if the cost of 2:dozen copies is Rs 720 , find the cost of 72 copies .
​

Answer:

5

Step-by-step explanation:

May be correct than follow me please

• {4, 7, 12, 19, … }

has 1st differences

7 - 4 = 3

12 - 7 = 5

19 - 12 = 7

and 2nd differences

5 - 3 = 2

7 - 5 = 2

• {-1, 2, 7, 14, …}

1st differences:

2 - (-1) = 3

7 - 2 = 5

14 - 7 = 7

2nd differences:

5 - 3 = 2

7 - 5 = 2

• {-2, -8, -18, -32, …}

1st differences:

-8 - (-2) = -6

-18 - (-8) = -10

-32 - (-18) = -14

2nd differences:

-10 - (-6) = -4

-14 - (-10) = -4

Answer:

Hello,

Step-by-step explanation:

I  am  going to explain the method with the 1th:

[tex]\begin{array}{ccccc}n & u_n&u_{n+1}-u_{n}&u_{n+2}-2u_{n+1}+u_{n}&v_{n}\\1&4&&6\\2&7&3&9\\3&12&5&2&14\\4&19&7&2&21\\...&&&\\\end{array}\\\boxed{u_{n+2}=2u_{n+1}-u_{n}+2}\\[/tex]

[tex]Let\ say\\v_{n}=u_{n}+2\\v_{n+2}=u_{n+2}+2=(2u_{n+1}-u_{n}+2)+2=2(v_{n+1}-2)-(v{n}-2)+4\\v_{n+2}=2v_{n+1}-v{n}+2\ (1)\\v_{n+3}=2v_{n+2}-v{n+1}+2\ (2)\\(2)-(1)==> \boxed{v_{n+3}=3v_{n+2}-3v_{n+1}+v_n}\\[/tex]

[tex]Caracteristic\ equation:\\P(r)=r^3-3r^2+3r-1=0\\P(r)=(r-1)^3\\v_n=\alpha+\beta*n+\gamma*n^2\\v_1=6 ==> \alpha+\beta*1+\gamma*1=6\\u_2=9 ==> \alpha+\beta*2+\gamma*4=9\\u_3=14 ==> \alpha+\beta*3+\gamma*9=14\\[/tex]

[tex]\begin{bmatrix}1&1&1\\1&2&4\\1&3&9\end{bmatrix}*\begin{bmatrix}\alpha\\\beta\\\gamma\end{bmatrix}=\begin{bmatrix}6\\9\\14 \end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\1&2&4&9\\1&3&9&14\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&2&3&3\\0&2&8&8\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&1&4&4\end{bmatrix}\\\\[/tex]

[tex]\begin{bmatrix}1&1&1&6\\0&1&3&3\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&1&1&6\\0&1&0&0\\0&0&1&1\end{bmatrix}\\\\\\\begin{bmatrix}1&0&0&5\\0&1&0&0\\0&0&1&1\end{bmatrix}\\[/tex]

[tex]\alpha=5\\\beta=0\\\gamma=1\\\boxed{v_n=5+0*n+1*n^2}\\\boxed{u_n=5+0*n+1*n^2-2}\\\begin{array}{ccccc}n & u_n\\1&5+1-2=4\\2&5+4-2=7\\3&5+9-2=12\\4&5+16-2=19\\...&...\\\end{array}\\[/tex]

Answer:

x = y² - 7

Step-by-step explanation:

the inverse function is simply an exchange of x and y (and then the simplification happens to transform the whole expression back into a form y = ....)

Answer:

All Real Number greater than 0 or

(0, positive infinity)

Step-by-step explanation:

The range is all possible y values of a function. We can tell a range by looking at the lowest y vaule then going to the highest possible y value.

Look at the graph. There is a open circle at y=0. So this means we are not going to include 0 in our function. The graph approaches f(x) to positive Infinity so our highest y value is Infinity.

So we know that the function y values cannot be zero and it must be positive. So our range is

All Real Number greater than 0. Or

(0, positive infinity)

Answer:

21.758

Step-by-step explanation:

If you draw the triangle out, you find that cos 41 = x/28.83, when x is equal to the side opposite the 49 angle

Simplify this into 28.83 cos 41, and plug it into the calculator and you get

21.75827.

Step-by-step explanation:

To convert 0.007407 into scientific notation, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 7.407, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 7.407 × 10-3

i think this may help you tq

Answer:

horizontal analysis

Step-by-step explanation:

vertical analysis uses line items in the financial statements as a percentage of the base year which is the same as common size

ratio analysis compares line items between two companies against a base year.

