Answer:
{3, 4, 5, 6, 7, 8, 9, 10, 11}
Step-by-step explanation:
Let integer be x
x > 2 and x < 12
gives
2 < x < 12
All such integers are {3, 4, 5, 6, 7, 8, 9, 10, 11}
Note that when two lines have slopes of m₁ and m₂, then
(i) If m₁ = m₂, then the lines are parallel.
(ii) If m₁*m₂ = -1, then the lines are perpendicular.
Let us evaluate the given lines.
a. y = 4x - 1 and 12x = 3y + 7
y = 4x - 1 => m₁ = 4
Write the second equation in standard form.
3y = 12x - 7
y = 4x - 7/3 => m₂ = 4.
m₁ = m₂.
Answer: PARALLEL
b. x - 7y = 10 and 2x + 14y = 21
In standard form,
7y = x - 10 or y = (1/7)x - 10/7 => m₁ = 1/7
14y = - 2x + 21 or y = -1/7 + 3/2 => m₂ = -1/7
m₁ ≠ m₂ and m₁*m₂ ≠ -1.
Answer: NEITHER
c. 5x + 6y = 18 and 18x - 15y = 36
In standard form,
6y = -5x + 18 or y = -(5/6)x + 3 => m₁ = -5/6
15y = 18x - 36 or y = (6/5)x - 12/5 => m₂ = 6/5
m₁*m₂ = -1
Answer: PERPENDICULAR
d. x =1 and y = 1
x = 1 => m₁ is undefined
y = 1 => m₂ = 0
m₁ ≠ m₂ and m₁*m₂ ≠ -1
Answer: NEITHER
The <em>correct answer</em> is:
4.16.
Explanation:
Since we know 25 goes into 100 (think quarters into a dollar), it will be easy to change this fraction to a decimal in the hundredths place.
25 goes into 100 4 times (again, 4 quarters make a dollar). This means we would also multiply 4 by 4, making 16/100.
16/100 is the decimal 0.16. Thus 4 and 4/25 is 4.16.
Answer:
(x ,y ) = (3, 12)
Step-by-step explanation: