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Dmitrij [34]
2 years ago
14

What is the difference between vertical and perpendicular?.

Mathematics
1 answer:
andrey2020 [161]2 years ago
4 0

Answer:

Vertical is straight up and down line or object

Perpendicular is more at an angle of 90 degrees to a line, plane, or surface ect

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Dima020 [189]
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8 0
4 years ago
Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos
Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$ P_{1} = (- 1, 4) $

$ P_{2} = (6, 2) $    and

$ P_{3} = (4, - 5) $

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $ (x_1, y_1) $ and $ (x_2, y_2) $ is:

                                 $ \sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+}   \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}} $

Length between $ P_1 $ and $ P_{2} $ , (Side 1) :

$ (x_1, y_1) = (- 1, 4) $     and

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2 $

$ = \sqrt{7^2 + 2^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53}} $

Length of Side 1 = $  \sqrt{\textbf{53}} $ units.

Distance between $ P_1 $ and P_2 , (Side 2):

$ (x_1, y_1) = (-1, 4) $

$ (x_2, y_2) = (4, - 5) $

Distance = $ \sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2 $

$ = \sqrt{ 25 + 81 } $

$ = \sqrt{\textbf{106}} $

Length of Side 2 = $ \sqrt{\textbf{106}} $ units.

Distance between $ P_2 $ and $ P_3 $ , Side 3 :

$ (x_1, y_1) = (4, 5) $

$ (x_2, y_2) = (6, 2) $

Distance = $ \sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2} $

$ = \sqrt{49 + 4} $

$ = \sqrt{\textbf{53} $

Length of Side 3  = $ \sqrt{\textbf{53}} $ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$ \bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2 $

i.e, 53 + 53  = 106

Hence, the triangle is a right - angled triangle as well.

7 0
4 years ago
Sue has 20 biscuits in a tin There are 12 plain biscuits 5 chocolate biscuits 3 currant biscuits Sue takes at 2 random biscuits
vagabundo [1.1K]

Answer:

111 / 190

Step-by-step explanation:

Total biscuits = 20

Plain, P = 12

Chocolate, C = 5

Currant, K = 3

Assume without replacement :

Probability that biscuit are of the same type :

P(plain) :

12 / 20 * 11 / 19 = 132 / 380

P(chocolate) :

5/ 20 * 4 / 19 = 20/ 380

P(currant) :

3/20 * 2 /19 = 6 / 380

Therefore,

Probability that biscuit is of the same type :

P(plain) + P(chocolate) + P(currant)

132/380 + 20/380 + 6/380

158 / 380 = 79 / 190

Therefore, probability that biscuit aren't of the same type :

1 - P(biscuit is of same type)

1 - 79/190

(190 - 79) / 190

111 / 190

7 0
3 years ago
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