a circle has a radius of 9. An arc in this circle has a central angle of 120°. What is the length of the arc?

Answer:

The factorization of [tex]729x^{15} +1000[/tex] is [tex](9x^{5} +10)(81x^{10} -90x^{5} +100)[/tex]

Step-by-step explanation:

This is a case of factorization by sum and difference of cubes, this type of factorization applies only in binomials of the form [tex](a^{3} +b^{3} )[/tex] or [tex](a^{3} -b^{3})[/tex]. It is easy to recognize because the coefficients of the terms are perfect cube numbers (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).

Let's solve the factorization of [tex]729x^{15} +1000[/tex] by using the sum and difference of cubes factorization.

1.) We calculate the cubic root of each term in the equation [tex]729x^{15} +1000[/tex], and the exponent of the letter x is divided by 3.

[tex]\sqrt[3]{729x^{15}} =9x^{5}[/tex]

[tex]1000=10^{3}[/tex] then [tex]\sqrt[3]{10^{3}} =10[/tex]

So, we got that

[tex]729x^{15} +1000=(9x^{5})^{3} + (10)^{3}[/tex] which has the form of [tex](a^{3} +b^{3} )[/tex] which means is a sum of cubes.

Sum of cubes

[tex](a^{3} +b^{3} )=(a+b)(a^{2} -ab+b^{2})[/tex]

with [tex]a= 9x^{5}[/tex] y [tex]b=10[/tex]

2.) Solving the sum of cubes.

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)((9x^{5})^{2}-(9x^{5})(10)+10^{2} )[/tex]

[tex](9x^{5})^{3} + (10)^{3}=(9x^{5} +10)(81x^{10}-90x^{5}+100)[/tex]

.

Answer:

1/2

Step-by-step explanation:

3+7+10=20

20/2=10=1/2

Answer:

Step-by-step explanation:

Lateral Area:

The formula of a Lateral Area of a cone:

[tex]L.A.=\pi rs[/tex]

r - radius

s - slant height

We have r = 5m and s = 12m. Substitute:

[tex]L.A.=\pi(5)(12)=60\pi\ m^2\\\\\pi\approx3.14\to L.A.\approx(6)(3.14)=188.4\ m^2[/tex]Surface Area:

The formula of a Surfaace Area of a cone:

[tex]S.A.=B+L.A.[/tex]

In the base we have the circle with the radius r = 5m.

The formula of an area of a circle"

[tex]A_O=\pi r^2[/tex]

Substiute:

[tex]B=\pi(5^2)=25\pi\ m^2\approx(25)(3.14)=78.5\ m^2[/tex]

[tex]S.A.=60\pi+25\pi=85\pi\ m^2\approx188.4+78.5=266.9\ m^2[/tex]

Here is the answer:...

Answer:

- Solve for y

- Subtract  2 x  from both sides of the equation then divide by  5 .

-y = 1 − 2 x 5

Step-by-step explanation:

Answer:

Point S coordinates= (-4,5)

Step-by-step explanation:

If you would just move the point 5 PLACES TO THE RIGHT, you would get -4, 5, which is the correct answer.

Answer:

- 864

Step-by-step explanation:

In the case of a 2 × 2 matrix the determinant may be defined as:

|A| = [tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]= ad-bc

Given in the question a matrix

[tex]\left[\begin{array}{cc}-30&-6\\6&30\\\end{array}\right][/tex]

(-30)(30) - (-6)(6)

-900 + 36

- 864

Answer:

Option A: -30

For Odyssey

**If you are on the pre-test then you might wanna take your time because they can suspect if you are cheating**

Answer:

the one for the arrow point to #26 is min # in summary of data

the one where the arrow points between#30 and 32:  median

arrow pointing to #44 is: outlier

and the bottom choice is: mean

Step-by-step explanation:

Answer:

The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Step-by-step explanation:

Given : Sample size(n)= 144

Sample mean [tex]\mu= 22 ug/m^3[/tex]

Standard deviation [tex]\sigma=3.5 ug/m^3[/tex]

To find : 99.7% confident that actual concentration of fine particulates at the school is?

Solution :

The formula for confidence interval is

[tex]CI=\mu \pm z\times\dfrac{\sigma}{\sqrt{n}}[/tex]

Substituting the values in the formula,

[tex]CI=22 \pm 3\times\dfrac{3.5}{\sqrt{144}}[/tex]

[tex]CI=22 \pm 3\times\dfrac{3.5}{12}[/tex]

[tex]CI=22 \pm 3\times 0.2916[/tex]

[tex]CI=22 \pm 0.8748[/tex]

[tex]CI=22+0.8748, 22-0.8748[/tex]

[tex]CI=22.8748, 21.1252[/tex]

Therefore, The class interval is from (22.8748 ug/m³ - 21.1252 ug/m³).

