Here are some of the equivalent fractions for 12/15 <span>4/5, 8/10, 12/15, 16/20, 20/25, 24/30, 28/35, 32/40, 36/45, 40/50, </span>
Let ab be a 2 digit number, then ab=10a+b, where a and b are digits, a≠0.
"the difference between the integer and the product of its two digits is 12"
10a+b - (a*b)=12
10a+b-ab=12
factorize b:
10a+b(1-a)=12
subtract 10 from both sides, to produce a factor (1-a) or (a-1) and then factorize:
10a-10+b(1-a)=2
10(a-1)+b(1-a)=2
(a-1)(10-b)=2
(a-1)(10-b) can be (1,2), (2, 1), (-1, -2), (-2, -1)
if a-1=1 and 10-b=2, then a=2, b=8
if a-1=2, and 10-b=1, then a=3, b=9
if a-1=-1, then a=0, which is not possible
if a-1=-2, then a=-1, which is not possible
so the solutions (a, b) are (2, 8) and (3, 9)
Then the integers are 28, 39
Answer: 28, 39
Okay, so a general rule for finding perpendicular lines in the form of y = mx + b is y = (-1/m) + b.
First, let's ignore b (-7) because we're going to find that later.
A perpendicular line to y = 4x + b is y = -1/4x + b.
Alright, so now let's plug in the values. They are in the form of (x,y), so let's plug them in accordingly.
3 = -1/4(4) + b
3 = -1 + b
b = 4
y = -1/4x + 4
So a line perpendicular to y = 4x - 7 is y = -1/4x + 4.
