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klasskru [66]
3 years ago
11

Mary wants to buy a small fence place around us semi circular garden demeanor of a semi circle is 18 feet Mary calculus that sh

e needs of about 28.3 feet of fence use a drop down menu to explain whether or not Mary's reasoning is correct use 3.4 for pie
Mathematics
1 answer:
nevsk [136]3 years ago
6 0

Diameter of a semi circular garden = 18 feet

Radius of the garden :

=  \tt\frac{diameter}{2}

=\tt  \frac{18}{2}

=\tt 9 \: feet

Thus, the radius of the semi circular fence = 9 feet

We know that :

\color{hotpink}\tt \: Circumference \: of \:a \:  semi \: circle \color{plum}=\pi r

Which means, the circumference of Mary's semi circular garden :

=\tt \pi r

(pi value = 3.14)

= \tt3.14 \times 9

=\tt 28.26 \: \:  feet

Thus, the circumference of fence needed for the semi circular garden = 28.26 feet

28.26 can be rounded off to 28.30 and 28.30 is the same as 28.3

Thus, Mary's reasoning is correct.

Therefore, Mary's reasoning is correct which means she needs 28.3 feet of fence to surround her garden.

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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
What can be concluded about the sequence 19, 15, 11,
Mariulka [41]

Option first and option second are correct because the common difference of the sequence is the same as the slope of the graph.

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The question is incomplete.

The question is:

What can be concluded about the sequences 19, 15, 11, 7, . . . represented on the graph? Check all that apply.

  • The common difference of the sequence is the same as the slope of the graph.
  • The slope of the graph is –4.
  • The next term in the sequence is represented by point (4, 3).
  • f(x) = –4x + 19 represents the sequence.
  • An infinite number of points can be determined to follow this sequence.

The graph is attached to the picture please refer to the graph.

We have an arithmetic sequence:

19, 15, 11, 7,...

The first term is:

a = 19

Common difference d = 15-19 = -4

The nth term:

a(n) = 19 + (n-1)(-4)

a(n) = 19 -4n + 4

a(n) = -4n + 23

We can write above expression as:

f(x) = -4x + 23

Slope of the equation = -4

The correct options are:

  • The common difference of the sequence is the same as the slope of the graph.
  • The slope of the graph is –4.

Thus, an option first and option second are correct because the common difference of the sequence is the same as the slope of the graph.

Learn more about the sequence here:

brainly.com/question/21961097

#SPJ1

4 0
2 years ago
Angelica’s bouquet of dozen roses contains 5 white roses. The rest of the roses. What fraction of the bouquet is pink? There are
Gennadij [26K]

Answer:

7/12

Step-by-step explanation:

total: 12 roses

white roses: 5

pink roses: 7

fraction of pink roses = 7/12

4 0
3 years ago
You have a jar with 91 raisins. How many are left after you have eaten some?
Lemur [1.5K]

Answer: you choke and die by the time you hit 41 left :)

5 0
3 years ago
Find the slope. ( include whether positive or negative.)​
dsp73

Answer:

that is a negative slope

but dont know how to find the slope sorry

Step-by-step explanation:

3 0
3 years ago
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