A circle has a radius of 5 in. A central angle that measures 150° cuts off an arc.
Explain how to find the arc length exactly, and then approximate it to one decimal place.​

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{a}~,~\stackrel{y_1}{b})\qquad (\stackrel{x_2}{c}~,~\stackrel{y_2}{d})\qquad \qquad d = \sqrt{\underset{\underset{\textit{horizontal distance}}{\uparrow }}{( x_2- x_1)^2} + ( y_2- y_1)^2} \\\\[-0.35em] ~\dotfill\\\\ \textit{so in short is just }x_2-x_1[/tex]

Answer:

Option A is correct.

Step-by-step explanation:

We are given:

[tex]\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi[/tex]

We need to find the value of a.

The LCM of (2+i) and (3+i)  is (2+i)(3+i)

[tex]=\frac{2i(3+i)}{(2+i)(3+i)}-\frac{3i(2+i)}{(2+i)(3+i)}\\=\frac{6i+2i^2}{(2+i)(3+i)}-\frac{6i+3i^2}{(2+i)(3+i)}\\=\frac{6i+2i^2-(6i+3i^2)}{(2+i)(3+i)}\\=\frac{6i+2i^2-6i-3i^2)}{5+5i}\\=\frac{-i^2}{5+5i}\\i^2=-1\\=\frac{-(-1)}{5+5i}\\=\frac{1}{5+5i}[/tex]

Now rationalize the denominator by multiplying by 5-5i/5-5i

[tex]=\frac{1}{5+5i}*\frac{5-5i}{5-5i} \\=\frac{5-5i}{(5+5i)(5-5i)}\\=\frac{5-5i}{(5+5i)(5-5i)}\\(a+b)(a-b)= a^2-b^2\\=\frac{5(1-i)}{(5)^2-(5i)^2}\\=\frac{5(1-i)}{25+25}\\=\frac{5(1-i)}{50}\\=\frac{1-i}{10}\\=\frac{1}{10}-\frac{i}{10}[/tex]

We are given

[tex]\frac{2i}{2+i}-\frac{3i}{3+i} = a+bi[/tex]

Now after solving we have:

[tex]\frac{1}{10}-\frac{i}{10}=a+bi[/tex]

So value of a = 1/10 and value of b = -1/10

So, Option A is correct.

Final answer:

After simplifying the complex fractions and subtracting them, the real part a is found to be 0.1, which corresponds to option A, 1/10.

Explanation:

To solve the equation (2i/2+i)-(3i/3+i)=a+bi, we want to find the real part (a) and the imaginary part (b) after simplifying the given expression. We will need to perform complex number arithmetic by simplifying each fraction separately and then subtracting them. This process involves multiplying the numerator and the denominator by the conjugate of the denominator to make the denominator real.

First, let's simplify (2i/2+i):

(2i)/(2+i) = (2i)(2-i)/(2+i)(2-i) = (4i-2i²)/(4+2i-2i-i²) = (4i+2)/(4+1) = (2+4i)/5 = 0.4+0.8i.

Now, let's simplify (3i/3+i):

(3i)/(3+i) = (3i)(3-i)/(3+i)(3-i) = (9i-3i²)/(9+3i-3i-i²) = (9i+3)/(9+1) = (3+9i)/10 = 0.3+0.9i.

Next, subtract the two results:

(0.4+0.8i) - (0.3+0.9i) = 0.4 - 0.3 + (0.8i - 0.9i) = 0.1 - 0.1i.

So, a = 0.1 and b = -0.1. Comparing this with the given options, we can conclude that a = A. 1/10.

The calculated value of the variable A from the table of values is -3x²

How to determine the value of the variable A

From the question, we have the following parameters that can be used in our computation:

The contingency table

The cell A is in the row -x and the column 3x

This means that

A = 3x * -x

When the product is evaluated, we have

A = -3x²

Hence, the value of the variable A is -3x²

Answer:

See explanation

Step-by-step explanation:

Consider triangles ABD and BEC. In these tirangles:

So, by AA similarity theorem, tringles DBA and CBE are similar. Similar triangles have proportional corresponding sides, thus

[tex]\dfrac{BD}{BC}=\dfrac{DA}{CE}=\dfrac{AB}{BE}\Rightarrow BE\cdot DA=AB\cdot CE[/tex]

Answer:

