X = larger number, y = smaller number
x = y + 12
x + y = 74
y + 12 + y = 74
2y + 12 = 74
2y = 74 - 12
2y = 62
y = 62/2
y = 31
x = y + 12
x = 31 + 12
x = 43
so ur 2 numbers are : 43 and 31
The answer is the option d, which is: d) 
The explanation for this problem is shown below:
1. Smplify the denominator and rewrite the numerator in this form:
2. Multiply the denominator and the numerator by the conjugated 
and simplify the expression, as following:
3. As you can see, you obtain the expression shown in the option mentioned above.
Answer:
Step-by-step explanation:
Rewrite
100
x
2
100
x
2
as
(
10
x
)
2
(
10
x
)
2
.
(
10
x
)
2
+
60
x
+
9
(
10
x
)
2
+
60
x
+
9
Rewrite
9
9
as
3
2
3
2
.
(
10
x
)
2
+
60
x
+
3
2
(
10
x
)
2
+
60
x
+
3
2
Check the middle term by multiplying
2
a
b
2
a
b
and compare this result with the middle term in the original expression.
2
a
b
=
2
⋅
(
10
x
)
⋅
3
2
a
b
=
2
⋅
(
10
x
)
⋅
3
Simplify.
2
a
b
=
60
x
2
a
b
=
60
x
Factor using the perfect square trinomial rule
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
a
2
+
2
a
b
+
b
2
=
(
a
+
b
)
2
, where
a
=
10
x
a
=
10
x
and
b
=
3
b
=
3
.
(
10
x
+
3
)
2
The perimeter of the circle is also known as the circumference that said figure out what the diameter is and multiply that by pi (3.14)
X/7 + 9 = 3
a number: x
a number divided by 7: x/7
sum of number divided by 7 and 9: x/7 + 9 (and means plus)
equals 3: x/7 + 9 = 3
