-4)^2 ] =

sqrt [ 16 + 16 ]  =  sqrt (32)  =  4sqrt(2)

Distance between  (-1,3)  and (2, 2)  = sqrt [ ( -1 - 2)^2 + ( 3 - 2)^2 ]  = sqrt [ (-3)^2 + (1)^2 ]  =

sqrt [ 9 + 1 ]  =  sqrt(10)

So.....the perimeter  =     sqrt (26) + 4sqrt(2) + sqrt(10) ≈  13.92 units

If UT is a perpendicular bisector of NW....T must be the midpoint of  NW

So....the midpoint of NW  =

[ (-4 + 2) / 2 , ( 3 + 5) / 2 ]  =   (-2/2 , 8/2) = (-1, 4)  = T

Check this.....slope of NW  =   [ 5 - 3] / [ 2 - - 4 ]  =  2 / 6  =  1/3

Slope of  UT  =  [ 1 - 4 ]/  [ 0, -  -1]   =  -3/1  =  -3

Since NW and UT have negative reciprocal slopes....they are also perpendicular

Write it out

(2/3)^2*4^0*3^-2

4/9*1*1/9

Can you solve it from here?

You are very welcome!

:P

I already solved this question as well. I got the same answer as you did.

\(x \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = 0\\ x \not \in \mathbb{Z} \Rightarrow \lfloor x \rfloor + \lfloor -x \rfloor = -1\)

Can you solve this question, and let me know what you got? I ended up with 6.13888 as the diameter.

A container of milk is in the shape of a cylinder with a height of 12 centimeters. If the container
holds 355 cubic containers of milk, what is the diameter of the container?

k=1;n=1; a=if((60^n + k*71^n) %1441==0, goto3, goto4);printn; n++; k++;if(n<=1000, goto2, 0);if(k<1000, goto2, discard=0;

The smallest positive ineger for k = 263

I'm pretty sure that I'm doing the same assignment as you. I just got this question answered. The answer is square. Basically, what shape do the points form? When the points are put into Desmos graphing calculator, it forms a square.

sort of I can see that they are perpendicular, but I am confused. Geometry is just realy hard for me to comprehend.

The formula is pi*d. Because of this, we need to figure out 3.14*3.24. This is equal to 10.1736.

The circumference is ~10.17m.

~~Hypotenuisance

3:5    is   3+5 = 8 units

2 + 3/8 (4-2) =   2 6/8 = 2 3/4  for x

-3 + 3/8 (2- -3) = -3+ 15/8 = - 1 1/8 for y

parallelogram area = base x height = 120 x 100 = 12 000 sq miles     1 500 000 people / 12 000 sq mile  = 1500/12= 125 ppl/sq mile

calculate the area of the triangle   1/2  6 x 8   = 24    then subtract the missing small squares   24 - 7 = 17 sq units

Slope of the line between (-5,-2)  and  (-4,2)   is    rise/run = 4/1 = 4

slope from (-4.2) to (4,0)  is      rise/run = -2/8 = -1/4 

     does that give you a clue?

Thanks!

Congratulations, Ruubirr!!

~~Hypotenuisance