Answer:
x = 20
Length = 20ft
Width = 12ft
Step-by-step explanation:
A = 240
x^2 - 8x = 240
x^2 - 8x - 240 = 0
x^2 - 20x + 12x - 240 = 0
x(x-20) + 12(x-20) = 0
(x+12)(x-20) = 0
x = 20
x = -12 (which we discard since x is a length)
So the dimensions are 20ft and 20-8 = 12ft
Answer:
They'll meet after 200 meters , if they simultaneously start running towards each other.
Step-by-step explanation:
Let x =distance travelled by dog and 200-x be the distance travelled by cat. Inorder to meet, the sum of their travelled distances shall be equal to 200 meters as they are far apart by 200 meters.
Dog: Distance =Speed x time: x=30t
Cat: Distance = 200-x
=24t
The sum of their distance travelled shall be 200 meters: 30t+ 24t= 200;54t=200;t=200/54=3.7secs
So they will meet after 3.7 seconds
To check:
Distance travelled by dog :x=30(3.7)
=111.11 meters
Distance travelled by cat: 24t=24(3.7)
=88.89 meters
Therefore since they are travelling towards each other and their distance apart is 200 meters, after 3.7 seconds they will meet because dog travelled 111.11 meters and cat travelled 88.89 meters and they covered already 200 meters as the sum of 111.11+ 88.89
=200 meters
Answer:
it should be (5,4)
Step-by-step explanation:
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Answer:
No, mn is not even if m and n are odd.
If m and n are odd, then mn is odd as well.
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Proof:
If m is odd, then it is in the form m = 2p+1, where p is some integer.
So if p = 0, then m = 1. If p = 1, then m = 3, and so on.
Similarly, if n is odd then n = 2q+1 for some integer q.
Multiply out m and n using the distribution rule
m*n = (2p+1)*(2q+1)
m*n = 2p(2q+1) + 1(2q+1)
m*n = 4pq+2p+2q+1
m*n = 2( 2pq+p+q) + 1
m*n = 2r + 1
note how I replaced the "2pq+p+q" portion with r. So I let r = 2pq+p+q, which is an integer.
The result 2r+1 is some other odd number as it fits the form 2*(integer)+1
Therefore, multiplying any two odd numbers will result in some other odd number.
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Examples:
- 3*5 = 15
- 7*9 = 63
- 11*15 = 165
- 9*3 = 27
So there is no way to have m*n be even if both m and n are odd.
The general rules are as follows
- odd * odd = odd
- even * odd = even
- even * even = even
The proof of the other two cases would follow a similar line of reasoning as shown above.
