k, n - integers
2k+1 - an odd integer
2n+1 - another odd integer
The product of them:
(2k + 1)(2n + 1) =
= 4kn + 2k + 2n + 1 =
= 2(2kn + k + n) + 1
The product of integers (2kn) is integer
and the sum of them (2kn+k+n) also is integer
So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer
Answer:
17ft wide
Step-by-step explanation:
The room is 9 by 19ft
Length (x) = 19ft
Width(y) = 9ft
Area of the rug = 119ft^2
x*y = 119 ...........(1)
For the second equation we will make sure the strip around the room is uniform in size
9 - x = 19 - y
-x = 19 - 9 -y
-x = 10 - y
x = y - 10 ..........(2)
Put the value x in equation 1
(y - 10)y = 119
y^2 - 10y = 119
y^2 - 10y - 119 = 0
a = 1, b = -10, c= -119
Use quadratic formula to solve the equation
y = (-b +/-√b^2 -4ac) / 2a
y = [-(-10) +/- √ (-10)^2 - 4(1)(-119)] /2(1)
y = (10 +/- √100 + 476) /2
y = (10+/-√ 576 ) / 2
y = (10 +/- 24) / 2
y = (10 + 24) /2 or (10 - 24)/2
y = 34/2 or -14/2
y = 17 or -7
y = 17 ft
Recall that x = y - 10
x = 17 - 10
x = 7ft
Answer:
Step-by-step explanation:
7.
y= -2x+2
8.
y= -x-3
9.
y= 2/3 x + 1
10.
I'd put a point on (0, 15) , (1, 30), (2, 45) and etc....
Use a ruler to connect these points and use it to draw a straight line that hits all these points.
Good luck
Answer:
Rs 38,640
Step-by-step explanation:
<u>Pay attention:</u>
The principle (p) : Rs 42,000
Rate of interest (r) : 8%
Time (n) : 1 years
Exact Amount (a) : P(1-R/100)^n
Value:
A = 42,000(1 - 8/100)^1
A = 42,000(1 - 2/25)
A = (42,000 * 23)/25
A = 1,680 * 23
A = Rs 38,640