(3x/6) + 2 = 8

=> 3x/6 = 8 - 2

=> 3x/6 = 6

=> 3x = 6 × 6

=> 3x = 36

=> x = 36/3

=> x = 12

Answer:

x=12

Step-by-step explanation:

3x/6+2=8

3x/6=8-2

      =6

3x/6(6)=6(6)

3x=36

x=12

Answer:

1,195,742.25 (final answer since instructions did not include rounding up or anything)

Step-by-step explanation:

n = 4

The given expression is:

9^8 ÷ 9n

USE PEMDAS order of operations and solve:

9^8 ÷ 9n

= 43046721 ÷ 9n

Substitue n with 4 and solve:

43046721 ÷ 9(4)

= 43046721 ÷ 36

= 1,195,742.25

Answer:

9^4

Step-by-step explanation:

We know that a^b ÷ a^c = a^ (b-c)

9^8 ÷ 9^4

9^(8-4)

9^4

Answer:

-49

-50

Step-by-step explanation:

When a negative number subtracts another negative number, the number becomes positive.

For example: -48-(-49)=1

-48-(-49) becomes -48+49=1

Answer:

Step-by-step explanation:

h=√[34²-24²]=√[(34-24)(34+24)]=√[10×58]=√(5×29)=√145 ≈12 m

The height of the building is 10 meters.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's call the height of the building "h".

We can use the Pythagorean theorem to relate the height, shadow, and hypotenuse of the right triangle:

h² + 24² = 34²

Simplifying and solving for h.

h² = 34² - 24²

h² = 676 - 576

h² = 100

h = 10

Therefore,

The height of the building is 10 meters.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

Answer:

a square plus 2ab plus b square......hope this will help you...thank you

[tex]\huge\text{Hey there!}[/tex]

[tex]\boxed{\huge\boxed{\mathsf{(a + b)^2}}}\\\boxed{\huge\boxed{\frak{= a + b \times a + b}}}\\\\\boxed{\huge\boxed{\rm{ = a^2 + 2ab + b^2}}}\huge\checkmark[/tex] [tex]\boxed{\huge\boxed{\leftarrow} \text{ YOUR ANSWER}}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\rm{Amphitrite1040:)}[/tex]

[tex]\\ \sf\longmapsto \left[{3a+b\atop a-b}\:\:\:{3c-d\atop a+b+d}\right]=\left[{3\atop 5}\:\:\;{6\atop 2d-1}\right][/tex]

Now constructing equations

[tex]\\ \sf\longmapsto 3a+b=3\dots(1)[/tex]

[tex]\\ \sf\longmapsto a-b=5\dots(2)[/tex]

[tex]\\ \sf\longmapsto 3c-d=6\dots(3)[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1\dots(4)[/tex]

[tex]\\ \sf\longmapsto 4a=8[/tex]

[tex]\\ \sf\longmapsto a=\dfrac{8}{4}[/tex]

[tex]\\ \bf\longmapsto a=2[/tex]

[tex]\\ \sf\longmapsto a-b=5[/tex]

[tex]\\ \sf\longmapsto b=a-5[/tex]

[tex]\\ \sf\longmapsto b=2-5[/tex]

[tex]\\ \bf\longmapsto b=-3[/tex]

[tex]\\ \sf\longmapsto a+b+d=2d-1[/tex]

[tex]\\ \sf\longmapsto 2+(-3)+d=2d-1[/tex]

[tex]\\ \sf\longmapsto d-1=2d-1[/tex]

[tex]\\ \sf\longmapsto d-2d=-1+1[/tex]

[tex]\\ \sf\longmapsto -d=0[/tex]

[tex]\\ \bf\longmapsto d=0[/tex]

[tex]\\ \sf\longmapsto 3c-d=6[/tex]

[tex]\\ \sf\longmapsto 3c-0=6[/tex]

[tex]\\ \sf\longmapsto 3c=6+0[/tex]

[tex]\\ \sf\longmapsto 3c=6[/tex]

[tex]\\ \sf\longmapsto c=\dfrac{6}{3}[/tex]

[tex]\\ \sf\longmapsto c=2[/tex]

Answer:

Step-by-step explanation:

I'm not sure but i think your right

Answer:

7474747448548

Step-by-step explanation:

I hope this helps

Answer:

(x-8)^2+(y-16)^2 = 4

Step-by-step explanation:

The equation of a circle is given by

(x-h)^2+(y-k)^2 = r^2 where (h,k) is the center and r is the radius

(x-8)^2+(y-16)^2 = 2^2

(x-8)^2+(y-16)^2 = 4

Answer:

-2.43655

Step-by-step explanation:

Answer:n=6

Step-by-step explanation:

Answer:

285

Step-by-step explanation:

B+A=360, B=360-75=285

An angle whose measure is greater than 180° but less than 360° is termed a reflex angle.

