Find (a) arc length and (b) Area of a sector.

Answer:  Angle Y is 90 degrees, angle X is 35.  

Answer:x=35 and y=35

Step-by-step explanation:

Angle on straight line =180

so 180/2=90

90-55=35

and x and y opposite angle so are eqaul

Using the combination formula, and supposing that you have n parts, it is found that the number of trains you can make is of:

[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]

The order in which the parts are taken is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, 3 parts are taken from a set of n, hence the total number of trains is given by:

[tex]N = C_{n,3} = \frac{n!}{3!(n - 3)!} = \frac{n!}{6(n-3)!}[/tex]

More can be learned about the combination formula at https://brainly.com/question/25821700

#SPJ1

At the end of the third year the population of beetles will be 11,576beetles

The standard form of an exponential function is given as:

y = ab^t

Given the following parameters

initial population 'a" = 10,000 beetles

Time = 3 years

rate b = 1.05

Substitute into the formula

y = 10,000(1.05)^3

y = 10,000(1.1576)
y = 11,576 beetles

Hence at the end of the third year the population of beetles will be 11,576beetles

Learn more on exponential function here: https://brainly.com/question/12940982

#SPJ4

Answer:

Step-by-step explanation:

Area of sector :

Answer:

x= -2 y= 36 (-2. 36)

x = -1 y = 6 (-1, 6)

x = 1 y = [tex]\frac{1}{6}[/tex] (1, [tex]\frac{1}{6}[/tex])

Step-by-step explanation:

Our function is [tex]y = (\frac{1}{6})^x[/tex]

all we need to do is fill in our x (given in the table) to solve for y

[tex]y = (\frac{1}{6})^{-2}[/tex]

[tex]y = 36[/tex]

[tex]y = (\frac{1}{6})^{-1}[/tex]

[tex]y = 6[/tex]

[tex]y = (\frac{1}{6})^1 = \frac{1}{6}[/tex]

Answer;

10

Step-by-step explanation:

from the question we observed that the shape is a right angled triangle.

and according to Pythagoras theorem, In a right angled triangle the square of the hypothenus is equal to the square of the sum of the other two side

hypothenus = 10

10^2= 8^ + X^2

100= 64 +X^2

X^2 = 100-64

X^2 = 36

X = √36

X= 6

Ok so firstly, you need to remember that when a radius is touching a tangent, the angle is always equal to 90°. So x + 57° = 90°. That means your angle is 33°. You have drawn a right angle which is correct so the left triangle's angle is 90° - 33° = 57°. Now because both sides of the triangle is radius, that means c and 57° are equal. That means c = 57°.

Answer:

c = 57 degrees.

Step-by-step explanation:

This is the Alternate Segment theorem:

The angle between a chord of a circle and a tangent to the circle = the angle subtended by the chord in the alternate segment.

So c = 57 degrees.

Answer:

50%

half of the numbers are even

Step-by-step explanation:

Answer:

It is the first one

Hope this helps!

Answer:

I believe it is 4x+10y=200, x+y=38

Explanation:

[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

   Find the gradient of the line joining (-1,9) and (3,5)

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with the numbers:-

[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]

[tex]\circ[/tex] On simplification,

[tex]\boxed{\frac{-4}{3+1}}[/tex]

[tex]\circ[/tex] On further simplification,

[tex]\boxed{\frac{-4}{4}}[/tex]

[tex]\circ\sf{SLOPE=-1}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

-2

Step-by-step explanation:

z - 7 ≥ 0

z ≥ 7

| z - 7 | = z - 7, z ≥ 7

| z - 7 | = -z + 7, z < 7

z - 9 ≥ 0

z ≥ 9

| z - 9 | = z - 9, z ≥ 9

| z - 9 | = -z + 9, z < 9

| z - 7 | = -z + 7

| z - 9 | = -z + 9

|z - 7| - |z - 9|

-z + 7 - (-z + 9)

-z + 7 + z - 9

= -2

The relation between the exponential and the logarithm is used. Then the expression [tex]e^{\ln3}[/tex] is given as 3.

Exponents can also be written as logarithms. A number base logarithm is similar to some other number. It is the exact inverse of the exponent expression.

The expression is given below.

[tex]\rightarrow e^{\ln3}[/tex]

We know the formula

[tex]\rm e^{\ln x} = x[/tex]

Then the expression can be written as

[tex]e^{\ln3} = 3[/tex]

More about the logarithm link is given below.

https://brainly.com/question/7302008

#SPJ1

Answer:

14 gm

Step-by-step explanation:

34 minutes is TWO half lives   1/2 * 1/2 = 1/4   will be left

   1/4 * 56 = 14 gm

The cone is a three dimensional shape, and the value of the height of the cone is 27 inches

The given parameters are:

The volume of the cone is calculated using:

[tex]V = \frac13 Bh[/tex]

So, we have:

[tex]45 = \frac13 * 5 * h[/tex]

Divide both sides by 5

[tex]9 = \frac13 * h[/tex]

Multiply both sides by 3

h = 27

Hence, the value of the height of the cone is 27 inches

Read more about volume at:

https://brainly.com/question/1972490

#SPJ4

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

[tex]\diamond\large\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond[/tex]

             What is the equation of the line that passes through the point  (2, 5) and has a slope of 5?

