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:
Answer:
X= 7
Step-by-step explanation:
Since x= 2 you would plug it in 3.5 times 2 = 7
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
==================
Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%
<h2>
Answer: <em>x = 7.5</em></h2>
<em />
Step-by-step explanation:
Use the Pythagorean Theorem ( 
)
The longest side is <em>c = the hypotenuse</em>, and <em>a and b = the other sides</em> of the triangle.
a = 4 First: 
b = x Second: 
c = 8.5 Third: 
Fourth: 
Fifth: x = 7.5
