The length of the rectangular fence is 4 feet greater than its width. The perimeter of the fence is less than 42 feet. What is the range of the lengths of the fence?

Answer:

- 920

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = 22- 30 = 14 - 22 = 6 - 14 = - 8

This indicates the sequence is arithmetic with sum to n terms given by

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 30 and d = - 8 , thus

[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [ (2 × 30) + (19 × - 8) ]

     = 10(60 - 152)

     = 10 × - 92

     = - 920

Answer:

35 ft

Step-by-step explanation:

The arch is in the shape of a semicircle.

The distance around the arch is about 110 feet. This is the same as the circumference of the arch.

The height of the arch is the radius of the arch.

The circumference of a semicircle is given as:

[tex]C = \pi r[/tex]

where r = radius

Therefore:

110 = πr

=> r = 110/π

r = 35.01 ft ≅ 35 ft

The height of the arch is 35 ft

The height of the arch in feet is 35 ft.

Since The distance around the arch is about 110 feet.

We know that

The circumference of a semicircle should be

110 = πr

[tex]r = 110/\pi[/tex]

r = 35.01 ft

≅ 35 ft

hence, we can conclude that The height of the arch in feet is 35 ft.

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Answer:

(x-5)

Step-by-step explanation:

x^2 -25

We know this is the difference of square

(x-5)(x+5)

Since the length is (x+5)  the width must be (x-5)

Given:

To be calculated:

Calculate the width of rectangle?

Formula used:

Area of Rectangle = L × b

Solution:

We know,

Area of Rectangle = L × b

⇒ x² - 25 = x + 5 × b

⇒ b = x² - 25 / x + 5

⇒ b = x² - 5² / x + 5

⇒ b = ( x + 5 ) ( x - 5 ) / x + 5

⇒ b = x - 5

Answer:

Step-by-step explanation:

The key here is knowing that the equation of the line that passes through these points is same

Thus having (6,14) and (0,0), the slope is as follows;

m = y2-y1/x2-x1 = 0-14/0-6 = -14/-6 = 7/3

Now we can use this slope here to get the value of y in the question

All we need to do is tie write the equation of the line for between the points (6,14) and (2,y)

That would be;

7/3 = y-14/1-6

7/3 = y-14/-5

cross multiply;

-35 = 3(y-14)

-35 = -3y + 42

-3y = -35-42

-3y= -77

y = -77/3

y = 77/3

Answer:

3:1

Step-by-step explanation:

Since there are 3 times more blue favorite kids, the ratio is

3:1

The ratio of the number of students who said blue to the number of students who said green is 3 : 1.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mark asked each student in a class to name their favorite color.

For this class,

the number of students who said blue is three times the number of students who said green.

Let n be the number of students who said green.

Then, 3n, the number of students who said blue.

The ratio of the number of students who said blue to the number of students who said green.

= 3n/ n

= 3/1

= 3: 1.

Therefore, the ratio is 3 : 1.

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[tex]answer \\ 71xy - 56x + 27y \\ solution \\ 7x(5y - 8) + 3y(12x + 9) \\ = 35xy - 56x + 36xy + 27y \\ combine \: like \: terms \\ = 35xy + 36xy - 56x + 27y \\ = 71xy - 56x + 27y \\ hope \: it \: helps[/tex]

Answer:

[tex] = 71xy - 56x + 27 \\ [/tex]

Step-by-step explanation:

[tex]7x(5y - 8 )+ 3y(12x + 9) \\ 35xy - 56x + 36xy + 27 \\ 35xy + 36xy - 56x + 27 \\ = 71xy - 56x + 27[/tex]

hope this helps

Answer:

t =1

Step-by-step explanation:

3t - 18 = 4(-3-3/4t)

Distribute

3t - 18 = -12 -3t

Add 3t to each side

3t -18+3t = -12 -3t+3t

6t -18 =-12

Add 18

6t -18+18 = -12+18

6t = 6

Divide by 6

6t/6 = 6/6

t =1

Answer:

t = 1

Step-by-step explanation:

start by distributing the 4 to whats in the parentheses.

