The diameter of a circle is 20 kilometers. What is the angle measure of an arc bounding a sector with area 10pi square kilometers?Give the exact answer in simplest form. ____°. (pi, fraction,)

Answer:

4490.5

Step-by-step explanation:

5(898)+0.5

=4490.5

The RELATION 1 and 3 represent a function

Rationale

There are no x value with several y values.

For a relation to be a function, there should only one y value fot each x

We need to choose 5 members from the general only

The number of general members = 31

As the arrangement is not required

So, the number of committees will be:

so, the answer will be 169,911 committees

STEP - BY - STEP EXPLANATION

What to find?

The power function that the given graph resembles.

Given:

f(x)=(x − 3)³

First, we need to note that;

If f(x) is shifted left q - units, then the new formula of the function becomes f(x+q).

Let q=3

ANSWER

y=x³

Given the function:

to find f(3), we have to make x = 3 and substitute on the function, to get the following:

therefore, f(3)=23

The equation of the vertical parabola in vertex form is written as

Where (h, k) are the coordinates of the vertex and p is the focal distance.

The directrix of a parabola is a line which every point of the parabola is equally distant to this line and the focus of the parabola. The vertex is located between the focus and the directrix, therefore, the distance between the y-coordinate of the vertex and the directrix represents the focal distance.

Using this value for p and (3, 1) as the vertex, we have our equation

Notice that there are two triangles between the parallel lines.

Also, notice that the angle 160° and y are same-side interior angles, so they sum 180°.

We solve for y.

On the other hand, angles 30 and x are alternate interior angles, which means they are congruent.

Given the sequence:

1/2, 3/4, 9/8, 27/16, ..........

We are to find the recursive formular

A recursive geometric formular has a pattern:

An = An - 1 * r

Where r is the common ratio. But before we write the formular, we need to look for the value of r.

This r value has to be the same between each consecutive number in the series.

Sinces it's geometric, r is multiplied in. To get from 1/2 to 3/2 we find the r value in this way:

x/2 = 3/4 where x/2 is the same as 1/2 x.

Cross multiply to get 4x = 6 and x = 3/2.

That means that if r is 3/2, then we can multiply every term in that sequence by 3/2 to get the next term in line.

3/4 times 32 is 9/8. So, r = 3/2 and the formulat is:

An = An - 1 * 3/2

Therefore, the crrect optio is B.

If the center of the circle is at O.then the measure of angle ABC is 28 degree

The measure of  angle ABC can be calculated by using central angle theorem

What is central angle theorem

The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points ie if the angle inscribes at the circumference is x, then the angle at the center is 2x.

The angle ABC = 1/2 angle AOC

the angle ABC = 1/2 x 56

the angle ABC is 28

Therefore, if the center of the circle is at O.then the measure of angle ABC is 28 degree

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The given expression is

First, we add x on each side

Then, we subtract 106 from each side

By the property of congruency of triangles, the following conclusions are taken from the figure

[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]

[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]

What is congruency of triangles?

Two triangles are said to be congruent if their corrosponding sides and corrosponding angles are same.

There are five axioms of congruency

They are SSS axiom, ASA axiom, AAS axiom, SAS axiom, RHS axiom

Here,

In[tex]\Delta AEB[/tex] and [tex]\Delta DEC[/tex]

[tex]\angle EAB = \angle ECD[/tex] [Alternate angle]

[tex]\angle EBA = \angle EDC[/tex] [Alternate angle]
AB = CD [Given]

So,

[tex]\Delta AEB \cong \Delta DEC[/tex] [ASA axiom]

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First, we need to identify the y-intercept that is the value of the coordinate y when the coordinate is 0 in this case our y-intercept is in 40

The y-intercept provide the start amount of water therefore the correct choice is D. the water level started at 40 mL

Here, we want to use the given information to calculate the lateral and the total surface area

To find the lateral area, we have to calculate the perimeter of the base and multiply this by the height of the triangular prism

Now, we will make the shape lie on its side

This mean the triangles will represent the base

Mathematically, the perimeter of a triangle is the sum of its side

We need the last side of the triangle

We can get this by the use of Pythagoras' theorem

As we can see, the side measure 5 is the hypotenuse as it faces the right angle

The square of the hypotenuse equals the sum of the squares of the two other sides

3,4 and 5 are a Pythagorean triple

This means that, the measure 3 is the last side of the triangle

So the perimeter is;

The height is the measure 8 inches

Thus, the lateral area is;

Now, we want the total surface area, but firstly, we need the area of the base

The area of the base is the area of the triangle

two times this is 12 in^2

The total suface area is thus;

The equation is,

The equation can be solved if on right side there is only variable with any number in multiplication. So equation can be solved as,

So to eliminate -2/3

Kevin recorded the distances he ran last week. The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday. How many miles did Kevin run on Wednesday?​

_______________________

The total number of miles he ran on Monday through Wednesday is the same as the total number of miles he ran on Thursday and Friday.

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

_____________________

Can you see the updates?

__________________

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

3x + 13 = 6x -2

6x - 3x = 13 + 2

3 x = 15

x = 15/3 miles

x = 5 miles

___________________________

5 + ( 5 + 9) + ( 5 + 4) = 2x + (4x - 2)

28 = 28

________________________

on Wednesday

x=5

x+ 4 = 9

_________________

Answer

On Wednesday he ran 9 miles

_________________

Can you see the updates?