Area of rhombus = 126 m²

Explanation:

We are given that the two diagonals of the rhombus are:

D₁ = 14 meters and D₂ = 18 meters

The area of the rhombus using its diagonals can be calculated using the following rule:

[tex]Area = \frac{D_1 * D_2}{2}[/tex]

Substitute with the given values to get the area as follows:

[tex]Area = \frac{14*18}{2}=126 m^2[/tex]

Hope this helps :)

Answer:

2.16m2

Step-by-step explanation:

It has 3 zeroes which are

[tex]\frac{-1}{2}, -1, \frac{4}{5}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

Distribute -0.2:

-0.2 * x = -0.2x

-0.2 * -4 = 0.8

-0.2x + 0.8 = -1.7

Subtract 0.8 from both sides:

0.8 - 0.8 = 0

-1.7 - .8 = -2.5

Divide -.2x from both sides:

-0.2x = -2.5

x = 12.5

Hence, the value of x is 12.5

Answer: C I think. My answers are all confusing so I apologize if I make u get it wrong.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Initial # = 176 fans

Final # = 202 fans

Increase = 202 - 176 = 26 fans

% increase = 100% x (Increase / initial #)

= 100 x (26/176)

= 100 x 0.1477

= 14.78%

Answer:

Option b) 6-10 lbs

Step-by-step explanation:

Given that X, the weight of  toy American Eskimo dog has mean of 8 pounds with a standard deviation of 1 pound

For 95% of the dogs according to normal distribution would lie between 2 std deviations on either side of the mean.

i.e. lower bound= Mean- 2 std deviation = 8-2 =6

Upper bound = Mean +2 std dev = 8+2 =10

Hence range of weights would be

6-10 lbs

Option b is the answer

The range of weights for 95% of toy American Eskimo dogs, assuming a normal distribution with a mean of 8 pounds and a standard deviation of 1 pound, would be 6 to 10 pounds.

To find the range of weights for which 95% of toy American Eskimo dogs fall under, given a mean weight of 8 pounds and a standard deviation of 1 pound, we use the properties of the normal distribution. The 95% interval is also known as the 95% confidence interval, and we can use the empirical rule or z-scores to calculate this. The empirical rule states that approximately 95% of data within a normal distribution lies within two standard deviations of the mean. Therefore, the range would be from 8 - (2 × 1) to 8 + (2 × 1), resulting in a weight range of 6 to 10 pounds.

Answer:

B. 16.2 ft

Step-by-step explanation:

one vertex to the stake is 8.1, and because the stake is the "halfway" point, the diagonal is twice that length.

8.1 * 2 = 16.2 ft

Answer:

The correct option is B.

Step-by-step explanation:

Given: Rectangle with the stake marking where diagonal intersect each other.

To find  : The length of the one of the diagonal.

Solution:

Diagonals of rectangle bisect each other into two equal parts.

So, the distance of all vertices from the stake will be same as that of the 8.1 feet.

So the length of the diagonal will be:

[tex]2\times \text{Distance from 1 vertex to the stake}[/tex]

[tex]=2\times 8.1 feet=16.2 feet[/tex]

Hence, the length of the diagonal will be 16.2.

Answer:

(x - 1)

Step-by-step explanation:

Given

8x² - 15x + 7

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term

product = 8 × 7 = 56 and sum = - 15

The factors are - 8 and - 7

Use these factors to split the x- term

8x² - 8x - 7x + 7 ( factor the first/second and third/fourth terms )

= 8x(x - 1) - 7(x - 1) ← factor out (x - 1) from each term

= (x - 1)(8x - 7) ← in factored form

The missing factor is (x - 1)

Answer:

1 and 4 should be the answer since 1 is 4 just angled differently

^-^

Answer:

p^3

--------

n^6

Answer: correct option is C

Step-by-step explanation:

Took test

Answer:

18:21 is equivalent to 18/21. When you simplify 18/21, you get 6/7

Answer:

85.714285714286%

Step-by-step explanation:

i hope this helps, if you are looking for the percentage.

Answer:   The answer is:  " 400 " .

____________________________________________

             →   20% of    400    is  80 .

