A community is building a square park with sides that measure 110 meters. To separate the picnic area from the play area, the park is split by a diagonal line from the opposite corners Determine the approximate length of the diagonal line that splits the square.

Given:

[tex]\tan 8\theta =\cot 7\theta[/tex]

To find:

The value of [tex]\theta[/tex].

Solution:

We have,

[tex]\tan 8\theta =\cot 7\theta[/tex]

We know that, [tex]\cot \theta =\tan (90^\circ -\theta)[/tex].

Using the trigonometric property, we get

[tex]\tan 8\theta =\tan (90^\circ -7\theta)[/tex]

On comparing both sides, we get

[tex]8\theta =90^\circ -7\theta[/tex]

[tex]8\theta +7\theta=90^\circ [/tex]

[tex]15\theta=90^\circ [/tex]

Divide both sides by 15.

[tex]\theta=\dfrac{90^\circ}{15}[/tex]

[tex]\theta=6^\circ[/tex]

Therefore, the value of [tex]\theta[/tex] is 6 degrees.

Answer:

(2) 22.44 cm^2

Step-by-step explanation:

A = bh/2

A = (8.8 cm)(5.1 cm)/2

A = 22.44 cm^2

Answer:

22.44 cm^2

Step-by-step explanation:

8.8 - 7.6 = 1.2

1.2 · 5.1 = 6.12 / 2 = 3.06

7.6 · 5.1 = 38.76 / 2 = 19.38

19.38 + 3.06 = 22.44 cm^2

Answer:

y = -5/4 x + 2

Step-by-step explanation:

the slope of line segment : (1+7) /(9+1) = 8/10

= 4/5

the mid point of line segment :

x = (-1+9)/2= 4

y= (-7+1)/2 = -3

the coordinate : (4, -3)

the slope of line perpendicular to line segment

= -1 ÷ 4/5 = -5/4

so the equation :

y+3= -5/4 (x-4)

y+3= -5/4 x +5

y = -5/4 x + 2

Answer:

y = 4/1 + 0

Step-by-step explanation:

we rise 4 units up and move 1 unit to the right

and the y intercept is 0 because its exactly in the center of x and y axis

Step-by-step explanation:

[tex] \tt{} \frac{155}{18} \times 2[/tex]

[tex]\tt{} \frac{155}{9} [/tex]

[tex]\tt{}17 \frac{2}{9} \\ \\ \\ [/tex]

Answer:

A = $ 4188.38

Step-by-step explanation:

A= $2500

r = 3.5% = 0.035

t = 15years

n = 1

     [tex]A = P(1 + r)^t[/tex]

        [tex]= 2500 ( 1 + 0.035)^{15}\\\\= 2500 (1.67535)\\\\= \$ 4188.38[/tex]

Answer:

$0.43

Step-by-step explanation:

Rate of increase = [(CPI in 1990 / CPI in 1980)^1/t] - 1

(130.7 / 82.4)^1/10

1.586165^0.1 = 1.047213 - 1  = 4.72%

Price of dish soap in 1990 = value in 1980 ( 1 + rate of increase)^10

0.74( 1.047213)^10 = 1.174

Price increase 1.174 - 0.74 = 0.43

Answer:

180

Step-by-step explanation:

to work out all possibilities you multiple the amount of options.

4x5x9=180

Answer:

The answer will be 441907200 not sure

Step-by-step explanation:

Answer: [tex]108^{\circ}[/tex]

Step-by-step explanation:

Given

The top left and right corners measures [tex]72^{\circ}[/tex] and the bottom right corner measures [tex]108^{\circ}[/tex].

Suppose the missing corner measures [tex]x[/tex]

So, the sum of the four angles of parallelogram is [tex]360^{\circ}[/tex]

[tex]\therefore x+72^{\circ}+108^{\circ}+72^{\circ}=360^{\circ}\\\Rightarrow x=360^{\circ}-252^{\circ}\\\Rightarrow x=108^{\circ}[/tex]

Therefore, the missing angle is [tex]108^{\circ}[/tex].

Answer:

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

hope it helps...

have a great day!!

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]\frac{4^2}{2^2} = 4\\\\(8-4)*4=4^2\\\\2^2 + 2^2 = 8[/tex]

»»————-　★　————-««  

Here’s why:  

[tex]\boxed{\text{Simplifying each expression:}}\\\\\frac{4^2}{2^2}\\---------\\\\\\rightarrow \frac{16}{4}\\\\\rightarrow \boxed{4}\\\\ \boxed{\frac{4^2}{2^2}=4}[/tex]

⸻⸻⸻⸻

[tex](8-4) * 4\\-----------\\\rightarrow (4)*4\\\\\rightarrow \boxed{16}\\\\\text{We can also tell...}\\\\4^2 = 4 * 4 = \boxed{16}\\\\\text{So...}\\\\\boxed{(8-4)*4 = 4^2}[/tex]

⸻⸻⸻⸻

[tex]2^2 + 2^2\\--------------\\\rightarrow 4 + 2^2\\\\\rightarrow 4 + 4\\\\\rightarrow \boxed{8}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Sleeping - 30.2%

School - 17.6%

Homework - 0%

EC - 6.73%

Computer - 13.45%

Phone - 0%

Television - 1.68%

Excercise - 6.73%

Family time - 20.18%

Other - 3.36%

Step-by-step explanation:

hope this helps :)

Answer:

180

Step-by-step explanation:

it is a quadrilateral that has 360 degrees in total. So if 1 and 2=180 then 3 and 4=360-180=180. Hope this is right.....

