Find the missing segment in the image below

Notice that

(1 - x)⁵ (1 + 1/x)⁵ = ((1 - x) (1 + 1/x))⁵ = (1 - x + 1/x - 1)⁵ = (1/x - x)⁵

Recall the binomial theorem:

[tex]\displaystyle(a+b)^n = \sum_{k=0}^n\binom nk a^{n-k}b^k[/tex]

Let a = 1/x, b = -x, and n = 5. Then

[tex]\displaystyle\left(\frac1x-x\right)^5 = \sum_{k=0}^5\binom5k\left(\frac1x\right)^{5-k}(-x)^k = \sum_{k=0}^5 (-1)^k\binom5k x^{2k-5}[/tex]

We get an x ³ term for

2k - 5 = 3   ==>   2k = 8   ==>   k = 4

so that the coefficient would be

[tex](-1)^4\dbinom54 = \boxed{5}[/tex]

Answer:

17

Step-by-step explanation:

8+4+5=17

Answer:

7

Step-by-step explanation:

(+8)-(-4)+(-5)

=8+4-5

=12-5

=7

Answer:

7/12

Step-by-step explanation:

3*4=12. 4/12+3/12=7/12.

Answer:

5/12

Step-by-step explanation:

you find the common factor of 12, divide 12 by the denominator, multiply the numerator by that, add the new numerators, put it on the denominator of 12, subtract it from 12/12

Answer:

The complete predicate is the following: "is going to a football game tomorrow."

Step-by-step explanation:

A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.

Answer:

The complete predicate is the following: "is going to a football game tomorrow."

Step-by-step explanation:

A sentence is spit into two main parts, the subject and the predicate. The subject is what the sentence is about and it typically occurs before the verb. Everything before the verb in this case would be the complete subject. What is left is the complete predicate. The complete predicate includes the verb and everything after it until the end of the sentence.

Answer:

8(h)=96

Step-by-step explanation:

Remember when you are writing a multiplication equation, it's a division backwards.

96/8=h

h×8=96

hope this helps you

goodluck

Answer: 8x=96

Step-by-step explanation:

8X = 96

X = 96/8

X = 12 hours

the formula for calculating the circumference is [tex]\pi[/tex] x diameter

so, 3.14 x 9 = 28.26ft (a)

Answer:

C = 28.26 ft

Step-by-step explanation:

The circumference of a circle is given by

C = pi *d

C = 3.14 *9

C = 28.26 ft

Answer:

Deandra completed the first 6 problems at a rate of 3 problems per hour and the last 12 at a rate of 4 problems per hour.

Step-by-step explanation:

6 problems ÷ 2 hours = 3 problems per hour

12 problems ÷ 3 hours = 4 problems per hour

Answer B is the answer

Answer:

1/9

Step-by-step explanation:

Answer:

x²−4x+4 = (x-2)²

x²−4x+4 = 1

(x-2)² = 1

x-2 = ±√1

x = 1+2 or =-1+2

  = 3  or = 1

Answer:

1/4

Step-by-step explanation:

2/5 divided by 8/5 is the same as 2/5 * 5/8. we cross out the same 5's to get 2/8. We simplify that to 1/4.

1/4 is our answer.

Answer:

Equivaldría a 45.9 litros de leche de vaca.

Step-by-step explanation:

Esta pregunta se resuelve por proporciones, usando una regla de tres.

Un litro de leche de búfala equivale a 1.7 litros de leche de vaca.

27 litros de leche de buffalo - x litros de leche de cava

1 - 1.7

Aplicando multiplicación cruzada :

[tex]x = 27*1.7 = 45.9[/tex]

Equivaldría a 45.9 litros de leche de vaca.

Answer:

zero of the function occurs at x = -6

Step-by-step explanation:

Given f(x) = -4(x+3)+6(x+4)

Since the question is incomplete, we can as well find the zero of the given function. The zero exists when f(x) = 0

Hence;

-4(x+3)+6(x+4) = 0

Expand

-4x - 12 + 6x + 24 = 0

Collect the like terms

-4x + 6x - 12 +24 = 0

2x + 12 = 0

2x = -12

x = -12/2

x = -6

Hence the zero of the function occurs at x = -6

Answer:

[tex] \bf \: {c}^{2} = {(56)}^{2} + ( {33)}^{2} \\ = > {c}^{2} = 3136 + 1089 \\ = > {c}^{2} = 4225 \\ = > c = \sqrt{4225} \\ = > c = 65 \: yards[/tex]

Answer:

65..

Step-by-step explanation:

[tex] \sqrt{(56) {}^{2} } + (33) {}^{2} \\ = 65[/tex]

Formula for the volume of a sphere: V = 4/3 x pi x r^3

V = 4/3 x pi x 6^3

V = 4/3 x pi x 216

V = 288 pi in^3

Hope this helps!

Answer:

288 pi in ^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3 where r is the radius

V = 4/3 pi *( 6)^3

V = 4/3  pi (216)

V = 288 pi in ^3

Answer:

6AJNSDJN

Step-by-step explanation:

Answer:

abcdsStep-by-step explanation:

Answer: -170

Concept:

When encountering questions that require multiple steps of the calculation, it is suggested to follow the PEMDAS.

Solve:

**Disclaimer** I assume that it is supposed to be (25 + 45). If it was, then you may refer to my answer. If the ")" after 45 is just a typo, you may point it out and I will redo it.

