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3 years ago

Find the distance between points (0,-8) and (3,-2)

2 answers:

7 0

$\bf~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-2})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[3-0]^2+[-2-(-8)]^2}\implies d=\sqrt{(3-0)^2+(-2+8)^2} \\\\\\ d=\sqrt{3^2+6^2}\implies d = \sqrt{9+36}\implies d=\sqrt{45}\implies d\approx 6.71$

Contact [7]3 years ago

7 0

Answer:

Step-by-step explanation:

Use the formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the given points (0, -8) and (3, -2):

$d=\sqrt{(3-0)^2+(-2-(-8))^2}=\sqrt{3^2+6^2}=\sqrt{9+36}=\sqrt{45}=\sqrt{(9)(5)}\\\\=\sqrt9\cdot\sqrt5=3\sqrt5$

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Step-by-step explanation:

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2 years ago

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A square park measures 170 feet along each side. Two paved paths run from each corner to the opposite corner and extend 3 feet i

Cerrena [4.2K]

Answer:

The total area, in square feet, taken by the paths is 2,004

Step-by-step explanation:

see the attached figure with lines to better understand the problem

I can divide the figure into four right triangles, one small square and four rectangles

step 1

Find the area of the right triangle of each corner of the path

The area of the triangle is

$A=(1/2)(b)(h)$

substitute the given values

$A=(1/2)(3)(3)=4.5\ ft^2$

step 2

Find the hypotenuse of the right triangle

Applying Pythagoras Theorem

Let

d -----> hypotenuse of the right triangle

$d^{2}=3^{2}+3^{2}$

$d^{2}=18$

$d=\sqrt{18}\ ft$

simplify

$d=3\sqrt{2}\ ft$

The hypotenuse of the right triangle is equal to the width of the path

step 2

Find the area of the small square of the path

The area is

$A=b^{2}$

we have

$b=3\sqrt{2}\ ft$ ----> the width of the path

substitute

$A=(3\sqrt{2})^{2}$

$A=18\ ft^2$

step 3

Find the length of the diagonal of the square park

Applying Pythagoras Theorem

Let

D -----> diagonal of the square park

$D^{2}=170^{2}+170^{2}$

$D^{2}=57,800$

$D=\sqrt{57,800}\ ft$

simplify

$D=170\sqrt{2}\ ft$

step 4

Find the height of each right triangle on each corner

The height will be equal to the width of the path divided by two, because is a 45-90-45 right triangle

$h=1.5\sqrt{2}\ ft$

step 5

Find the area of each rectangle of the path

The area of rectangle is $A=LW$

we have

$W=3\sqrt{2}\ ft$ ----> width of the path

Find the length of each rectangle of the path

$L=(D-2h-d)/2$

where

D is the diagonal of the park

h is the height of the right triangle in the corner

d is the width of the path (length side of the small square of the path)

substitute the values

$L=(170\sqrt{2}-2(1.5\sqrt{2})-3\sqrt{2})/2$

$L=(170\sqrt{2}-3\sqrt{2}-3\sqrt{2})/2$

$L=(164\sqrt{2})/2$

$L=82\sqrt{2}\ ft$

Find the area of each rectangle of the path

$A=LW$

we have

$W=3\sqrt{2}\ ft$

$L=82\sqrt{2}\ ft$

substitute

$A=(82\sqrt{2})(3\sqrt{2})$

$A=492\ ft^2$

step 6

Find the area of the paths

Remember

The total area of the paths is equal to the area of four right triangles, one small square and four rectangles

substitute

$A=4(4.5)+18+4(492)=2,004\ ft^2$

therefore

The total area, in square feet, taken by the paths is 2,004

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3 years ago

How do I solve 9x-4= -44

gulaghasi [49]

9x - 4 = -44
•add 4 to both sides to isolate the variable
9x = -40
•divide both sides by 9 to isolate the variable
x = -40/9 or −4.444...

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The answer is: C. 1/5

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3 years ago

A standard number cube is rolled one time what is p(rolling)2

cluponka [151]

Answer:

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Step-by-step explanation:

A standard cube has 6 sides, numbered from 1 - 6.

You are solving for the:

P(rolling a 2).

There is only one side that is number 2, out of the 6 sides, so your answer is:

P(rolling a 2) = 1/6

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3 years ago