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Lelu [443]
2 years ago
6

Identify the distance between points (−1,7,10) and (6,−3,2), and identify the midpoint of the segment for which these are the en

dpoints. Round to the nearest tenth, if necessary.
Mathematics
1 answer:
svetlana [45]2 years ago
3 0

Answer:

d ≈ 14.6 units; M (2.5, 2, 6)

Step-by-step explanation:

Using the distance formula for 3-D dimensions, you get the √(213) which equals 14.6

Then, using the midpoint formula for 3-D dimensions, you find the coordinates 2.5 for x, 2 for y, and 6 for z.

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Find the distance between each set of points. Round to the nearest tenth, when necessary. (-3, 2) and (1, -6)
vovangra [49]

Answer:

<h2>The answer is 8.9 units</h2>

Step-by-step explanation:

The distance between two points can be found by using the formula

d =  \sqrt{ ({x1 - x2})^{2} +  ({y1 - y2})^{2}  } \\

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-3, 2) and (1, -6)

The distance between them is

d =   \sqrt{ ({ - 3 - 1})^{2}  +  ({2 + 6})^{2} }   \\  =  \sqrt{ ({ - 4})^{2} +  {8}^{2}  }  \\  =  \sqrt{16 + 64}  \\  =  \sqrt{80}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 4 \sqrt{5}  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \\  = 8.9442719...

We have the final answer as

8.9 units to the nearest tenth

Hope this helps you

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Please answer, thank you and have a nice day
taurus [48]

Answer:

The inequality represented by the graph is y >  \frac{1}{3} x - 3

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

  • m is the slope of the line
  • b is the y-intercept

The rule of the slope is m = \frac{y2-y1}{x2-x1} , where

  • (x1, y1) and (x2, y2) are two points on the line

<em>To find the inequality represented by the graph, find at first the equation of the line</em>

∵ The line passes through points (0, -3) and (3, -2)

∴ x1 = 0 and y1 = -3

∴ x2 = 3 and y2 = -2

→ Substitute them in the rule of the slope above to find it

∵ m = \frac{-2--3}{3-0} = \frac{-2+3}{3} = \frac{1}{3}

∴ m =  \frac{1}{3}

→ Substitute it in the form of the equation above

∴ y =  \frac{1}{3} x + b

∵ b is the y-intercept ⇒ value y at x = 0

∵ y = -3 at x = 0

∴ b = -3

→ Substitute it in the equation

∴ y =  \frac{1}{3} x + -3

∴ y =  \frac{1}{3} x - 3

→ Let us change it to inequality

∵ The line is dashed

∵ The shading area is above the line

∴ The sign of inequality should be >

∴ y >  \frac{1}{3} x - 3

∴ The inequality represented by the graph is y >  \frac{1}{3} x - 3

8 0
2 years ago
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