Answer:
19 or √145 ≈ 12.04
Step-by-step explanation:
Use the distance formula to determine the distance between the two points.
Distance = √
(
x
₂ − x
₁
)² + (
y
₂ − y
₁
)
²
Substitute the actual values of the points into the distance formula.
√
(
4 − ( − 5
))
² + (
(
−
5
)
−
3
)
²
Simplify:
√
145
The result can be shown in multiple forms.
Exact Form:
√
145
Decimal Form:
12.04159457 … ≈ 12.04
Answer:
4
Step-by-step explanation:
Let x be a number.
The statement can be interpreted as:
- 5 is subtracted <u>from</u> a number : x - 5
- A number is greater than 6 : x > 6
- When 5 is subtracted <u>from</u> 3 times a number, the result is greater than 6 : 3x - 5 > 6
And then we simplify 3x - 5 > 6:
- 3x - 5 > 6
- 3x > 11
- x > 11/3
- x > 3.666...
To get the smallest whole number satisfying the inequality above, we can take the "ceiling" of 3.66 which is 4.
Note:
The ceiling of a number is the nearest integer (or in this case, nearest whole number) of a number. It can be denoted by ceil(x).
For example, the ceiling of 0.1 is 1. The ceiling of 5 is 5 since 5 itself is a integer.
Answer:
Step-by-step explanation:
1)
x = -45
2)
Answer:
See attached for the cyclic quadrilateral
To prove: <BAD + <BCD =180°
Construction: Join B and D to the centre O of circle ABCD
Proof
With the lettering of the attached drawing,
<BOD = 2y (angle at centre is 2 X angle at circumference)
Reflex <BOD = 2x (angle at centre is 2 X angle at circumference)
∴ 2x + 2y = 360° (angle at point)
∴ x + y = 180°
∴ <BAD + <BCD = 180°
Step-by-step explanation:
The vertices of a cyclic quadrilateral lie on the circumference of the circle and the opposite angles of a cyclic quadrilateral lie in opposite segment of a circle.
The question is to prove that the opposite angles of a cyclic quadrilateral are supplementary that is 180°. Another way of stating this theory is 'Angles in opposite segments are supplementary'.
Note that the sum of supplementary angles is 180°.