[tex]\large{\textrm{{{\color{navy}{∠A \: + \: ∠B \: = \: 360°}}}}}[/tex]

[tex] \bf \large \longrightarrow \: \:75 \degree \: + \: ∠ B \: = \: 360°[/tex]

[tex] \bf \large \longrightarrow \: \: \angle B \: = \: 360° \: - \: 75 \degree[/tex]

[tex] \bf \large \longrightarrow \: \: \angle B \: = \:285 \degree[/tex]

Answer:

342.8 is the amount of money

Answer:

Open in answr appOpen_in_app

(i)

15

7

=

30

x

⇒x=

15

7×30

=14

(ii)

3

x

=

18

12

⇒x=

18

12×3

=2

(iii)

x

30

=

24

45

⇒x=

45

30×24

=16

(iv)

16

8

=

x

25

⇒x=

8

25×16

=50

Step-by-step explanation:

yeah

Answer:

4,3

Step-by-step explanation:

Rearrange the equation :

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

Then, we must square both sides:

x-3 = x²-6x+9

x²-6x+9-x+3=0

x²-7x+12=0

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

So x =4,3

Answer:

x = 3, x = 4

Step-by-step explanation:

Given

[tex]\sqrt{x-3}[/tex] + 3 = x ( subtract 3 from both sides )

[tex]\sqrt{x-3}[/tex] = x - 3 ( square both sides )

x - 3 = (x - 3)²

x - 3 = x² - 6x + 9 ( subtract x - 3 from both sides )

0 = x² - 7x + 12 ← in standard form

0 = (x - 3)(x - 4) ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 4 = 0 ⇒ x = 4

As a check

Substitute these values into the equation and if both sides are equal then they are solutions

x = 3 : [tex]\sqrt{3-3}[/tex] + 3 = [tex]\sqrt{0}[/tex] + 3 = 3  = 3 = right side

x = 4 : [tex]\sqrt{4-3}[/tex] + 3 = [tex]\sqrt{1}[/tex] + 3 = 1 + 3 = 4 = right side

solutions are x = 3, x = 4

Answer:

17

Step-by-step explanation:

these positive integers are :

4, 64, 124, 184 ... , 964

964 = 4 + (n-1) (60)

964 = 4 + 60n -60

964 = 60n -56

60n = 1020

n = 1020/60

n = 17

so, the number of special integers smaller than 1000 are = 17

The digits n, n+1 and n+2 implies that the special numbers are consecutive i.e. they follow one another. The count of special numbers less than 1000 is 17.

Given that:

[tex]\{n,n+1,n+2\} = \{4,5,6\}[/tex]

[tex]Range = 1000[/tex]

First, calculate the LCM of 4, 5 and 6.

[tex]4 = 2 \times 2[/tex]

[tex]5 = 5[/tex]

[tex]6 = 2 \times 3[/tex]

So, the LCM is:

[tex]LCM = 2 \times 2 \times 5 \times 3[/tex]

[tex]LCM = 60[/tex]

This means that the special digit occurs after every other 60 digits (i.e. the difference between a special digit and another is 60)

To calculate the count of special digits, we make use of arithmetic progression formula

[tex]L = a + (n - 1) \times d[/tex]

Where

[tex]L = 1000[/tex] --- the last term

[tex]a = 4[/tex] --- the first special digit

[tex]d = 60[/tex] --- the common difference as explained above

So, we have:

[tex]L = a + (n - 1) \times d[/tex]

[tex]1000 = 4 + (n - 1) \times 60[/tex]

Collect like terms

[tex]1000 - 4 =(n - 1) \times 60[/tex]

[tex]996 =(n - 1) \times 60[/tex]

Divide both sides by 60

[tex]16.6 =n - 1[/tex]

Add 1 to both sides

[tex]1 + 16.6 =n[/tex]

[tex]17.6 =n[/tex]

Rewrite as:

[tex]n =17.6[/tex]

Remove the decimal part (do not approximate)

[tex]n =17[/tex]

Hence, the special numbers are 17 in total (that are less than 1000).

Read more about arithmetic progression at:

https://brainly.com/question/21093837

Answer:

-2

Step-by-step explanation:

The output of the chart and graph drops by 2 for every input.

For a geometric sequence

a, ar, ar ², ar ³, …

the n-th term in the sequence is ar ⁿ ⁻ ¹.

The first sequence is

1, 3, 9, 27, …

so it's clear that a = 1 and r = 3, and so the n-th term is 3ⁿ ⁻ ¹.

The second sequence is

400, 200, 100, 50, …

so of course a = 400, and you can easily solve for r :

200 = 400r   ==>   r = 200/400 = 1/2

Then the n-th term is 400 (1/2)ⁿ ⁻ ¹.

Similarly, the other sequences are given by

3rd: … 4 × 2ⁿ ⁻ ¹

4th: … 400 (1/4)ⁿ ⁻ ¹

5th: … 5ⁿ ⁻ ¹

6th: … 1000 (1/2)ⁿ ⁻ ¹

7th: … 2 × 5ⁿ ⁻ ¹

Answer:

20%

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

If the ratio of water to lemon juice is 4:1, that means that for every 5 portions of the cordial drink, 4 are water and 1 is lemon juice. In other words, 4/5 of the drink is water and 1/5 is lemon juice. The percentage of the lemon juice would be 1/5 = 20%. The answer is 20%.