3. Angle r* = 2wº. What is the measure of angle rº1 Show your work. 125⁰ Thangle A wo Wo Triangle B 125⁰ 3. Angle r * = 2wº . What is the measure of angle rº1 Show your work . 125⁰ Thangle A wo Wo Triangle B 125⁰​

By the binomial theorem,

[tex]\displaystyle \left(x^2 + \frac px\right)^6 = \sum_{n=0}^6 \binom 6n \left(x^2\right)^n \left(\frac px\right)^{6-n} = \sum_{n=0}^6 p^{6-n} \binom 6n x^{3n-6}[/tex]

where

[tex]\dbinom kn = \dfrac{k!}{n!(k-n)!}[/tex]

is the so-called binomial coefficient.

The term that's independent of x is the constant term, which occurs when [tex]3n-6=0[/tex], or [tex]n=2[/tex]. Given that this constant 240, we have

[tex]p^{6-2} \dbinom62 = 240 \implies p^4 = 16 \implies p = \pm2[/tex]

but [tex]p[/tex] must be positive, so [tex]\boxed{p=2}[/tex]

The sum of the measures of all the interior angles of the pentagon is 540°. Option B

Note that

Sum of Interior Angles in a Pentagon = 540°

A pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°

If one of the interior angles = 108°, then the other two angles = 2 * 108° = 216°

The sum of the interior angles = 108° + 216° = 540°

Therefore, the sum of the measures of all the interior angles of the pentagon is 540°

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Answer:

Step-by-step explanation:

Comment

This is an arithmetic series. It has the following givens.

a = 27     The first term

d = - 2       The difference between one term and the one behind it.

n = quite small

Tn = a + (n - 1)*d

tn = 27 - 2n  + 2

tn = 29 - 2n

Answer: 43

Step-by-step explanation:

Step 1: Simplify inside the parenthesis

(12 ÷ 3) + 3+ (16-7) × 4

4 + 3 + 9 × 4

Step 2: Multiply 9 by 4

4 + 3 + 36

Step 3: Combine Like Terms

43

The number of seconds it takes for the waste to hit the ground for the given function is: 5 seconds.

We are given the function of height to time as, h(t) = -16t² + initial height, and we have the following:

Plug in the values into the equation of the function

0 = -16t² + 400

Solve for t

0 - 400 = -16t²

-400 = -16t²

-400/-16 = t²

400/16 = t²

√(400/16) = t

20/4 = t

5 = t

t = 5

The number of seconds it takes is: 5 seconds.

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Answer:

First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

Step-by-step explanation:

This question deals with Slope of a line.

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

For first climbing equipment rise = 6 feet, run(horizontal) = 4 feet

Thus, slope =  6/4 = 3/2 ≈ 1.5

For second climbing equipment rise = 10 feet, run(horizontal) = 6 feet

Thus, slope=   10/6 = 5/3 ≈ 1.66

Thus,

Slope of first climbing equipment = 3/2 < slope of second climbing equipment = 5/3

Thus, First Option i.e 5/3 > 3/2 , the slope of Climbing equipment at Gym is greater is Correct

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The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

As per the law of cosine, the measure of angle x can be written as,

[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]

Hence, the value of x is 117.8°. thus, the correct option is A.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )= \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)= \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)= \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

properties to be used here :

[tex]\qquad \tt \rightarrow \:\cfrac{d}{dx}( {x}^{ n } ) = n \sdot{x}^{n - 1} [/tex]

[tex]\large \textsf{Question : 1} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ( {x}^{ \frac{3}{2} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3}{2} - 1 } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{3 - 2}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} x { }^{ \frac{1}{2} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \dfrac{3}{2} \sqrt{x} [/tex]

[tex]\large \textsf{Question : 2} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ {x}^{3} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - 3} } )[/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 3 - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = - 3 { {x}^{ - 4} } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{- 3}{ {x}^{4} } [/tex]