Answer:

21 ug/m^3 - 23 ug/m^3

Step-by-step explanation:

Just got it right

Answer:

the pattern would be W

Step-by-step explanation:

W should be the answer. Hope I helped you lots please count me brainy

Answer:

4/21

Step-by-step explanation:

In this case, carry out the indicated operations from left to right:

8      1

---- * --- = 4/21

7       6

"1/4 of a package of pencils shared equally among three friends" this expression represents expression [tex]\frac{1}{4} /3[/tex].

What is Division?

The action of separating something into parts or the process of being separated is known as Division. Ex: "The division of the land into small fields"

The meaning of the given expression is to divide one fourth part into three persons.

This is clearly represents in option A....1/4 of a package of pencils shared equally among three friends.

Thus, option A express perfectly for the given expression [tex]\frac{1}{4} /3[/tex] as "1/4 of a package of pencils shared equally among three friends".

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Final answer:

The expression 1/4÷3 matches Scenario A, which represents 1/4 of a package of pencils being shared equally among three friends.

Explanation:

The expression 1/4÷3 represents taking one fourth of something and then dividing it into 3 equal parts. Out of the scenarios provided:

Therefore, the expression 1/4÷3 best matches with Scenario A, where 1/4 of a package of pencils is shared equally among three friends.

The 1st and 4th ones

Answer: the correct answers are

1. <EGO ≈ <EOG

4. TW = 1/4GO

Step-by-step explanation:

1. all the angles are corresponding therefore it’s correct

4. TW is 1/2 of PQ therefore it would be 1/4 of GO

ANSWER: Multiply out front and multiply under the radicals. "The radical of a product is equal to the product of the radicals of each factor." "The radical of a quotient is equal to the quotient of the radicals of the numerator and denominator."

Use the half-angle identities.

[tex]\sin^2x=\dfrac{1-\cos2x}2[/tex]

[tex]\implies\sin^4x=\left(\dfrac{1-\cos2x}2\right)^2=\dfrac{1-2\cos2x+\cos^22x}4[/tex]

[tex]\cos^2x=\dfrac{1+\cos2x}2[/tex]

[tex]\implies\sin^4x=\dfrac{1-2\cos2x+\frac{1+\cos4x}2}4=\dfrac{3-4\cos2x+\cos4x}8[/tex]

sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

Rewrite sin^4(x) in terms of cosine by using the Pythagorean identity for trigonometric functions, which relates sin^2(x) and cos^2(x):

sin^2(x) + cos^2(x) = 1

Now, solve for sin^2(x):

sin^2(x) = 1 - cos^2(x)

Now, square sin^2(x) to get sin^4(x):

(sin^2(x))^2 = (1 - cos^2(x))^2

sin^4(x) = (1 - cos^2(x))^2

So, sin^4(x) can be expressed in terms of cosine as (1 - cos^2(x))^2.

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Answer:

(x-2)(x+4)

Step-by-step explanation:

So it would be A.

Explanation: The middle number is 2 and the last number is -8.

Factoring means we want something like

(x+_)(x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get 2

Multiply together to get -8

Can you think of the two numbers?

Try -2 and 4:

-2+4 = 2

-2*4 = -8

Fill in the blanks in

(x+_)(x+_)

with -2 and 4 to get...

(x-2)(x+4)

Answer:

(x−2)(x+4)

A. (x+4)(x-2). The factorization of the quadratic equation x²+2x-8 given by the graph is (x+4)(x-2).

From the graph shown in the image we can see the parabola's cut points, in the y-axis is -4 and the x-axis is 2, then we write the product changing the signs (x+4)(x-2) = x²+2x-8

Answer:

16

Step-by-step explanation:

Input it in the calculator

Answer: 16

Step-by-step explanation:

5 1/7 is 36/7=5.142857

3 1/9 is 28/9=3.1

Do 5.142857 times 3.1

And it equals 15.94 but rounds up to 16.

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of squares on the other 2 sides, that is

x² + 12² = 13²

x² + 144 = 169 ( subtract 144 from both sides )

x² = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

Answer:

x = 25

Step-by-step explanation:

We are given a right angled triangle and we are to find the value of x.

For that, we will use the Pythagoras Theorem.

