CPhill

Here's the graph..........https://www.desmos.com/calculator/zysdb0bmhq

a)  The "vertical" intercept  is at (0, 9000)  ad the "horizontal" intercept occurs at (15, 0)

b) The vertical intercept is interpreted as the distance remaining between the cities at the start of the flight  [ where t  = 0 ].....this is 9000 miles

The horizontal intercept is the number of hours it takes to complete the trip  [ t = 15]....note that, at that time, the remaining distance between the cities = 0

c) The slope = -600.....this means that, for every hour of flight, the distance between the cities is lessened by 600 miles.....

Note the logic here :  15 hrs x 600miles per hour = 9000 miles of the whole trip covered

Hope that helps......

P.S.  -  In reality, Los Angeles to Boston is WAY LESS than 9000 miles   !!!!

Besides the date of her birthday, there are 30 more days in August........let x be the number of days after her birthday and 5x be the number of days before her birthday....then....

5x + x = 30

6x = 30    divide both sides by 6

x = 5

But, this means there are 5x = 5(5)  = 25 days before her birthday.....thus....her birthday falls on the 26th

Mmmmm.....I just did it with the calculator.....

20 km  / 1.4  cm =  d / 5.5 cm    where d is the distance we are looking for....

Cross-multiply

5.5 (20)  = 1.4 d    divide both sides by 1.4

d = about 78.57 km

He bought

6  pens @ .15 each           =    .90

1 rubber (eraser ?? )    = .21

1 calculator = 2.99

1 writing pad = 1.89

.90  + .21 + 2.99 + 1.89 = 5.99

Very nice diagram, reinout.......!!!!!!

At 10:00 the balloon's height, ( h )  =

tan 25 = h / 300  →   h = 300tan 25 = 139.89 m

At 10:02, the height is ;

h = 300tan 60  = about 519.62 m

So  in 120 seconds, the balloon  rises at

[ 519.62 - 139.89 ] / 120   = about 3.16 m/s

Remember, Melody....too many G&Ts  never mix well with pizza.....especially around Christmas.........Leave those for the reindeer....!!!!!!

x+ 2y+ 3z+ 4u=20    (1)

-x + 5 y +2 u=13      (2)

x+ y+ z+ u =10        (3)

-x+y-z+u= -2            (4)

Add (3)  and (4)   →  2y + 2u = 8 →   y + u = 4  →  y = 4 -  u  (5)

Sub this into (2)

-x + 5(4 - u) + 2u = 13 →  -x + 20 - 5u + 2u  = 13  → -x - 3u  = - 7  →   x + 3u = 7  → x  = 7 - 3u    (6)

Subbing into (1) and (4) for x and y we have the following system ;

[7 - 3u] + 2(4 - u] + 3z + 4u = 20 

[3u - 7] + [ 4 - u] - z + u = -2

Simplifying both of these, we have

-1u  + 3z =  5     (7)

 3u   - 1z   =  1

Multiply the top equation by 3 and add to the bottom, and we have

8z = 16   →  z = 2

Subbing this into (7),    -1u + 3(2)  = 5 →  -1u = -1  →  u = 1

Subbing this result into (6), we have   x = 7 - 3(1)   = 4

And subbing  u = 1 into (5), we have   y = 4 - 1  = 3

So

{x , y,  z , u }   =  { 4,  3, 2, 1 }

88ft/s = 60mph

607200ft/ hr = 607200/3600 = about 506/3 ft/s

So

60 / 88 = x / [506 / 3]    cross-multiply

[506 / 3] (60)  = 88x      divide both sides by 88

[ (506 / 3) (60) / 88 ] =  115 mph