Prove that any number n of the form abcabc, where a, b, and c are decimal digits, is divisible by 7, 11 and 13.

Answer:

photo not clear sorry

Step-by-step explanation:

re-upload the question

Answer:

[tex]x = -2, x = \frac{1}{6}[/tex]

completing square method:

Factorise :

[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 4x= 2 - 7x}[/tex]

[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 4x + 7x - 2 =0}[/tex]

[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 11x - 2 =0}[/tex]

[tex]\qquad \sf \: { \dashrightarrow {6x}^{2} + 12x - x - 2 =0}[/tex]

[tex]\qquad \sf \: { \dashrightarrow {6x}^{} (x+ 2) -1( x + 2 )=0}[/tex]

[tex]\qquad \sf \: { \dashrightarrow ({6x}^{} - 1) (x+ 2) =0}[/tex]

[tex]\qquad \sf \: { \therefore 6x - 1=0} [/tex]

[tex] \qquad \sf \: \dashrightarrow6x =1 [/tex]

[tex]\qquad \sf \: { \dashrightarrow x= \dfrac{1}{6} }[/tex]

[tex]\qquad \sf \: { \therefore x + 2=0} [/tex]

[tex]\qquad \sf \: { \dashrightarrow x = - 2} \\ [/tex]

Answer:

236 visitors purchased no costume.

202 visitors purchased exactly one costume.

40 visitors purchased more than one costume.

The total number of customers is, N = 236 + 202 + 40 = 478.

Let X denote the number of costumes purchased by the next person.

Compute the probability that the next person will purchase no more than one costume as follows:

Thus, the probability that the next person will purchase no more than one costume .

Answer:

8 crabs and 2 octopi

Step-by-step explanation:

Let c represent the amount of crabs and o represent the amount of octopi.

We can use this to set up a system of equations:

6c+8o=64

c=4o

We can solve this system using substitution. In this case, we can substitute 4o for c:

6(4o)+8o=64

24o+8o=64

Combine like terms

32o=64

Divide both sides by 32

o=2

Substitute 2 for o to solve for c:

c=4o=4(2)=8

There are 8 crabs and 2 octopi

Answer:

Looks like a horizontal shift right 2 units

Step-by-step explanation:

the vertex would normally be at (0,0) so it seems it moved to the right 2 units

Casey will pay $156.00 in 3 years, the correct option is C.

The interest rate is the amount a lender charges a borrower and is a percentage of the principal—the amount loaned.

Given

Casey has a loan for $400 at a rate of 13% annually.

The interset Casey pay in three years for the loan is given by;

[tex]\rm Interest = Amount \times Rate \ of \ interest \times Time\\\\Interest = 400 \times 0.13 \times 3\\\\Interest = 156[/tex]

Hence, Casey will pay $156.00 in 3 years.

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Answer:

Ronnie is a bakery maker (i dont know what you call those, baker?). He has 5/6 feet length of cake. He the order says to cut pieces that are 1/12 long. How many pieces did Ronnie cut?

Step-by-step explanation:

a story? in that case...

i dont know if thats good. im not that good at stories for fractions hope this helps tho!

Answer:

80% of 50 is 40

Step-by-step explanation:

Dont know how I would show it on a tape diagram but yea

Answer:

The slope is the bit attached to the x:

In this case, it is -5.

Step-by-step explanation:

Answer: -5

just took the quiz

Answer:

You are right the one u clicked is correct

Step-by-step explanation

brainiest please

Answer:

the system will be worth $1892.25 after 2 years.

Explanation:

as the value decreases: [tex]\sf A = P(1 - \frac{r}{n})^{nt}[/tex] ......notice the ' - '  as its *decreases*

given:

solve:

[tex]\sf A = 2500(1 - \frac{0.13}{1})^{1*2}[/tex]

[tex]\sf A = 1892.25[/tex]

another way of doing it easily is:

[ $2500 * (100- 13)% ] * (100- 13)% = $1892.25

Use compound interest formula

[tex]\\ \rm\hookrightarrow P(1-r/100)^t[/tex]

[tex]\\ \rm\hookrightarrow 2500(1+0.13)^2[/tex]

[tex]\\ \rm\hookrightarrow 2500(0.87)^2[/tex]

[tex]\\ \rm\hookrightarrow 2500(0.76)[/tex]

[tex]\\ \rm\hookrightarrow 1900[/tex]

The sum using summation notation will be - 312. The sum of the following progression is found by the formula as [tex]S_n = \frac{a(1 - r^n)}{(1 - r)}[/tex].

Geometric Progression (G.P.) is a sort of sequence in which each successive phrase is obtained by multiplying the prior term by a set number known as a common ratio.

This progression is also known as a pattern-following geometric sequence of integers. Here you may also learn about mathematical progression.