[tex] 1 3 ^ 2 = x ^ 2 + 1 2 ^ 2 [/tex]

[tex] 1 6 9 = x ^ 2 + 1 4 4 [/tex]

[tex] x ^ 2 = 1 6 9 - 1 4 4 [/tex]

[tex] x ^ 2 = 2 5 [/tex]

Taking square root on both sides to get:

x = 25

Answer:

x = -4 and x = -12

Step-by-step explanation:

x^2 + 16x + 48 = 0 is to be factored.

Note that 48 is the product of 4 and 12 and that the sum of 4 and 12 is 16.

Therefore,

x^2 + 16x + 48 = 0 in factored form is:

(x + 4)(x + 12) = 0, so that x + 4 = 0 → x = -4, and

                                        x + 12 = 0  → x = -12

Answer:

(x + 4) (x + 12)

Step-by-step explanation:

to factor x² + 16x + 48 = 0, you need to find 2 numbers that when multiplied together give you 48 and when added together give you 16

you can list the factors of 48 and see what adds up together to give you 16, but here is a hint:

the numbers probably end in a 2, 4, 0, 6, 5, or 1, as a pair of these numbers added together give us 6. i looked at a factor chart and saw that 12 and 4 that when added together, give us 16 and when multiplied, give us 48

in factored form it looks like the following:

(x + 4) (x + 12)

this would be the answer in factored form

Answer: Edgur eats 12 ounces of popcorn. Before he ate any, he had 2 pounds of popcorn. How much popcorn, in ounces, of popcorn does Edgur have now? Edgur has 20 ounces of popcorn.

Step-by-step explanation:

Pounds to ounces: 1 pound = 16 ounces.

2 * 16 = 32.

He ate 12 of those ounces. 32 - 12 = 20.

Final answer:

To solve a problem involving subtraction of pounds and ounces, convert everything to ounces, subtract, and convert back if necessary. In this example, after removing 3 pounds 5 ounces from 9 pounds 8 ounces, the remaining weight is 6 pounds 3 ounces.

Explanation:

Let's create a subtraction problem involving pounds and ounces. Imagine you have a sack of potatoes weighing 9 pounds 8 ounces, and you remove a bag of potatoes weighing 3 pounds 5 ounces. How much does the sack of potatoes now weigh?

First, we need to ensure that both weights are in the same units. We have:

Initial weight: 9 pounds 8 ounces

Weight removed: 3 pounds 5 ounces

To subtract these weights, we will convert pounds to ounces for each weight, then subtract, and finally convert back to pounds and ounces if necessary.

Convert 9 pounds to ounces: 9 × 16 = 144 ounces

Therefore, the initial weight in ounces is 144 ounces + 8 ounces = 152 ounces.

Convert 3 pounds to ounces: 3 × 16 = 48 ounces

The weight removed in ounces is 48 ounces + 5 ounces = 53 ounces.

Subtract the smaller weight from the initial weight: 152 ounces - 53 ounces = 99 ounces

Now we convert 99 ounces back to pounds and ounces. Since 1 pound is 16 ounces:

99 ÷ 16 = 6 pounds with a remainder of 3 ounces.

So, the sack of potatoes now weighs 6 pounds 3 ounces.

Answer:

the population would be 30.28 billion by 2020

Step-by-step explanation:

y=6.08 + 1.21x

y = 6.08 + 1.21(20)

y = 6.08 + 24.2

y = 30.28

Answer:

Yes he is Correct

Step-by-step explanation:

When multiply with numbers like 10,100,1000 ect or even like 20,200,2000 then you have to break it down. Since multiply by zero equals 0 anyways you will only have to focus on the number that is in front of it. And just and the zeros to the back of the number.

Answer:

Yes he is correct

Step-by-step explanation:

Whenever we are multiplying any number with  10 or multiples of ten we simply add the zeros to the end of that number.

For example:

134 x  10   =  1340

As you can see, to get the answer, you simply need to add 0 to the end of 134

Also 10 x 10 = 100

To get the answer we simply added zero to the end of ten which then give us   100

12 x 10= ?  all you need to do is to add zero to the end of 12 which will give us 120

13 x 100 =?  In this case, since the zeros are two, you will simply add two zeros to the end of  13 which will give you the answer 1300

So Marcel can find 52 times 10 by simply adding a 0 to the end of 52 to get 520 as the correct answer.

Answer:

(1/2)/(3/4) = (1/2)(4/3) = 2/3

Step-by-step explanation:

Answer:

Not all relationships are functions, but all functions are also relationships

Step-by-step explanation:

A relationship is a correspondence between two sets of values.

A relationship assigns values from an output set called range to a set and input called a domain.