4 (-3 - 3/4t)

-12 - 3t

*helpful tip: if you multiply a fraction by its denominator the product is equal to its numerator

now you have:

3t - 18 = -12 - 3t

add 18 to both sides

3t = 6 - 3t

add 3t to both sides

6t = 6

divide both sides by 6

t = 1

[tex]answer \\ (3x - 5)(2x + 2) \\ solution \\ {6x}^{2} - 4x - 10 \\ = {6x}^{2} - (10 - 6)x - 10 \\ = {6x}^{2} - 10x + 6x - 10 \\ = 2x(3x - 5) + 2(3x - 5) \\ = (3x - 5)(2x + 2) \\ hope \: it \: helps[/tex]

Answer:

x = 1⅔ or -1

Step-by-step explanation:

6x² -4x - 10

a=6, b=-4, c=-10, ac= -60

factors -10 & 6

6x² + 6x - 10x -10 =0

(6x² + 6x) - (10x - 10) =0

6x(x +1) - 10(x+1) =0

(6x-10)(x+1)=0

6x-10=0 or. x+1=0

6x= 10 or x= -1

x= 10/6 or. x= -1

x=1⅔ or x= -1

Answer: 22

Step-by-step explanation:

22+5= 27

27-4=23

23+7=30

30-8=22

Answer:

22+m+ 7n - 8

Step-by-step explanation:

22+5m-4m+7n-8

22+m+ 7n - 8

you subract 4m from 5m because there are like terms

none of the others are like terms so you cant add or subract them

Answer:

The answer is D.

Step-by-step explanation:

Given that f(x) = g(x) which means that both functions intersect to each other. By looking at the graph, x = -2 or 0 or 2 are the places where they intersect.

Answer:

2

Step-by-step explanation:

Add the students that take math and physics and subtract the ones that take both so that they are not double counted

65+43-10 =98

There are 100 students

100-98 =2

There are 2 that take neither math nor physics

Answer:

Step-by-step explanation:

6 more than a number is 36: x+6=36

36 more than a number is 6: x+36=6

6 times a number is 36: 6x=36

Answer:

1

Step-by-step explanation:

500/500=1

x / x = 1

Answer:

Step-by-step explanation:

This is because when you divide a number with each other then they cancel out to equal 1. This can happen with the letter x. So, x/x = 1.

Going back to the question 500/500 can cancel out to become 1.

Answer:

[tex]a_{n}[/tex] = 3n - 1

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 5 - 2 = 8 - 5 = 11 - 8 = 14 - 11 = 3

This indicates the sequence is arithmetic with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 2 and d = 3 , thus

[tex]a_{n}[/tex] = 2 + 3(n - 1) = 2 + 3n - 3 = 3n - 1

The expression for the nth term of the series is [tex]a_n = 3n-1[/tex].

Given that,

Sequence; 2, 5, 8, 11, 14.

We have to find, the expression in terms of n for the nth term of the following given sequences?

According to the question,

The nth of the arithmetic sequence is,

[tex]\rm a_n = a+ d(n-1)[/tex]

Where a is the first term of the sequence,

d is the common difference between the terms,

n is the number of terms.

Then,

The given sequence is 2, 5, 8, 11, 14.

Here, the common difference between the terms is 3.

And the first term of the sequence is 2.

Substitute all the values in the formula,

Therefore,

The nth term of the given terms is,

[tex]\rm a_n = a+ d(n-1)\\\\a_n = 2+ 3(n-1)\\\\a_n + 2+3n-1\\\\a_n = 3n-1[/tex]

Hence, The required expression for the nth term of the series is [tex]a_n = 3n-1[/tex].

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Answer:

6.8

How many 6's can go into 40?

6 + 6 + 6 + 6 + 6 + 6 = 36

6 6's

Subtract the amount off

40.8-36=4.8

How many 6's can go into 4.8?

0.6 + 0.6 +0. 6 + 0.6 + 0.6 + 0.6 + 0.6 + 0.6 = 48

0.8 6's

4.8 = 4.8 = 0

6 6's + 0.8 6's = 6.8 6's

6.8 is the answer

If you have any questions you can ask

Step-by-step explanation:

Answer:

We use cosine rule also called cosine law which states

c^2=a^2+b^2-2abcosC

given

a=8cm, b=7cm, c=9cm cos C?

9^2=8^+7^2-2*8*7 cos C

expand

81=64+49-112 cos C

like terms together

81-113=-112 cos C

-32=-112cos C

multiply both sides by -1

32=112cos C

divide both sides by 112

32/112=cos C

cosC=0.2857

find cos inverse of 0.2857

angle C= 73.40

Answer:

8

Step-by-step explanation:

2n

Let n =4

2*4

8

Answer:

8

Step-by-step explanation:

= 2 * 4 (we know that n = 4)

= 8

Hope this helps!

