CPhill

This is the ceiling function shifted down 3 units

To find out which graph is correct....

Let  x  =2

ceiling (2)  - 3=   2  - 3  =  -1

Let x = 2.5

ceiling (2.5) - 3  = 3 - 3  = 0

Let x  = 3

ceiling (3) - 3   =  3 - 3  = 0

The botom right graph is the correct one....

Here's a more formal way to do this, ACG

Let  the radius of the smaller circle  = R

Then the radius of the larger circle is just the radius of the smaller circle plus the width of the track, W

So

The circumference of the smaller circle plus 10pi ft  = the circumference of the larger circle

So we have

2pi(R) + 10pi   =  2pi (R + W)

2pi (R) + 10 pi  =  2pi (R)  + 2pi(W)        subtract 2pi (R) from  both sides

10 pi  = 2pi (W)

10  = 2W

5 (feet)  = W   = width of the track

E(x)=(1-x)(6x-8)+16-9x^2

(1 - x) * 2 * (3x - 4) +  (4 - 3x) ( 4 + 3x)

-2 (1 - x) (4 - 3x)  + (4 - 3x ) (4 + 3x)   take out the GCF

(4 - 3x )  [ -2(1-x) + (4 + 3x ) ]

(4 - 3x ) [ -2 + 2x + 4 + 3x ]

(4 - 3x)  ( 5x + 2 )

1. The area of her garden is  25 * 15    = 375 ft^2

So......we can find the side of a square with the same area, thusly :

375  = side^2      take the square root of both sides

√375  =  side

So....the perimeter of the square is 4 times this  =  4√375 = 77.4 ft

2.   Area of rectangle 14 * 16  =  224

Side of square  = √224.....  15 mm   GOOD JOB  !!!!

3.   The perimeter is given by    4√ [50 *32]  = 4 √1600  = 4*40  =  160 ft

You may have forgoten to multiply the side of the square by 4 to get the perimeter  ???

Nice, qualitystreet   !!!

The scale factor  of the larger triangle to the smaller  =  6/4  =  3/2

The  area of the larger triangle  =

(Area of smaller triangle )  *  (scale factor)^2  =

20    *  (3/2)^2  =

20  * 9/4  =

(20/4) * 9  =

5 * 9   =

45 cm^2

Area of rectangle  = 15 * 27   = 405 mm^2

Area of square   =  side^2   .......so...

405 = side^2       take the square root of both sides

√405  =  side  ≈  20.1 mm

V  =  2(3.14)r^2h

Soving for r^2  

V = 6.28 r^2 h     divide both sides by   6.28h

V / [ 6.28h]  = r^2

Solving for h

v = 6.28r^2h     divide both sides by 6.28r^2

V / [ 6.28r^2 ]  =  h

The face forms a triangle.....Area of triangle  =    (1/2) base * height

The slant height is the height of the triangle....so....

75  = (1/2) base *(30)

75 = 15 * base        divide both sides by  15

5 m  =   base 

So.....a side of  the base  = 5m 

We can choose  any 2  of the 5....so....the number of possible groups  is

C(5,.2)   =    10 different groups