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Karolina [17]
2 years ago
12

Can someone please help me with this table question . I don't understand :(

Mathematics
1 answer:
vichka [17]2 years ago
7 0
32. given (0,3)
fond slope by formula y2-y1/x2-x1 with any two points in the table ( you are lucky to be able to use formula in this equation!!) 5.3-3/1-0
2.3/1= 2.3 is slope you are able to check if this is true by doing it with every (x,y) point they give you.. luckyly the slope holds true for all the equation is
y=2.3x+3

33. this one the way I did it was plugging in (x,y) onto each equation and see of any hold true
y=4x+2.1
y=4x^2+2.1
y=2.1×4^x
y=4x

Let's plug in (1,8.4)
8.4=4 (1)+2.1
8.4=4+2.1
8.4=6.1 not true

8.4=4 (1)^2+2.1
8.4=4+2.1
8.4=6.1 not true

8.4=2.1×4^1 (1)
8.4=2.1×4
8.4=8.4 TRUE

8.4=4 (1)
8.4=4 not true
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(9, 19) (2, 16)<br> Write the coordinates as decimals or integers.
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Answer:

In decimal 0.428571428

Step-by-step explanation:

The slope = (y2 - y1)/(x2 - x1) y2 = 16, y1 = 19x2=2 and x1=9

The slope = (16 - 19)/(2 -9)

The slope = (-3)/(-7)

The slope = 0.428571428

So in decimal form the coordinates are going to be written as 0.428571428

Slope is the steepness of a line, it is the difference between the y coordinates divided by the difference in x coordinates.

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<em><u>It's 30</u></em>

<em>Hope that helped!</em>


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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
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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.

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