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:
The percentage increase; you'll need to take the new value and subtract it by the old value.
16 - 13 = 3
Next, you'll divide 3 by the original value.
3 ÷ 13 = 0.23
And multiply by 100
The percentage increase of friends is 23%
Answer:
a = 2, b = 3.5
Step-by-step explanation:
Expanding 
using Binomial expansion, we have that:
=
We have that the coefficients of the first two terms are 128 and -224.
For the first term:
=> 
=> ![a = \sqrt[7]{128}\\ \\\\a = 2](https://tex.z-dn.net/?f=a%20%3D%20%5Csqrt%5B7%5D%7B128%7D%5C%5C%20%5C%5C%5C%5Ca%20%3D%202)
For the second term:
Therefore, a = 2, b = 3.5
180-50 would be 130.
The missing angle is 130 degrees
Answer:
Step-by-step explanation:
Suppose the base formula is y = x^2
You want to go two units left.
basically that is y = (x + 2)^2 just the opposite of what you might think it should be.
Where does the base function have a minimum? It's minimum is as x = 0 and y = 0
Where does y = (x + 2)^2 have it's minimum?
(-2,0)
conclusion. The base function has moved 2 units to the left.
