Answer:
Derived from the Pythagorean Theorem, the distance formula is used to find the distance between two points in the plane. The Pythagorean Theorem,
a
2
+
b
2
=
c
2
, is based on a right triangle where a and b are the lengths of the legs adjacent to the right angle, and c is the length of the hypotenuse. The relationship of sides
|
x
2
−
x
1
|
and
|
y
2
−
y
1
|
to side d is the same as that of sides a and b to side c. We use the absolute value symbol to indicate that the length is a positive number because the absolute value of any number is positive. (For example,
|
−
3
|
=
3
. ) The symbols
|
x
2
−
x
1
|
and
|
y
2
−
y
1
|
indicate that the lengths of the sides of the triangle are positive. To find the length c, take the square root of both sides of the Pythagorean Theorem.
c
2
=
a
2
+
b
2
→
c
=
√
a
2
+
b
2
It follows that the distance formula is given as
d
2
=
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
→
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
We do not have to use the absolute value symbols in this definition because any number squared is positive.
A GENERAL NOTE: THE DISTANCE FORMULA
Given endpoints
(
x
1
,
y
1
)
and
(
x
2
,
y
2
)
, the distance between two points is given by
d
=
√
(
x
2
−
x
1
)
2
+
(
y
2
−
y
1
)
2
Step-by-step explanation:
-2x + 6 = 30 - 6x
--> -2x + 6x = 30 - 6
<span>--> 4x = 24
</span><span>--> x = 24/4
</span><span>--> x = 6</span>
Answer:
acute
Step-by-step explanation:
Combine like terms
8u+3u= 11u
and
9v-5v= 4v
So the answer is 11u+4v
Answer:
c. 3680
Step-by-step explanation:
In 2010, the population was 8000.
In 2014, it increased by 15%.
Population in 2014 :
= 8000 + 15/100×8000
= 8000 + 1200
= 9200.
Now, 2/5 of the population was age 12 or under.
= 2/5 × 9200
= 2×1840
= 3680
Answer - c) 3680