[tex]\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}\diamond[/tex]

First let's write the equation of the line in point-slope form:-

[tex]\sf{y-y_1=m(x-x_1)}[/tex]

Substitute 5 for y₁, 5 for m and 2 for x₁:-

[tex]\sf{y-5=5(x-2)}[/tex]

That's the equation of the line in Point-slope form.

Now let's convert it into slope-intercept:-

[tex]\sf{y-5=5x-10}[/tex]

Adding 5 to both sides results in our slope intercept equation, which looks like this:-

[tex]\dashrightarrow\bigstar\boxed{\boxed{\bold{\underline{y=5x-5}}}}\bigstar\dashleftarrow[/tex]

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

Answer:

yes not function because 1 is repeated

Answer:

660 cubic cm

Step-by-step explanation:

Volume= bhl/2

Solution, Diameter = 30[tex]radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ [/tex]

Now, []area = \pi {r}^{2} [/tex][tex] = 3.14 \times 15 \times 15[/tex][tex] = 706.5 [/tex]Hence the area is 706.5now........[tex]circumference = 2 \: \pi\: r[/tex][tex] = 2 \times 3.14 \times 15[/tex][tex] = 94.2[/tex]hence the answer is 94.2...

Solution,

Diameter = 30

[tex]radius = \frac{diameter}{2} = \frac{30}{2} = 15 \\ [/tex]

Now,

[tex]area = \pi {r}^{2} [/tex]

[tex] = 3.14 \times 15 \times 15[/tex]

[tex] = 706.5 [/tex]

Hence the area is 706.5

now........

[tex]=Circumference = 2 \: \pi\: r[/tex]

[tex] = 2 \times 3.14 \times 15[/tex]

[tex] = 94.2[/tex]

hence the answer is 94.2...

Answer:

1st option

Step-by-step explanation:

the equation for an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 7 and d = a₂ - a₁ = 3 - 7 = - 4 , then

[tex]a_{n}[/tex] = 7 - 4(n - 1)

Answer:

The answer is option A

Step-by-step explanation:

The solution is in the image

Step-by-step explanation:

it shows that all the small triangles that together make the complete square (c²) under the Hypotenuse consist of exactly all the composing triangles of the squares above the legs (a² and b²).

we find the 2 purple, the 2 orange, the 2 yellow and the 2 blue triangles there.

so, the area of c² must be the same as the sum of the areas of a² and b².

Answer:

Step-by-step explanation:

Sum of all angles of triangle = 180

     5x - 11 + 3x - 3 + 3x + 18 = 180

      5x + 3x + 3x  -11 - 3 + 18 = 180

Combine like terms

                             11x  + 4 = 180

                                   11x = 180 - 4

                                   11x = 176

                                      x = 176/11

                                       x = 16

∠R = 5x - 11

   = 5*16 - 11

   = 80 - 11

    = 69

Apply angle sum property

m<R

Answer:

Option 2

Step-by-step explanation:

Checking whether P(A) × P(B) = P(A∩B) :

Since this does not obey the Multiplication rule of probability, these events are not independent.

So, the answer is :

No, they are dependent because P(A) ⋅ P(B) ≠ P(A ∩ B)

Answer:

Option B

Step-by-step explanation:

Option A should be true if they are independent

So

They are dependant

Answer:

- 95/18

Step-by-step explanation:

1st you have to convert the mixed number to an improper fraction so 2 ×6 = 12 +1 = 13 and that together equals 13/6 same goes for the next take away the parentheses 13/6 - 8/3 - 4 7/9

then you have to do the same thing with the 1st fraction convert it 4 × 9 = 36 + 7 = 43 that equals together 43/9

lastly you have to calculate the difference 13/6 - 8/3 - 43/9 and that equals negative 95/18

by the way the 95 isnt a negative the fraction itself is

Answer:

Yes

Step-by-step explanation:

But not all rational numbers are natural numbers, so be careful of that.

Answer:

(x+y)(z+1)

Step-by-step explanation:

trust me .......

Answer:

(x+y) (z+1)

Step-by-step explanation:

xz + x + yz + y

- group the first two terms and the last two terms.

(xz + x ) + yz + y

- factor out the greatest common factor (GCF) from each group.

x (z + 1) + y (z + 1)

- factor the polynomial by factoring out the greatest common factor, z + 1.

(x+y) (z+1)

Explanation:

Choice A simplifies to 9n-8 after combining the like terms -7n+16n to get 9n

Choice C simplifies to 9n-8 for similar reasoning. The n+8n turns into 9n

This shows choices A and C are equivalent to choice D. Choice B isn't the same because 9(n-8) = 9n-9*8 = 9n-72. Use the distributive property.

Answer:

B. 9(n - 8)

Step-by-step explanation:

- 8 - 7n + 16n

-8 (-7n + 16n or 16n - 7n)

-8 + 9n

9n - 8

9(n - 8)

9n - 72

n - 8 + 8n

9n - 8

9n - 8