____________________________________________

Step-by-step explanation:

____________________________________________

  20% of  "x" = 80 ;  Solve for  " x " ;  

20%   =  20/100 ;

         =   20 ÷  100 ;

         =   20.  ÷ 100 ;

         =   0.20  ;  

____________________________________________

Note that when dividing by 100 , we move the decimal        

point backward (when "dividing") — 2 (two) spaces —

                                since "100" has 2 (two) "zeros" .

____________________________________________

         →   0.20 = 0.2 ;  

____________________________________________

          →   (0.2) x = 80 ; Solve for "x" ;

In this case, multiply each side of the equation by "10" ; to get rid of the "decimal value" ; as follows:

          →  (10) * (0.2) x = 80 * 10) ;

   to get:

          →   2x  =  800  ;

Now, divide Each Side of the equation by "2" ;

     to isolate "x" on one side of the equation ;

      & to solve for "x" ;  as follows:

          →   2x / 2  =  800 / 2  ;

          →     x  =  400 .

____________________________________________

The answer is:  " 400 " .

____________________________________________

   →  20% of    400    is  80 .

__________________________________________________

Hope this is helpful to you!

        Best wishes in your academic pursuits

              — and within the "Brainly" community!

____________________________________________

Answer:

400

Step-by-step explanation:

20% of 400 is 80.

20% × x = 80

Multiply both sides by 100 and divide both sides by 20,.

x = 80 ×  100/20

x = 400

Answer:

B. y + 1 = 6(x - 6)

Step-by-step explanation:

First, find the rate of change [slope], then insert the coordinates into the formula with their CORRECT signs. Remember, in the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE term of what they really are.

Answer:

-6 is not in the domain of f(x) but is in the range of f(x)

Step-by-step explanation:

we have

[tex]f(x)=-2\sqrt{x-7}+1[/tex]

Find the domain of the function

we know that the radicand must be greater than or equal to zero

so

[tex]x-7\geq 0\\ \\x\geq 7[/tex]

The domain is all real numbers greater than or equal to 7

The range is the interval -----> (-∞,1]

[tex]y\leq1[/tex]

All real numbers less than or equal to 1

see the attached figure to better understand the problem

therefore

The statement that best describes the function f(x) is

-6 is not in the domain of f(x) but is in the range of f(x)

Answer:

B is the right choice. -6 is not the domain of f(x) but is in the range of f(x)

Answer:

The second choice, 55 cm.

Step-by-step explanation:

Formula for circumference:

[tex]\pi * d[/tex]

[tex]\frac{22}{7} * \frac{35}{2} = \frac{770}{14}  \\\\770 / 14 = 55[/tex]

The circumference of the circle is 55 cm.

Answer:

Circumference of circle is:

55 cm

Step-by-step explanation:

we are given diameter d of a circle=35/2 cm

We have to find its circumference.

We know that circumference of circle in terms of its diameter is:

Circumference=πd

Circumference=[tex]\dfrac{22}{7}\times \dfrac{35}{2}[/tex]

                        =55 cm

Hence, circumference of circle is:

55 cm

Answer:

base= 2 cm

Step-by-step explanation:

A=1/2bh

(1/2x)40=1/2b(10)x(1/2)

20=b(10)/10

2=b

Answer:

base = 8 cm

Step-by-step explanation:

A= 1/2bh

40=1/2*b*10

40/ 1/2= 80

80/10= 8

b=8

Answer:

z = [tex]\frac{50}{3}[/tex]

Step-by-step explanation:

The ratio of corresponding sides are equal, that is

[tex]\frac{z}{10}[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )

12z = 200 ( divide both sides by 12 )

z = [tex]\frac{200}{12}[/tex] = [tex]\frac{50}{3}[/tex]

Answer:

[tex]x=1(+/-)0.5i\sqrt{10}[/tex]

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to

[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]2x^{2}=4x-7[/tex]  

[tex]2x^{2}-4x+7=0[/tex]  

so

[tex]a=2\\b=-4\\c=7[/tex]

substitute

[tex]x=\frac{4(+/-)\sqrt{(-4)^{2}-4(2)(7)}} {2(2)}[/tex]

[tex]x=\frac{4(+/-)\sqrt{-40}} {4}[/tex]

Remember that

[tex]i=\sqrt{-1}[/tex]

[tex]x=\frac{4(+/-)2i\sqrt{10}} {4}[/tex]

[tex]x=1(+/-)0.5i\sqrt{10}[/tex]

Add the like terms:

8x2+x2=9x2

-9y2-3y2=-12y2

-4x-7x=-11x

Combine each term:

9x2-12y2-11x

Hope this helps!!

