Step-by-step explanation:
Before we proceed, we must understand that we are dealing with a system of right angled triangles.
There are two types of right angle triangles';
45° - 45° - 90° 30° - 60° - 90°
In 45° - 45° - 90°, the adjacent is equal to the opposite
30° - 60° - 90°, there are three different sides
The longest side faces 90°, the shortest side will face the smallest angle and the intermediate will face 60°
A.
To find AB, use Pythagoras theorem;
AB² = AC² + BC²
AB² = 13² + 4²
AB² = 169 + 16 = 185
AB = √185 = 13.6
AB = 13.6
Angle A = 30°
Angle B = 60°
B.
AB² = BC² + AC²
The unknown is AC;
AC² = AB² - BC²
AC² = 5² - 4²
AC² = 9
AC = √9 = 3
Angle A = 60°
Angle B = 30°
C.
AB² = AC² + BC²
Insert the parameters and find AC;
AC² = AB² - BC²
AC² = 11² - 4.4²
AC² = 101.64
AC = √101.64
AC = 10.1
Angle A = 30°
Angle B = 60°
AC = 13
Answer:
10 + 8i
Step-by-step explanation:
noting that i² = - 1
Given
2i(4 - 5i) ← distribute the parenthesis
= 8i - 10i² = 8i - 10(- 1) = 10 + 8i
Answer:
inequality form:
x<17
interval notation:
(-∞,17]
Step-by-step explanation:
The result is
9
a
2
−
16
The reason is the following:
The problem is an example of a notable product: "the sum multiplied by the diference is equal to the difference of squares", that is to say:
(
a
+
b
)
⋅
(
a
−
b
)
=
a
2
−
b
2
.
By applying this to our question, we obtain that:
(
3
a
−
4
)
⋅
(
3
a
+
4
)
=
(
3
a
)
2
−
(
4
)
2
=
9
a
2
−
16
.
Answer:
8.5
Step-by-step explanation:
slope of the line that contains KL
(y2 - y1)/(x2-x1)
(0-1)/(7-3)
m = -1/4
slope of the line that contains JK
(5-1)/(4-3)
m = 4
the linea are perpendicular so triangle is right
area = (leg1 x leg2)/2
KL = 
KJ = 
area = (√17)^2/2 = 17/2 = 8.5