Given expression

 13 + {16 + 2 - [(25 + 45) × 3] + 9}

Do the parenthesis of the inner most

=13 + {16 + 2 - [70 × 3] + 9}

=13 + {16 + 2 - 210 + 9}

Do addition first, then subtraction

=13 + {18 - 210 + 9}

=13 + {27 - 210}

=13 - 183

=-170

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Download gauthmath it will help

Jesus loves u

Answer:

Step-by-step explanation:

We know that the interior angle sum of a polygon is (n − 2) × 180°, where n is the number of sides.

Here, number of sides (n) = 12

So, interior angle sum = (n − 2) × 180°

=> interior angle sum = (12 - 2) × 180°

=> interior angle sum = 10 × 180°

=> interior angle sum = 1800°

So, the interior angle sum of this polygon is 1800°.

Answer:

The answer is below

Step-by-step explanation:

The general form of a line is given by:

Ax + By + C = 0

The slope intercept form of a line is give by:

y = mx + b;

where m is the slope and b is the y intercept

Given a line with equation Ax + By + C = 0; the slope of the line can be gotten by representing in slope intercept form, hence it becomes:

By = -Ax - C

y = (-A/B)x - C/B

The slope is -A/B

For a line with equation Bx - Ay + C = 0:

Ay = Bx + C

y = (B/A)x + C/A

the slope is B/A

Two lines are said to be perpendicular if the product of the slopes is -1. Hence:

-A/B * B/A = -1; hence the two lines are perpendicular

Answer:

g(x) = 3·sin(x + π/2) - 4

Step-by-step explanation:

The given (general form of a) sin function is g(x) = A·sin(x + C) + D

Where;

A = The amplitude (the vertical stretch) = 3

C = The phase shift, left = π/2

D = The vertical shift = 4 units down = -4

Therefore, given that in the parent function, we have f(x) = sin(x), by substituting the values of A, C, and D to complete the equation modeling the function g, we get;

g(x) = 3·sin(x + π/2) - 4

Answer:

x=1

Step-by-step explanation:

3x+9 = 12

Subtract 9 from each side

3x+9-9=12-9

3x = 3

Divide by 3

3x/3 = 3/3

x=1

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]x = 1[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the answer...}}\\\\3x + 9 = 12\\-------------\\\rightarrow 3x + 9 - 9 = 12 - 9\\\\\rightarrow 3x = 3\\\\\rightarrow \frac{3x=3}{3}\\\\\rightarrow \boxed{x=1}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

E

Step-by-step explanation:

(leg of big triangle)² = (part of hypotenuse below it) × (whole hypotenuse)

15² = x × 20

225 = 20x ( divide both sides by 20 )

[tex]\frac{225}{20}[/tex] = x , that is

x = [tex]\frac{45}{4}[/tex] → E

The value of the x in the given triangle is 45/4.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Given is right triangle ABC, divided into two more right triangles, ADC and ADB, also, triangle ABD ~ triangle CAD.

Therefore, according to the definition of similar triangles, the corresponding sides are in proportion.

we have,

CA / CB = CD / CA

15/20 = x/15

x = 15²/20

x = 225/20

x = 45/4

Hence, the value of the x in the given triangle is 45/4.

Learn more about similar triangles click;

https://brainly.com/question/14926756

#SPJ7

Answer:

my x is ;

x= -0.6205

this is because for the first equation to be equal to the second equation we need to multiply the second equation with 20

Answer:

1

-----

(t+4)^2

Step-by-step explanation:

(t+3)

------- ÷ (t^2+7t+12)

(t+4)

Copy dot flip

(t+3)         1

------- * --------------------

(t+4)      (t^2+7t+12)

Factor

(t+3)         1

------- * --------------------

(t+4)      (t+4)(t+3)

Cancel

1         1

------- * --------------------

(t+4)      (t+4)

1

-----

(t+4)^2

Answer:

answer is b

Step-by-step explanation:

Answers:

[tex]a = 18\sqrt{2}[/tex]

[tex]b = 18[/tex]

==============================================================

Explanation:

For any 45-45-90 triangle, the two legs are the same length. We consider triangles like this to be isosceles. So we have b = 18 as the vertical leg because the horizontal leg is also 18 units long.

The hypotenuse of these types of triangles is always [tex]\sqrt{2}[/tex] times longer compared to the leg length. So the hypotenuse is [tex]a = 18\sqrt{2}[/tex]

As an alternative, you can use the pythagorean theorem to find the hypotenuse.

Answer:

8.5 km

Step-by-step explanation:

The distance is given by sqrt(8^2+3^2)=sqrt(64+9)=sqrt(73)=8.5 km

Answer:

Step-by-step explanation:

Let y is the required number.

a/c to question,

y² + greatest three digit prime number + smallest two digit prime number = 32²

we know, greatest three digit prime number = 997

smallest two digit prime number = 11

now, y² + 997 + 11 = 32²

or, y² + 1008 = 1024

or, y² = 1024 - 1008

or, y² = 16

or, y = 4

hence, required number number is one digit even number e.g., y = 4

Hope this answer helps you :)

Have a great day

Mark brainliest

Answer:

15

Step-by-step explanation:

(3x-1+2x+1)(3) -> 3 is the plug-in for x

3x-1+2x+1=5x

5*3=15

15

Answer:

15

Step-by-step explanation:

f(x) = 3x -1

g(x) = 2x+1

(f+g)(3)

find g(3) = 2(3)+1 = 6+1 = 7

Then find f(3) = 3(3) -1 = 8

f(3) + g(3) = 7+8 = 15