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Y_Kistochka [10]

3 years ago

14

Find the value of r.

1 answer:

fgiga [73]3 years ago

6 0

Answer:

r = 10.5

Step-by-step explanation:

using the Pythagorean theorem:

(7 + r)² = 14² + r²

49 + 14r + r² = 196 + r²

subtract r² from both sides of the equation:

14r + 49 = 196

subtract 49 from both sides:

14r = 147

divide both sides by 14:

r = 10.5

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Sindrei [870]

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6 0

4 years ago

Point A is located at (-5, 2) on a coordinate grid. Point A is translated 8 units to the right and 3 units up to create point A.

Molodets [167]

The closest distance between point A and point A' is 8.5 ⇒ B

Step-by-step explanation:

Let us revise the translation of a point

If the point (x , y) translated horizontally to the right by h units then its image is (x + h , y)
If the point (x , y) translated horizontally to the left by h units then its image is (x - h , y)
If the point (x , y) translated vertically up by k units then its image is (x , y + k)
If the point (x , y) translated vertically down by k units then its image is (x , y - k)

∵ Point A is located at (-5 , 2)

∵ Point A is translated 8 units to the right and 3 units up

- That means add x-coordinate by 8 and add y-coordinate by 3

∴ Point A' located at (-5 + 8 , 2 + 3)

∴ Point A' located at (3 , 5)

The distance between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$

is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

∵ Point a = (-5 , 2) and point A' = (3 , 5)

∴ $x_{1}$ = -5 and $x_{2}$ = 3

∴ $y_{1}$ = 2 and $y_{2}$ = 5

- Substitute these values in the rule of the distance

∵ $d=\sqrt{(3--5)^{2}+(5-2)^{2}}$

∴ $d=\sqrt{(3+5)^{2}+(3)^{2}}$

∴ $d=\sqrt{(8)^{2}+(3)^{2}}$

∴ $d=\sqrt{64+9}=73$

∴ d = 8.544 ≅ 8.5

The closest distance between point A and point A' is 8.5

Learn more:

You can learn more about the distance between two points in brainly.com/question/6564657

#LearnwithBrainly

5 0

4 years ago

Read 2 more answers

How do you factor this

Sladkaya [172]

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4 0

3 years ago

Substitution for y=4x+6 -5x-y=21

Sergio039 [100]

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4 0

3 years ago

8. Jasmine is playing a game where she moves a piece on a coordinate grid. Over three turns, she moves her

olga2289 [7]

Answer:

28 units.

Step-by-step explanation:

The distance between two given points ( $x_{1},y_{1}$ ) and ( $x_{2},y_{2}$ ) is given by the formula

$\sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

So, the distance between points (-2,-4) and (-1,6) is

$\sqrt{(-2 - (- 1))^{2} + (-4 - 6)^{2}} = \sqrt{101} = 10.05$ units.

Now, the distance between points (-1,6) and (3,8) is

$\sqrt{(-1 - 3)^{2} + (6 - 8)^{2}} = \sqrt{20} = 4.47$ units

Again, the distance between the points (-2,-4) and (3,8) is

$\sqrt{(- 2 - 3)^{2} + (-4 - 8)^{2}} = 13$ units.

Therefore,the perimeter of the triangle is (10.05 + 4.47 + 13) = 27.52 ≈ 28 units. (Approximate)

7 0

4 years ago