On the other hand, a relation is a function if and only if there is only one value of the output set (Range) assigning to each value of the input set (Domain).

In other words, if an input value [tex]x_1[/tex] is assigned two or more output values [tex]y_1[/tex], [tex]y_2[/tex], [tex]y_3[/tex] .. then the relationship is not a function. This means that not all relationships are functions.

[tex]y=\±\sqrt{x} +3[/tex]   is a relation but it is not a function.

because when x = 4 then y = 1 and y = 5.

Not all relationships are functions, but all functions are also relationships

Final answer:

A relation is a set of ordered pairs, while a function is a relation where each input value is associated with only one output value. Not every relation is a function, but every function is a relation.

Explanation:

A relation is a set of ordered pairs where each input value is associated with one or more output values. On the other hand, a function is a relation where each input value is associated with only one output value.

Not every relation is a function. For example, the relation {(1,2), (1,3), (2,4)} is not a function because the input value 1 is associated with two different output values (2 and 3). However, every function is a relation because it establishes a relationship between the input and output values.

Answer:

the number of sheet available is 75, 000

you take the total number of pages available = 8 x 75,000

= 600,000 pages

then each notebooks contains 200 pages

= 600,000 / 200

= 3000 notebooks can be made

Step-by-step explanation:

Answer:

3000 notebooks

Step-by-step explanation:

75,000*8=600000

600000/200=3000

There would be 3 basketballs?

3 basketball because subtract

Answer:

the answer is D. 1.52

Step-by-step explanation:

you want to add all the numbers then divide by 10

15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21

                             10

then you find the difference between the mean and data point

Data point = 15    15    17    18     18     18     19    20    20     21

Mean Diff  = 3.1   3.1     1.1    0.1   0.1   0.1    .9      1.9    1.9    2.9

then add the differences

3.1 + 3.1 + 1.1  + 0.1 + 0.1  +  0.1 + .9 + 1.9 + 1.9  + 2.9 and divide by 10

                                    10

absolute deviation is 1.52 wings.

The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.

The mean can be calculated only for numeric variables, no matter if they are discrete or continuous. It's obtained by simply dividing the sum of all values in a data set by the number of values. The calculation can be done from raw data or for data aggregated in a frequency table.

here, we have,

we want to add all the numbers then divide by 10

15 + 15 + 17 + 18 + 18 + 18 + 19 + 20 + 20 + 21

__________________________________

                            10

then you find the difference between the mean and data point

Data point = 15    15    17    18     18     18     19    20    20     21

Mean Diff  = 3.1   3.1     1.1    0.1   0.1   0.1    .9      1.9    1.9    2.9

then add the differences

3.1 + 3.1 + 1.1  + 0.1 + 0.1  +  0.1 + .9 + 1.9 + 1.9  + 2.9    [and divide by 10]

_______________________________________

                                   10

=1.52

absolute deviation is 1.52 wings.

Hence, The solution is : the answer is D. 1.52 is the mean absolute deviation of the data set shown.

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Answer:

14n-16

Step-by-step explanation:

Given

[tex]2n - 7 + 3(4n - 3)\\[/tex]

Simplification requires the expression to be in its shortest and concise form. The brackets are opened and addition or subtractions are performed

So,

Multiplying 3 inside bracket

[tex]2n - 7 + 12n - 9[/tex]

Combining alike terms:

[tex]2n+12n-7-9[/tex]

Performing addition and subtractions:

[tex]14n-16[/tex]

Hence the simplified form is:

14n-16 ..

Answer:

C

Step-by-step explanation:

Charlene has 8 more dollars so you would have to add it all together to get 86.

Answer:

x = -4

x = -1

Step-by-step explanation:

We have been given the following quadratic equation;

x^2 + 5x + 4 = 0

We are required to determine the roots of the above quadratic equation via graphing.

To do this we formulate the following equations;

y = x^2 + 5x + 4

y = 0 (x -axis)

We then proceed to graph these functions on the same graph. The roots of the original quadratic equation will be the points where the graphs of the above functions will intersect.

The attachment below is the graphical solution obtained from desmos graphing tool;

The graph of the functions intersect at;

x = -4 and x = -1

These are the roots of the given quadratic equation

Answer: b) -5 ≤ y ≤ 1

Step-by-step explanation:

y = 3 cos (4x) - 2

     ↓                 ↓

amplitude       vertical shift

The amplitude is 3 which gives a range of -3 to 3 but there is also a shift down of 2 units so the new range is: -3 - 2 = -5 to 3 - 2 = 1

-5 ≤ y ≤ 1