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Mazyrski [523]
2 years ago
8

Richard has two circular sprinklers to water his rectangular backyard as shown.

Mathematics
1 answer:
makvit [3.9K]2 years ago
8 0

Answer:

109.88 ft² (nearest hundredth)

Step-by-step explanation:

<u>Formulae</u>

  • Area of a rectangle = width × length
  • Area of a circle = πr²

To find the area of the lawn that is not watered, subtract the area of the 2 circles from the area of the rectangle.

From inspection of the diagram

  • width of rectangle = 2r
  • length of rectangle = 4r
  • area = 512 ft²

Substituting the values into the area of a rectangle formula, and solving for r:

⇒ 512 = 2r × 4r

⇒ 512 = 8r²

⇒ r² = 64

⇒ r = ±8

As distance is positive, r = 8 ft

Area of one circle = π8² = 64π  ft²

Therefore,

Area not watered = area of rectangle - 2 × area of circle

                             = 512 - 2(64π)

                             = 109.88 ft² (nearest hundredth)

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Graph the linear equation. Find three
belka [17]

Answer:

Part 1) The graph in the attached figure

Part 2) Three points that solve the equation could be (-18,0),(0,4.5) and (-2,4)

Step-by-step explanation:

we know that

To graph a line we need to plot two points

If a point solve the linear equation, then the point is a solution of the linear equation

step 1

Find the first point that solve the equation

<em>Find the x-intercept</em>

The x-intercept is the value of x when the value of y is equal to zero

For y=0

x - 4(0) =-18

x=-18

The x-intercept is the point (-18,0)

step 2

Find the second point that solve the equation

<em>Find the y-intercept</em>

The y-intercept is the value of y when the value of x is equal to zero

For x=0

0 - 4y =-18

-4y=-18

y=4.5

The y-intercept is the point (0,4.5)

step 3

With the intercepts graph the line

Plot the intercepts and join the points to graph the line

using a graphing tool

see the attached figure

step 4

Find the third point that solve the equation

Assume a value for x and then solve for y

I assume x=-2

substitute in the linear equation and solve for y

-2 - 4y =-18  

-4y=-18+2

-4y=-16

y=4

The third point is the point (-2,4)

7 0
3 years ago
3x(-2x)8(-2)=30 what value of x makes the equation true.<br><br> A. 24<br> B.26<br> C.5<br> D.6
Leokris [45]

Answer:

Step-by-step explanation:

5 0
3 years ago
Question 1: Find the equation of the line through point (5,4) and perpendicular to y=−43x−2. Use a forward slash (i.e. "/") for
Mariulka [41]

Answer:

Question 1: y = 3/4x + 1/4.

Question 2: y = 6/5x + 7/5.

Step-by-step explanation:

Question 1: A line perpendicular to another line would have a slope that is the negative reciprocal of the other line. If the slope of the first line is -4/3, the slope of a line perpendicular to the first would have a slope of 3/4.

Since the line goes through (5, 4), we can just put the points into the equation, y = 3/4x + b.

4 = 3/4(5) + b

b + 15/4 = 4

b = 16/4 - 15/4

b = 1/4

So, the equation of the line is y = 3/4x + 1/4.

Question 2: 5x + 6y = -6

6y = -5x - 6

y = -5/6x - 1

As stated before, a line perpendicular to another will have a slope that is the negative reciprocal of the other. So, the slope of the other line is 6/5.

The line goes through (-2, -1), so we can put the points into the equation, y = 6/5x + b.

-1 = 6/5(-2) + b

b - 12/5 = -5/5

b = -5/5 + 12/5

b = 7/5

So, the equation of the line is y = 6/5x + 7/5.

Hope this helps!

8 0
3 years ago
Please answer it in two minutes
ch4aika [34]

Answer:

67 in

Step-by-step explanation:

Because these are congruent figures, you know that the last remaining segment is 67in

3 0
3 years ago
20 point for however can tell me what event in rodeo this is and a brainliest
Savatey [412]

The activity pictured is called goat tying.

7 0
3 years ago
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