[tex]\large \textsf{Question : 3} [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{ \sqrt{x}^{} } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} \bigg( \cfrac{1}{{x}^{ \frac{1}{2} } } \bigg)[/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{d}{dx} ({ {x}^{ - \frac{1}{2} } } )[/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ - \frac{1}{2} - 1} } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 1 - 2}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = -\cfrac{1}{2} { {x}^{ \frac{ - 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2{x}^{ \frac{ 3}{2} } } [/tex]

[tex]\qquad \tt \rightarrow \:y = \cfrac{ - 1}{ 2\sqrt{{x}^{ { 3}{} } }} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The angles at which the fences will meet is 27 , 38 ,114 degree.

A triangle is  a polygon with three sides , three angles and three vertices.

It is given that the triangle has sides

1.1 miles * 1.5 miles * 2.2 miles

The law of cosines can be used to calculate the angle

a² = b² + c² -2bc cosA

1.1²  = 1.5² + 2.2² -2 *1.5 *2.2 cosA

A = 27.01 degree

Similarly

b² = c² +a² -2ac cosB

1.5²  = 2.2² +1.1²  -2 * 2.2*1.1 cos B

B = 38.27 degree

By angle sum property

Angle C = 180-38.27-27.01

C = 114.72 degree

Therefore , the angles at which the fences will meet is 27 , 38 ,114 degree.

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To design a simulation for this situation, one can generate a set of four numbers by using the number generator with numbers 0 to 5 representing those who prefer watching a movie at a theatre and 6 to 9 representing those who do not.

From the information given about the probability, the goal here is to design a simulation for this situation.

In this case, to design a simulation for this situation, one can generate a set of four numbers by using the number generator.

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Answer:An algorithm is a set of instructions for solving a problem or accomplishing a task.

Step-by-step explanation:

Any series of well defined steps that shows a procedure for solving a given type of problem is called an algorithm.

Step-by-step explanation:

The function of the given data would be F(x) = y = 4x.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

X(input)    Y ( output)

0                0

1                  4

2                  8

3                 12

We can see that

When the input is zero the output is also zero.

And when the input is some real number the output gives the multiple of 4.

Thus, The function could be

f(x) = 4x

The given function is represented by x as the independent variable.

Therefore, The function of the given data would be F(x) = y = 4x.

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Answer: A. The function has two distinct real zeros.

Answer:

C. The function has four distinct real zeros.

Step-by-step explanation:

The function intersects y=0 at x=1/2, 4, and 6 twice. It has two solutions at 6 twice as it is a behavior of polynomial or rational functions

Answer:

Step-by-step explanation:

One equivalent can be obtain by distributing multiplication with 3 over subtraction 5-2i

3(5-2i) =

3·5 -3·2·i =

15 -6i or -6i +15

From calculations, we can say that the given tiles will not fit together perfectly.

If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.

Expression for the measure of the interior angle of a polygon,

Interior angle of a polygon = [(n - 2) * 180]/n

Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°

Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°

Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°

To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°

Sum of all interior angles = 108° + 120° + 135° = 363°

Therefore, given tiles will not fit together perfectly.

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An expression is defined as a set of numbers, variables, and mathematical operations. The total number of students is 54.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let the number of columns in the rollercoaster be represented by x.

If students sit 4 per row on a rollercoaster, 6 students are left without a seat. Therefore, the number of students can be written as,

Total number of students = 4x + 6

If they sit 6 per row, there are 3 rows left empty. Therefore, the total number of students can be written as,

Total number of students = 6(x-3)

The total number of students can be written as,

4x + 6 = 6(x - 3)

4x + 6 = 6x - 18

2x = 24

x = 12

Now, the total number of students in the class are,

4x + 6 = 4(12) + 6 = 54

Hence, the total number of students are 54.

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Answer:

(n/m) - p

Step-by-step explanation:

Image attached

Answer:

2 1/4

Step-by-step explanation:

Answer: I love the picture example

Step-by-step explanation:

We will first find the heigh of the kite from his hand to a point in the air.