Do you have any questions regarding the solution?

solution

diferent trim levels = 4

different colors = 5

different interior options = 3

then:

answer: 60 different versions of this model

SOLUTION

From this question, it means that

To be sure the required translation, let us see a quick look at the graph of the function and it's image

And

Now, we can see that the image is an enlarged form of the original function

Therefore this is a dilation. And since the increase in size is vertical, that is across the y-axis, It is a Vertical dilation.

Hence the correct answer is Vertical dilation.

Given that the baker has a total of 18 cups of flour, you know that the baker needs:

- This amount of flour for a batch of banana pancakes:

- This amount of flour for a batch of apple pancakes:

You know that the baker makes 8 batches of banana pancakes.

Let be "x" the greatest number of whole batches of apple pancakes that the baker can make.

You can set up this equation using the given data:

Now you need to solve for "x", in order to find its value:

Since the number of cups cannot be greater than 18 cups, you need to round down:

Hence, the answer is: Third option.

We can find the horizontal asymptote of this kind of functions using the limit:

Therefore the equation of the horizontal asymptote is:

You have the following interval:

(-∞,-2]

the previous interval can be written as follow:

x ≤ -2 as an inequality

and on the number line you have:

The answer is option B

Given:

/16x^2 + x^2/3 + 3/8x^5

You need to simplfiy the expression given which will give you

6 3/x^5 or the second option

For the given function,

             Vertical Asymptote:-  x =-3

             Horizontal asymptote:- y =20

             Oblique asymptote :- No oblique asymptote

Asymptote:

                     A vertical asymptote is found by letting the denominator equal zero. A horizontal asymptote is found by comparing the leading term in the numerator to the leading term in the denominator. The degree of the numerator is greater than the degree of the denominator, so there is no horizontal asymptote.

                                                            Oblique asymptotes occur when the degree of the denominator of a rational function is one less than the degree of the numerator

given,

            R(x) = [tex]\frac{20x}{x+3}[/tex]

Vertical Asymptote:-

                                  Equate denominator to zero

                                    x +3 = 0

                                        x = -3

Horizontal asymptote:-

                                   Here degree on x in numerator and denominator is same,

              so horizontal asymptote will be,  

                                y= 20/1

                                y = 20

Oblique asymptote:-

                                 There won't be any slant asymptote, because degree in numerator is equal to the degree in denominator.

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The function is given as,

For x = -1 , the value of y is calculated as,

For x = 0 , the value of y is calculated as,

For x = 1 , the value of y is calculated as,

For x = 2, the value of y is calculated as,

From the question we are to determine Britta most likely task in preparing a budget.

First let's know what a budget is.

A budget is an estimation of revenue and expenses over a specified future period of time and is utilized by governments, businesses, and individuals. A budget is basically a financial plan for a defined period, normally a year that is known to greatly enhance the success of any financial undertaking.

So with the above explanation of what a budget is, Britta most likely task is to allot a set amount of money for her expenses.

Therefore the correct option is C, which is She is allotting a set amount of money for her expenses.

1) Firstly, let's express each plan by using linear equations.

Plan A:

5x+320

Note that the $320 payment is done once, then 5 per session.

Plan B

15x

2) To get to know when opting for plan A or Plan B is not relevant, we need to equate both equations and solve it for x (x stands for the number of sessions)

So if you attend 32 sessions then, doesn't really matter which plan is it.

3) Now, let's figure out which plan is more interesting to take:

So the plan B is cheaper to attend 1 session

a.

Therefore, your score would be 70% then you will get a C

b.

Your score would be 82.5%, then you will get a B

c.

Your score would be 86.4%, then you will get a B

f(x) = x +57

g(x) =7x+15

The solution is (7,64). To rent the cabin for 7 days cost $64

1) Let's examine the graph. We can see two linear equations.

Picking two points for f(t) = (7,64) and (0,57) and for g(t) (0,15) and (7,64) let's find out their respectives slopes:

2) For f(t) , let's plug into the slope-intercept formula, plugging one point:

(0,57)

y=mx+b

57=0x +b

57= b

So the rule for the function is, in terms of f(x) = x +57

(0,15)

y=mx +b

15=0x +b

15 =b

So the rule for the function g(t) , in terms of g(x) is g(x) =7x+15

Interpreting the solution:

The solution to this Linear System of Equations is the common point (7,64).

So filling in the blanks we have:

The solution is (7,64). To rent the cabin for 7 days cost $64

Given: The coordinates of a trapezoid as below

To Determine: The final step on the trapezoid after it is reflected over the x-axis and then reflected over the axis

Solution

Please note that a reflection over the x-axis and reflection over the y-axis is different from the last step, which is a reflection over the y-axis

The reflection over the y-axis could either be a rotation of 90^0 clockwise or anticlockwise.

So get the trapezid onto itself after a reflection over the y-axis from a reflection over teh x-axis requires two steps

We have step 1: Reflection over the x-axis, then

Step 2: Reflection over the y-axis

Hence, the final step is reflection over the y-axis

We have the distribution;

74, 90, 21, 68, 62, 84, 34, 87,74.

Let's arrange this from ascending to descending order, we obtain;

i. The mean or average of this distribution is

ii. The median is the central value, in this distribution, there are 9 values, so the median value is the 5th value.

iii. The mode is the value with the highest frequency, this is the most occurring value, in this distribution;

iv. The range is the difference between the highest and lowest values, this is;