Answer:
The set U includes all positive integers from 1 to 20.
a)
<u>x is subset U and 14 < x ≤ 23, then x is:</u>
- x = {15, 16, 17, 18, 19, 20}
b)
<u>x is subset U and includes multiples of 4, so x is:</u>
Answer:
The answer is LB= 8 feet
Step-by-step explanation:
x / 3 ≤ -6
---Multiply both sides by 3 to cancel out the denominator on the left side
x ≤ -18
Hope this helps!
10^2 + 5^2 = Diagonal length. so, 100 + 25 = 125 diagonal length
A)
y varies inversely as (x-1).
Implies y α 1/(x -1)
y = k/(x-1). Where k is constant of proportionality.
y*(x - 1) = k
when y = 12, x = 1/2
12*(1/2 - 1) = k
12*(0.5 - 1) = k
k = 12*(-0.5) = -6.
k = -6.
Equation connecting x and y
y*(x - 1) = k, recall k = -6
y*(x - 1) = -6
b)
when x = a.
y*(x - 1) = -6
y*(a - 1) = -6
y = -6 / (a -1)
when x = 2a.
y*(2a - 1) = -6
y = -6 / (2a -1)
Difference in y is 1.8
-6 / (2a -1) - -6/(a - 1) = 1.8
-6 / (2a -1) + 6/(a - 1) = 1.8
6 / (a -1) - 6 /(2a -1) = 1.8
6( 1/(a-1) - 1/(2a - 1)) = 1.8
1/(a-1) - 1/(2a - 1) = 1.8/6
1/(a-1) - 1/(2a - 1) = 0.3
((2a - 1) - (a - 1)) / ((a-1)(2a -1)) = 0.3
(2a - 1 -a + 1) /((a-1)(2a -1)) = 0.3
a / (2a² - 3a + 1) = 0.3
a/0.3 = 2a² - 3a + 1
10a/3 = 2a² - 3a + 1
2a² - 3a + 1 = 10a/3
2a² - 3a -10a/3 + 1 = 0
2a² - 19a/3 + 1 = 0
6a² - 19a + 3 = 0
This is a quadratic expression which can be factored.
6a² - 18a - a + 3 = 0
6a(a - 3) - 1(a - 3) = 0
(6a - 1)(a - 3) = 0
6a - 1 = 0 a = 1/6
a - 3 = 0 a = 3.
a = 3 or 1/6
Since a is positive integer, a = 3 only.
