In ΔDCE + ΔGFH,
∠C = ∠F (given)
∠D = ∠C (angle sum of a triangle)
∠H = ∠E (angle sum of a triangle)
∴ ΔDCE is similar to ΔGFH
Hope this helps!
Answer:
Hi! I believe this is your answer:
$750
Step by step explanation:
interest + interest = total interest
0.08*x + 0.09*(9000-x) = 750 dollars
0.08x + 810 - 0.09x = 750
-0.01x = 750 - 810 = -60 ====> x = %28-60%29%2F%28-0.01%29 = 6000.
Final answer:
$6000 was invested at 8%. The rest 9000-6000 = 3000 dollars were invested at 9%.
Check. 0.08*6000 + 0.09*3000 = 480 + 270 = 750 dollars.
Answer:
the slope in the equation is 5, while the slope on the graph is 2
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:
