The area of a opening rectangular window is to be 440 square centimeters. If the length measures x centimeters and the width measures x-2 centimeters, what are the dimensions?

Answer:

The fourth coefficient is 4.

Step-by-step explanation:

Pascal's Triangle in this case has 5 rows of coefficients because the highest power in (y + w)^4 is 4.  4 plus 1 is 5.

     Here's the appropriate Pascal's Triangle:

     1

    1  1

   1  2  1

 1   3  3   1

1  4  6  4    1          Use this row when expanding the 4th power of (v + w).

Notice that in the given expansion, the coefficients are

1, 4, 6, 4  1

This corresponds to the last (5th) row of Pascal's Triangle (above).

So the correct coefficient to be placed in the box is 4.

Answer:

Step-by-step explanation:

14.

A.  

x = 5.0081818181..

10x = 50.08181818181....

100x = 500.81818181818...

100x - x = 500.8181818... - 5. 008181818....

99x = 495.81

[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]

[tex]x = \frac{5509}{1100}[/tex]

14.

B.

[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]

15.

[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex]                           [tex][ \ rationalizing \ the \ denominator \ ][/tex]

[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex]                    [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]

[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]

[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]

16

[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]

[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex]     [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]

[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex]                     [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]

Answer:

34,833.21 ft³

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

Given

height h = 19 3/4 ft

d = 1 1/5h

d = 6/5 * h

d = 6/5 * 19 3/4

d = 6/5 * 79/4

d = 474/20

radius r = 474/20 * 1/2

radius r = 474/40

radus r = 11 34/40

radus r = 11 17/20 ft

Get the volume

V = 3.14 * (474/40)² * 79/4

V = 3.14 * 561.69 * 19.75

V = 34,833.20535

Hence the volume of the cylinder to the nearest hundredth is 34,833.21 ft³

Answer:

Step-by-step explanation:

Distance traveled by walking = x

i) The distance Mary run = 2 *x = 2x

ii) Distance traveled by bus = 65 m more than the distance she ran

                                             = 65 m more than 2x

Distance traveled by bus  = 2x + 65

Total distance traveled = 600 m

x + 2x + 2x +65 = 600

            5x + 65 = 600

                   5x = 600 - 65

                   5x = 535

                     x = 535/5

x = 107

Distance Mary walked = 107 m

Answer:

pi

Step-by-step explanation:

First find the area of a full circle with radius 2

A = pi r^2

A = pi 2^2

A = 4 pi

We know that this is 1/4 of a circle so take 1/4 of the area

1/4 A = 1/4 (4 pi) = pi

Answer:

x = 134

Step-by-step explanation:

Exterior angle = sum of opposite interior angles

                      = 90 + 44 = 134

OR

Sum of angles of triangle = 180

that is,

90 + 44 +y = 180

y = 180 - 134

 y = 46

x + y = 180                [ straight line angles ]

x + 46 = 180

x = 180 - 46 = 134

Answer:

x = 134

Step-by-step explanation:

triangle sum theorem states that the sum of all angles within a triangle is equal to 180 degrees. using this we can figure out that the missing angle in the triangle is 46.

a straight line is also equal to 180 degrees, so to find the adjacent angle, we subtract 46 from 180, and we get 134

Answer:

a) No

b) Sí

Step-by-step explanation:

a) En la inauguración de unos Juegos Olímpicos, los 38 representantes de una nación quieren desfilar en columnas de 6, ¿es posible?

Esto se calcula como

38 representantes / 6 columnas

= 6 2/6 = 6 1/3 columnas

No, no es posible, tendríamos 7 columnas con 6 columnas con representantes iguales de 6 y la séptima columna tendría solo 2 representantes allí

b) ¿Cómo podrían desfilar en columnas iguales?

Sí pueden

Esto se calcula como 38 representantes ÷ 2

= 19 columnas

Podemos tener 19 columnas con 2 representantes cada una

Answer:

R = 13%

Step-by-step explanation:

P = $4000

I = $780

T = 18 months = 18/12 years

[tex]I = \frac{PRT}{100} \\\\780 = \frac{ 4000 \times R \times \frac{18}{12}}{100}\\\\780 = \frac{6000 \times R }{100}\\\\780 = 60R\\\\R = \frac{780}{60} = 13 \%[/tex]

Answer:

7.9m

Step-by-step explanation:

We solve using the Trigonometric function of Tangent

tan θ = Opposite/Adjacent

Opposite = x

Adjacent = 7.05m

We solve for x

tan 42 = x /7.05m

Cross Multiply

tan 42 × 7.05 = x

x = 6.3478485123m

Approximately = 6.35m

Height of the statue = x + 1.55

Hence, = 6.35m + 1.55m

= 7.9m

The height of the statue = 7.9 meters

Answer:

I think the answer is yes

Multiply x by 12 to get y

Answer:

If the question is asking which line is the radius then yes

Step-by-step explanation:

Answer:

$128

Step-by-step explanation:

2/5 × $40= $16

$16×8= $128

Answer:

The number of books are 189.

Step-by-step explanation:

ratio of note books to the books = 2 : 3

total notebooks = 126

Let the number of books is x.

So, the ratio is

[tex]\frac{2}{3} = \frac{126}{x}\\\\x = 189[/tex]

So, the number of books are 189.

Answer:

to survive

Step-by-step explanation:

if you don't eat you are gonna died➡

Answer:

jojo reference

Step-by-step explanation:

Answer:

gloves cost $5

hats cost $4

Step-by-step explanation:

four pairs of gloves and four hats for $36.00

4g + 4h = 36

three pairs of gloves and four hats for $31.00

3g + 4h = 31

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

Subtract the second equation from the first

  4g + 4h = 36

-( 3g + 4h = 31 )

––––––––––––

   g           = 5

gloves cost $5

substitute for g = 5 into either equation

4(5) + 4h = 36

20 + 4h = 36

Subtract 20 from both sides

4h = 16

Divide both sides by 4

h = 4

hats cost $4

Answer:

Step-by-step explanation:

The x and y intercepts occur when either x or y = 0

For the y intercept, x = 0

3(0) - 5y + 15 = 0

- 5y + 15 = 0                  Subtract 15 from both sides.

-5y = - 15                       Divide by - 5

-5y / -5 = - 15/-5

y = 3

For x intercept, y = 0

3x - 5(0) + 15 = 0

3x + 15 = 0                    Subtract 15 from both sides

3x = - 15                        Divide by 3

3x/3 = - 15/3

x = - 5

xintercept = (-5,0)

yintercept = (0,3)

Answer:

[tex]y=0.5x+2[/tex]

Step-by-step explanation:

Finding the inverse of a function is essentially finding the complete opposite of a given function. An easy trick can be used to find the inverse of a function. This trick is essentially thinking of the evaluator (f(x)) as another variable. Solve the function for (x) in terms of (f(x)); use inverse operations to do so. After completing this process, rewrite the function such that it is in the inverse function notation; switch the position of the (f(x)) and the (x), then indicate that it is an inverse function.

[tex]f(x)=2x-4[/tex]

Inverse operations,

[tex]f(x)=2x-4[/tex]

[tex]f(x)+4=2x[/tex]

[tex]\frac{f(x)+4}{2}=x[/tex]

Simplify,

[tex]0.5f(x)+2=x[/tex]

Rewrite in inverse function notation,

[tex]f^-^1(x)=0.5x+2[/tex]

[tex]y=0.5x+2[/tex]

Answer:

√2 ft.

Step-by-step explanation:

⇒ Area of square board = 2 ft.²

⇒ (Side of the board)² = 2 ft.²

⇒ Side of the board = √(2 ft.²)

⇒ Side of the board = √2 ft.

i dont know anymore

ok it was arithmetic

Answer:

arithmetic

Step-by-step explanation:

because this number is increasing by 7 in each

Answer:

Step-by-step explanation:

.....

Answer:

1

Step-by-step explanation:

additive identity =1/2

multiplicative =2

Product = 1/2*2

So the answer is 1

Answer:

x = 80

Step-by-step explanation:

Both angles together form 180, therefore x is 80

Answer:

x = 80

Step-by-step explanation:

100 and x form a straight line so they add to 180

x+100 =180

Subtract 100 from each side

x = 180-100

x = 80

Answer:

5

Step-by-step explanation:

Evaluate and substitute:

Sqrt of 7 - (-18)

Sqrt of 7 + 18 = 25

Sqrt of 25 = 5

Therefore, our answer!

Hope this helps, best of luck! :p

Answer: I did it in the explanation thingy-

Step-by-step explanation:

Step 1. 8792 - 6886 = 1906

Step 2. 12 x 9 108

That... OR the answer is 205848X

Answer:

11 years

Step-by-step explanation:

Double of the amount deposited = $350 × 2 = $700

First, convert R as a percent to r as a decimal

r = R/100

R = 6.3%

Hence,

r = 6.3/100

r = 0.063 per year,

Then, solve the equation for t = time, the formula is given as:

t = ln(A/P) / r

A = Doubled amount = $700

P = Principal = Initial amount = $350

t = ln(700.00/350.00) / 0.063

t = 11.002 years

Approximately , t = 11 years

Therefore, it will take 11 years for your money to double.

Answer:

[tex] \boxed{k = 7} [/tex]

Step-by-step explanation:

When interpreting this piecewise function, to determine whether or not the function is continuous, the limit to the left must be the same as the limit to the right.

Therefore to find an a value where the function is continuous at every point, we must determine where the limit is for the function.

In this case, the function is continuous at x = 7.

lim x→7 [x²] = lim x→7 [kx].

(7)² = k(7)

49 = 7k

÷7 ÷7

7 = k

k = 7.

Answer:

  ab = 2

Step-by-step explanation:

You know that ...

  (a +b)^2 = a^2 +2ab +b^2

Rearranging, we can solve for ab ...

  2ab = (a^2 +b^2) -(a +b)^2

  ab = ((a +b)^2 -(a^2 +b^2))/2 = (3^2 -5)/2

  ab = 2

Answer:

8

Step-by-step explanation:

4/x=3/6

4=3/6x

4*6=3x

24/3=x

8=x

Please mark me as brainliest