CPhill

The relative max of -3 occurs at about x = 1.5

The relative min of -14 occurs at about x = 4.5

Thus....#4  is the correct choice....

Rate of change from 7 - 9 =    [5760 - 1920 ] / [9 - 7] = 1920

Rate of change from 4- 6 =   [945 - 105] / [ 6 - 4 ] = 420

1920 / 420    ≈   4.57 times as great

Note that we can write this as

1 x 3/3 x 5/5 x 7/7 x.......x 1/99 =

1/99

There are  24 * 60 =  1440 minutes in a 24-hr period

The LCM of 2 and 5  = 10

So....they back up at the same time every 10 minutes

So

1440 / 10   =     144 times

Don't know that this is the correct answer, JGA....but here's my best attempt :

If we have 10 ditinct positive integers....the median is the average of the 5th and 6th data values [ assuming the we have ordered the values in increasing order from left to right ]

It's obvious that the first four integers will be 1, 2, 3 , 4

To have the smallest overall average, we need to have the 5th and 6th values as close to 10 as possible such that their average is 10.....these are 9 and 11

And the remaining integers are 12, 13, 14 and 15

So....the data set is

1,2, 3, 4, 9, 11, 12, 13, 14, 15

The median  = 10

The average = 8.4

I'll show you how to find the after-image point for one point, Kyinx.....you can figure the other three from this....

After-image point =   [ old point - center of dilation ] *scale factor + dilation center

So.....to find the new after-image point for the point (-1, 1)  we have

[ (-1, 1) - (-7, -2) ] * 2   + (-7, - 2)     =

[ 6, 3] *2   + (-7, -2)   =

(12, 6) + (-7, -2)  =

(5, 4)

Use the same proceedure for each of the other three points on the graph above

5.  An isosceles trapezoid has side lengths 13,3,13 and 14. What is the perimeter of its Varignon parallelogram?

I didn't actually know what a Varignon parallelogram was.....the parallelogram is formed by joining the midpoints of the sides of the trapezoid...

See the image below :

EFGH is the Varignon parallelogram

A = (0,0)

B = (14,0)

The height of the trapezoid is  sqrt (13^2 - 5.5^2] = sqrt (138.5)

C = (8.5, sqrt (138.75) )

D = (5.5, sqrt (138.75) )

In this case, the sides of the parallelogram are congruent....so....we only need to multiply the distance from F to H  by 4 to find ts perimeter

F =  (5.5/2 , sqrt (138)/2 ) =  (2.75, sqrt (138)/ 2 )

H = (7, 0)

So  FH  =    sqrt [  (7 - 2.75)^2 + 138/4 ]   =  sqrt ( 4.25^2 + 34.5) =

sqrt ( 18.0625 + 34.5)  =  sqrt ( 56.5625)  =  7.25

And the perimeter is 4 times this =  4 * 7.25 = 29 units

P.S. - Just wonder if it's a coincidence that the sum of the lengths of the three shortest sides of the trapezoid = the perimeter of the parallelogram????

Correct....!!!

Not quite, NSS

The legs are YZ and ZX   ⇒  "C"

1. Consecutive angles in a parallelogram are supplemental (sum to 180 degrees)

x - y = 40      implies that   x = 40 + y

Thus

 x + y = 180

(40 + y) + y = 180

2y + 40  = 180        subtract 40 from both sides

2y = 140      divide both sides by 2

y = 70°