Then, we will add 3 feet to the result.

So, how to find the vertical line of the right triangle?

Well, we have the vertical line = x

We also got the hypothenuse, equal to 100 feet

And also theta, equal to 25 degrees.

We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse

sin(25) = x/100 feet

multiply 100 feet on both sides, to cancel to 100 feet on the right side.

100sin(25) = x

100(0.442) = x

x = 42.2  feet

Height = 42.2 + 3 feet (the yoda's hand =) =  45.2 feet (total)

Rounded to the nearest tenth.

I also did the verification, so it is the correct answer.

Easy as that =]]

Height of the kite from 3ft above the ground

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]

[tex]\\ \rm\Rrightarrow P=100sin25[/tex]

[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]

Height from the ground

Answer:

1.5kg

Step-by-step explanation:

The mean for the packages on day 1 will be:

= (1 + 8 + 1 + 12 + 1 + 11 + 7 + 6)/8

= 47/8

= 5.875

The mean for day 2 will be:

= (47 + 12)/8

= 59/8

= 7.375

The increase in mean:

= 7.375 - 5.875

= 1.5

Answer:

460

Step-by-step explanation:

if you look at the values you'll notice the next month is just half their value

7360 / 2 = 3680

3680 / 2 = 1840

1840 / 2 = 920

so

920 / 2 = 460 which should be month 5

Answer:

$5.50

Step-by-step explanation:

For one water bottle you divide the 55 dollars by 10

55/10= 5.5

Answer:

$5.50

Step-by-step explanation:

We must divide to solve so lets do that now :)

55/10 = 5.50

Each bottle will cost 5 dollars and 50 cents :)

Have an amazing day!!

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Answer:

x=65

Each NBA team can have a maximum of 15 players, 13 of which can be active each game.

65/5=13 so it's safe to say tgat 5 team can be crated

Step-by-step explanation:

x/5-2=11-->transposing x/5=11+2---->x=13×5--->x=65

verification 65/5-2=11--->13-2=11

The value of  θ = pi /3 , Option B is the correct answer.

A statement in mathematics used to correlate two algebraic expressions by using an equal sign is called an Equation.

x = rcosθ

y = rsinθ

The equation given is

[tex]y = -\sqrt{3} \;x[/tex]

rsinθ = - [tex]\sqrt{3}[/tex] [tex]\rm {r \; cos\; \theta}[/tex]

sin θ / cos θ = -  [tex]\sqrt{3}[/tex]

tan θ = -[tex]\sqrt{3}[/tex]

 θ = pi /3

Therefore Option B is the correct answer.

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Answer:

In the circle, the measure of the arc AC is 21°.

Step-by-step explanation:

Concept: We can use the Inscribed Angle theorem to get the measure of AC.

Given that the inscribed angle ∠ABC is 3x-1.5 and the Intercepted arc AC is 3x+9.

Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of the intercepted arc.

So,

3x - 1.5 = 0.5(3x + 9)

6x - 3 = 3x + 9

3x = 12

x = 4

Since the intercepted arc AC is 3x + 9, putting the value of x = 4 we get,

intercepted arc AC is 21°.

Hence the intercepted arc AC is 21°.

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Answer:

A

Step-by-step explanation:

First, simplify the numerator:

[tex]\frac{3 }{\sqrt{3} + \sqrt{x} } \\[/tex]

Next, multiply the numerator and denominator by the opposite of the denominator to rationalize the expression.

[tex]\frac{3}{\sqrt{3}+\sqrt{x} }*\frac{\sqrt{3}-\sqrt{x} }{\sqrt{3}-\sqrt{x}}[/tex]

Finally, evaluate the denominator by multiplying them together.

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {(\sqrt{3}+\sqrt{x})(\sqrt{3}-\sqrt{x})}[/tex]

Simplify:

[tex]\frac{3(\sqrt{3}-\sqrt{x})} {3-x}[/tex]

And done! :)