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Bogdan [553]
3 years ago
7

A circular hedge surrounds a sculpture on a square base. The radius of the hedge is 6x. The side length of the square sculpture

base is 4x. What is that area of the hedge? Write your answer in factored form.
Mathematics
1 answer:
andrey2020 [161]3 years ago
6 0
Hi, thank you for posting your question here at Brainly.

Since the hedge is surrounding the square base, the area of the base can be determined by subtracting the area of the base from the hedge.

A = pi*r^2 - (4x)^2
A = pi*(6x)^2 - (4x)^2
A = 2x^2*(3pi - 2)

I hope I was able to answer your question. Have a good day.
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Find the slope of the line that is ​(a) parallel and ​(b) perpendicular to the line through the pair of points.
ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m=\frac{-1}{4}

Step-by-step explanation:

Step1:-

<u>Slope of a line</u><u> :-</u>

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m=\frac{y_{2}-y_{1}  }{x_{2} -x_{1} }

<u>Parallel lines:-</u>

<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel

<u>Perpendicular lines:-</u>

<u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

m_{2} = \frac{-1}{m_{1} } \\

<u>Step 2</u>:-

a)The slope of a line when given two points (-1,-4) and (0,0)

m = \frac{0-(-4)}{0-(-1)} =4

<u>Two </u>non-vertical lines are parallel if and only if their slopes are parallel

m_{1} = m_{2}

Therefore the slope of the line that is parallel to the another line

m_{1} =m_{2} =4

<u>Step 3</u>:-

b) <u>Two </u>non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

m_{2} = \frac{-1}{m_{1} } \\

m_{2} =\frac{-1}{4}

Therefore the slope of the line is perpendicular to the another line is

m=\frac{-1}{4}

3 0
3 years ago
Read 2 more answers
A loan of $16,840 is borrowed at 9% simple interest and is repaid with $4,167.90 interest. What is the duration of the loan?​
rewona [7]

9514 1404 393

Answer:

  2 3/4 years

Step-by-step explanation:

The interest is given by the formula ...

  I = Prt . . . . . . principal P at annual rate r for t years

Solving for t gives ...

  t = I/(Pr)

  t = 4167.90/(16840×0.09) = 2.75

The duration of the loan is 2 3/4 years.

5 0
3 years ago
Monica took a survey of her classmates' hair and eye color. The results are in the table below.
jolli1 [7]

Answer:

let R represent red hair

let G represent green eyes

<em>from</em><em> </em><em>Baye's</em><em> </em><em>theorem</em><em>:</em>

<em>P( \frac{R}{G} ) =  \frac{P(RnG)}{P(G)}</em>

P(RnG) = 5

P(G) = { \sum}(green \: hair) \\  = (3 + 5 + 5) \\  = 13

Therefore:

P( \frac{R}{G} ) =  \frac{5}{13}  \\  = 0.385

The conditional relative frequency = 0.385

4 0
3 years ago
Greg deposits $500 into an account that pays simple interest at a rate of % 3 per year. How much interest will he be paid in the
Klio2033 [76]

Answer: 90 dollars

Work Shown:

i = p*r*t

i = 500*0.03*6

i = 90

6 0
2 years ago
Mary works in a factory that produces 1000 computers each day. When 25 computers were sampled, 7 were found to be defective. Est
astra-53 [7]

Answer:

about 280

Step-by-step explanation:

brainliest pls :)

8 0
3 years ago
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