4x^3+6x^2-9x+1 is an example
4x12 = 48 and4x6 = 24 so
Add 48 and 24 =72
Pattie runs at 5 ft/sec
She has got a head start of 15 feet.
So after 1 second, Pattie runs = (5+15) ft
<span>
= 20 </span>
ft
After 2 second Pattie runs = (20+5)ft
= 25 ft
After 3 second Pattie runs = (25+5) ft
= 30 ft
After 4 seconds Pattie runs = (30+5) ft
= 35 ft
After 5 seconds Pattie runs = (35+5) ft
= 40 ft
After 6 seconds Pattie runs = (40+5) ft
= 45 ft
Now Keith runs at 8 ft/sec
After 1 second Keith runs = 8 ft
After 2 second Keith runs = (8+8) ft
= 16 ft
After 3 second Keith runs = (16+8) ft
= 24 ft
After 4 second Keith runs = (24+8) ft
= 32 ft
After 5 second Keith runs = (32+8) ft
= 40 ft
After 6 second Keith runs = (40+8) ft
= 48 ft
So Pattie will stay ahead of Keith upto 4 seconds. In the 5th second Pattie and Keith will be level and in the 6th second Pattie will be overtaken by Keith.
The rectangle problem:
First, create some variables.
w = width
l = length
Then you know that the length is 3 times the width, so
l = 3w
The equation for perimeter is
P = 2(l+w)
Now you use substitution, substituting the 3w for l because you found that earlier.
P = 2((3w) + w)
And simplify.
P = 2(4w)
P = 8w
And you know P = 30 because they told you that.
30 = 8w
w = 15/4 inches, or 3.75 inches
Now substitute that value back into that first equation,
l = 3w
l = 3(15/4)
l = 45/4 inches, or 11.25 inches.
The dimensions are 11.25in for length and 3.75in for width.
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The volleyball problem:
100 minutes of stretching and scrimmaging combined, and you know 10 have to be stretching, so 90 is scrimmaging.
s = scrimmaging
T = total time
s = 2/3T (they gave you this)
90 = 2/3T
T = (90*3)/2
T = 270/2
T = 135 minutes, or 2 hours and 15 minutes.