Answer:

50 and C

Step-by-step explanation:

Remark.

The geometric mean is the middle number between two numbers that are 2 places apart. It's easier just to make up an example to show what the mean is

4 8 16

8 is the geometric mean of 4 and 16. The first term (4) is multiplied by 2. The third term is derived from 8 (the mean) multiplied by 2

So to solve this problem you need to find what a is multiplied to get get the mean, and multiplied again by the same thing you did before to go from the mean to the third term.

Solution

12 / mean = mean / a      Cross multiply

mean^2 = 12*a

But the mean is given as 10sqrt(6)

12a = 100 * 6

12a = 600

a = 50

20 / mean = mean /a

mean^2 = 20 a

mean = 10 sqrt (10)

100 * 10 = 20*a

a = 1000 / 20

a = 50

Step-by-step explanation:

• the area of circle M = 3.14×11² = 379.94

• the circumference of circle M =

2×3.14×11 = 69.08

• XY =√36²-11²=√1296-121=√1175=34.28

• L M = cos~¹ 11/36 = cos~¹0.3055 = 72.21°

• the area of triangle XY = ½×11×34.28

= 188.54

• the area of minor sector

= 72.21/360 × 379.94 = 76.20

• the minor arc from point X to

the point where YM intersects

withthe circle

= 72.21/360 × 69.08 = 13.86

Answer:33

Step-by-step explanation:

trust

Answer:

The length of ribbon is [tex]\sqrt{32}[/tex].

Step-by-step explanation:

Length of the side of square = 4 inches

let the length of the diagonal is x.

By use of Pythagorean theorem

[tex]x^2 = 4^2 + 4^2 \\\\x =\sqrt {16 + 16}=\sqrt{32}[/tex]

Answer:

1/3 x + 40 = 5/7 x

7x +(21)(40) = 15x

21*40 = 8x

x = 105cm3

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

you showed no diagram or any picture / screenshot

Answer:

B. Symmetry

Step-by-step explanation:

They are symmetrical, meaning they are mirrored or both look the same.

Hope this helps! :)

Answer:

a:c=1:8

Step-by-step explanation:

a:b=1:3

therefore a=1 and b=3

b:c=5:8

therefore b=5 and c=8

then,

a:c=1:8

Answer:

a : c = 5 : 24

Step-by-step explanation:

[tex]a : b = 1 : 3\\\\\frac{a}{b} = \frac{1}{3} \ => b = 3a\\\\b : c = 5 : 8 \\\\ \frac{b}{c} = \frac{5}{8} \ => \ \frac{3a}{c} = \frac{5}{8}[/tex]                  [tex][substituting \ b = 3a ][/tex]

                 [tex]\frac{a}{c} = \frac{5}{24}[/tex]

    [tex]=> a : c = 5 : 24[/tex]

Answer:

2022

Step-by-step explanation:

The duration of the loan David takes = 20 year loan

The amount David takes as loan = 70,000

The year David takes the loan = 2010

The year/loan balance relationship is y = -98·x² - 1,531·x + 69,710 (We note that the proper constant for the loan balance should be approximately 70,000, therefore the added zero)

Where;

x = The number of yeas

y = The balance

The year his loan balance will be $37,234.7, is given as follows;

37,234.7 = -98·x² - 1,531·x + 69,710

-98·x² - 1,531·x + 69,710 - 37,234.7 = 0

-98·x² - 1,531·x + 32,475.3 = 0

Factorizing with a graphic calculator, gives;

-98·(x - 11.998)·(x + 27.62) = 0

∴ x = 11.998 ≈ 12 or -27.62

The number of years it takes for the loan balance to be $37,234.7 = 12 years

Given that he took the loan in 2010, the loan balance will be $37,234.7 in 2010 + 12 = 2022

Answer:

The mode is 2

Step-by-step explanation:

Mathematically, the mode of a given data set represents the most recurring number or the number with the most count

Looking at the given dataset, we can see that the number 2 recurred 3 times

Compared with the other numbers, it has the most count

this means it is the mode of the given or displayed dataset

Answer:

[tex]-1\frac{2}{9}[/tex]

Step-by-step explanation:

         _

y = - 1.2

                 _

y × 10 = - 1.2 × 10

                _

10y = - 12. 2

                _

10y = - 12. 2

-         _

y = - 1.2

____________

9x = 11

9x ÷ 9 = 11 ÷ 9

[tex]x = -1\frac{2}{9}[/tex]

   _

- 1.2 = - 1 2/9

Answer:

4 im correct I don't care i used my brain and guessed

Step-by-step explanation:

Answer:

the  range is 16 mode is 5 and median is 11

Step-by-step explanation:

u can cheat if u exit out of  the assignment and then keep trying

Step-by-step explanation:

5(4× - 2)

5x4=20

5×2=10

Answer = 20x - 10

Answer:

20x-10

Step-by-step explanation:

Simply multiply.

5 × 4X = 20X

5× -2 = -10

Combine both

20X - 10