Answer: [tex]y=-6x^2[/tex] never touches the y-axis

[tex]y=-6x^2-4[/tex] touches the y-axis at -4

Step-by-step explanation:

Because -4 means that the graph touches the y-axis at negative 4, not having it means that it never touches the y-axis

Answer:

$10.25

Step-by-step explanation:

95/.1=9.5

9.5*9=85.5

85.5/8

=10.25

Answer:

You should be right

Step-by-step explanation:

Srry if I am wrong though

Answer:

C. 5.4

Step-by-step explanation:

Range means highest number minus lowest number.

7.5 - 2.1 = 5.4

[tex]answer =5.4 \\ given \: data = 2.1 , 2.6 , 7.2 , 5.5 ,4.1 , 5.5 ,7.5 , 6.1 \\ range = highest \: score - lowest \: score \\ \: \: \: \: \: \: \: \: = \: 7.5 - 2.1 \\ \: \: \: \: \: = 5.4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

4 hours

Step-by-step explanation:

20-5x=0

5x= 20

x=4 hours

Answer:

slope = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, - 8)

m = [tex]\frac{-8-2}{2-0}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5

The value of the gradient is -1/5.

In order to find the gradient of a line either of the two ways can be used. First, the equation of line should be written in terms of y, then the coefficient of x is the gradient.

The other method is to find the two points on the graph and then take the ratio of the difference of corresponding coordinates.

The given points are (0,2) and (2,-8).

Since the gradient of the line segment between points (x₁, y₁) and (x₂, y₂) is given as,

Gradient = (y₂-y₁)/(x₂-x₁)

Substitute the corresponding values to obtain,

Gradient = (2-0)/(-8-2)

               = -2/10

               = -1/5

Hence, the gradient of the line segment joining the points (0,2) and (2,-8) is -1/5.

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Answer:

B

Step-by-step explanation:

Because you subtract 14 from the right and left of the = sign

and now we add one on tbe right and left of the = sign. so the quadratic problem would be 3x^2 + 9x -13

Answer:

see below

Step-by-step explanation:

f(x) = x^2 – 2x – 3

To find the roots, set the equation equal to zero

0  = x^2 – 2x – 3

Factor, what two numbers multiply to -3 and add to -2

-3 * 1 = -3

-3 + 1 = -2

0 = (x-3)( x+1)

Using the zero product property

x-3 =0   x+1 =0

x=3          x=-1

Answer:

3

Step-by-step explanation:

cuz i said so lol

Answer:

hope this helps you

Answer:

2/5.

Step-by-step explanation:

1/4 / 5/8

= 1/4 * 8/5

= 1*8 / 4*5

= 8/20

= 2/5.

Group 'em together

a b − a + 1 − b

a b − a = a ( b − 1 )

Notice that there will be a 1 as without it it'll simply be  ab

1 − b = 1 ( 1 − b )

Notice that it doesn't match with the upper one... so we'll change the signs

1 ( 1 − b ) = − 1 ( b− 1 )

(try to multiply them now!!

Jot them down in one expression

a ( b − 1 ) − 1 ( b − 1 )

You get!!!!!!

( a − 1 ) ( b − 1 )

Answer:

83.5%

Step-by-step explanation:

200-33= 167

167/200=x/100

167/2= 83.5

about 83.5%

Plss brainliest

The total weight of the person decrease is 167 pounds and the percentage by which person's weight decrease is 84%.

Percentage decrease is the value which is deducted or reduced from the initial value in the percentage part.

The weight of the person is 200 pound. The person's weighs on the  moon is 33.​

The change in the weight of the person is the difference of weight of the person and weight of the person on moon. Thus the change in weight of the person is,

[tex]\Delta W=200-33\\\Delta W=167[/tex]

The change in person's weight is 167 pounds and the original weight of the person is 200 pounds. Thus the percentage change is,

[tex]\Delta W=\dfrac{167}{200}\times100\\\Delta W=83.5\%\\\Delta W\approx84\%[/tex]

Thus, the total weight of the person decrease is 167 pounds and the percentage by which person's weight decrease is 84%.

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