The sum of the polynomial will be,9x²-6y²-11x. Option B is correct.

A polynomial is an algebraic statement made up of variables and coefficients. Variables are sometimes known as unknowns.

We can use arithmetic operations like addition, subtraction, and so on. However, the variable is not divisible.

⇒(8x²-9y²-4x)+(x²-3y²–7x)

⇒9x²-6y²-11x

The sum of the polynomial will be,9x²-6y²-11x.

Hence, option B is correct.

To learn more about polynomials, refer:

https://brainly.com/question/17822016

#SPJ2

Answer:

(x + 2)²

Step-by-step explanation:

x² + 4x + 4 ← is a perfect square of the form

(x + a)² = x² + 2ax + a²

Comparing coefficients of like terms

4 = 2² ⇒ a = 2 and 2ax = (2 × 2)x = 4x

Hence

x² + 4x + 4 = (x + 2)²

Answer:

7 Hours 12 Minutes

Step-by-step explanation:

So they one of the printer increases at a rate of 1/12 and the other increases at a rate of 1/18. Since you don't know the time it actually takes, you will replace both numerators with and x. (x/12 and x/18). You want to set these up so that they are adding. (x/12 + x/18=1). Since you're adding, you want to change it to the same denominator. The lowest is 36 so you multiply x/12 by 3/3 (so you don't unbalance the equation) and x/18 by 2/2. You'll end up with 3x/36 + 2x/36= 1 which will simplify to 5x/36=1. Multiply each side by 36 to leave the variable by itself. It becomes 5x=36 and when you divide it by 5 you get 7.2. So it's seven and .2 hours, which is equivalent to7 and 1/5 of an hour or 7 hours and 12 minutes.

Final answer:

When the two printing presses work together, they complete the job in 7.2 hours by adding their rates of work.

Explanation:

To solve how long it will take for two printing presses to complete a job when working simultaneously, one needs to add their individual rates of work. The first press can print the newspaper in 12 hours, and the second press can print it in 18 hours. Their rates are 1/12 and 1/18 newspapers per hour, respectively.

To find out how many newspapers per hour they can produce together, we simply add their individual rates:

1/12 newspaper per hour (first press) + 1/18 newspaper per hour (second press) = (1/12 + 1/18) newspapers per hour

Finding a common denominator, which is 36, we get:

(3/36 + 2/36) newspapers per hour = 5/36 newspapers per hour

Now, to find how long it takes for the combined presses to print one newspaper, take the reciprocal of the combined rate:

1 / (5/36) = 36/5 hours

Therefore, if both presses work together, they will complete the job in 7.2 hours.

Answer: First Option

Walter needs to make at least 5 more cookies but no more than 40

[tex]5 \leq x \leq 40[/tex]

Step-by-step explanation:

If we call x the number of cookies that Walter needs to make, then we know that the amount of cookies will be:

[tex]x +15[/tex]

Then this amount must be greater than or equal to 20 and must be less than or equal to 55 then.

[tex]x + 15 \geq20[/tex] and [tex]x + 15 \leq55[/tex]

This is:

[tex]20 \leq x + 15 \leq 55[/tex]

We solve the inequality for x.

[tex]20-15 \leq x + 15-15 \leq 55-15\\\\5 \leq x \leq 40[/tex]

Then the amount of cookies that Walter must make must be greater than or equal to 5 and less than or equal to 40

Answer: It is A

Step-by-step explanation:

Answer:

4th option

Step-by-step explanation:

Solve and rearrange the second equation for y

y= 2 +3

y =5

The substitute y in first equation to get x

Answer:

The answer in the procedure

Step-by-step explanation:

Let

m1 and m2 ----> the slopes of the lines constructed

we know that

If two lines are perpendicular, then the product of their slopes is equal to -1

therefore

To verify if the lines constructed are perpendicular

Multiply their slopes

if m1*m2=-1 ------> the lines are perpendicular

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

Answer:

7/78 - 35/78i

Step-by-step explanation:

A complex number is a real number, an imaginary number or a number with both real and imaginary number. Its standard form is:

a + bi

For the expression, 7/ 3-15i

(7/ 3-15i) (3+15i)

21 - 105i / (234)

7/78 - 35/78i