A non-zero value is obtained by multiplying the common ratio by each phrase to obtain the next term 5 - 15 45 - 135.. is an example of a geometric series with a common ratio of -3.

The common ratio will be;

[tex]\rm r= \frac{-15}{3} \\\\ \rm r= -5[/tex]

The first term is 3

So  the sum using summation notation will be;

[tex]S_n = \frac{a(1 - r^n)}{(1 - r)} \\\\ S_n = \frac{3(1 - (-5)^4)}{(1 - (-5))} \\\\ S_n =- 312[/tex]

Hence the sum using summation notation will be - 312.

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[tex]f(2) = - 3(2) + 3[/tex]

[tex]f(2) = - 6 + 3[/tex]

[tex]f(2) = - 3[/tex]

Answer:

Step-by-step explanation:

Answer:

47.725%

sry if its wrong

hope this helps :)

Step-by-step explanation:

Answer:

10.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

8.8 ^2 + 6.2 ^2 = x^2

77.44+38.44=x^2

115.88=x^2

Take the square root of each side

10.76475731=x

Round to 3 significant figures.

10.8 =x

Answer:

10.8 =x

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

8.8 ^2 + 6.2 ^2 = x^2

77.44+38.44=x^2

115.88=x^2

Take the square root of each side

10.76475731=x

Round to 3 significant figures.

10.8 =x

The exact volume of the considered cone is given by: Option C: [tex]\dfrac{196}{3} \pi \: \rm in^3[/tex]

Suppose that the radius of the base of the considered right circular cone be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \dfrac{1}{3}\pi r^2 h \: \rm unit^3[/tex]

Right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.

The missing figure of the cone is attached below.

Thus, the volume of the considered cone is given by:

[tex]V = \dfrac{1}{3} \times 7 ^2 \times 4 \times \pi = \dfrac{196\pi}{3} \: \rm in^3[/tex]

Thus, the exact volume of the considered cone is given by: Option C: [tex]\dfrac{196}{3} \pi \: \rm in^3[/tex]

Learn more about volume of the cone here:

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[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]

Here's the solution ~

[tex]\qquad \sf  \dashrightarrow \: (3 {a}^{2} {b}^{4} )( - 8a {b}^{3} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (3 \times - 8)( {a}^{2} \times a)(b {}^{4} \times {b}^{3} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 24( {a}^{3} )( {b}^{7} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: - 24 {a}^{3} {b}^{7} [/tex]

So, The Correct choice is D

Answer:

The answer is (2, -1)

Step-by-step explanation:

Plug in x and y into the equation:

y=2x-5

-1=2(2)-1

and then u get -1 = -1 which is true

Step-by-step explanation:

We're going to be evaluating if we can round 2. (Values in the 10's place)

The value in the 'ones' place has to be greater than or equal to 5 in order to round up 2.

Since 8 is greater than 5, we can round up 2.

Rounded answer:

38830

The degree of the sum and difference of the polynomials are 6 and 7 respectively.

given polynomials are:

[tex]3x^5-2x^3y^4-7xy^3[/tex]

[tex]-8x^5y+2x^3y^4+xy^3[/tex]

the sum of polynomials = [tex]-5x^5y-6xy^3[/tex]

the difference of polynomials = [tex]11x^5y-4x^3y^4-8xy^3[/tex]

A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.

degree of sum = monomial with highest power = 5+1=6

degree of difference = monomial with highest power = 3+4 = 7

therefore, the degree of the sum and difference of the polynomials are 6 and 7 respectively.

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The function f(x) = log4x does not have a y-intercept Because there is no power of 4 that is equal to 0.

Exponentiation's inverse function is the logarithm. That is, the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised in order to obtain that number x.

The logarithm counts the number of times the same factor appears in repeated multiplication in the simplest case.

Following are the reason why f(x) = log4x does not have a y-intercept

1. There is no power of 4 that is equal to 0.

2. Its inverse does not have any x-intercepts.

3. f(x) approaches negative infinity.

Hence  f(x) = log4x does not have a y-intercept.

To learn more about the logarithm refer to the link;

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Answer:

1.There is no power of 4 that is equal to 0.

3.Its inverse does not have any x-intercepts

Step-by-step explanation:

Answer: 3 and 192

Step-by-step explanation:

Answer:

1 % of 300 is 3, because 1 times 300 equals 300 divided by 100 is 3.

64 times 300 equals 19200 divided by 100 is 192.

Therefore the answer of 1 % of 300 is 64 times smaller than 64 % 300. Basically, 64 % of 300 = y and y= 64 (1 % of 300)

Answer:

(i) 226 ltr

(ii) 2 m²

(iii) 16 cm

(iv) 178 ltr

Step-by-step explanation:

(i)

volume of a cylinder = [tex]\pi r^2h[/tex]  (where r is the radius and h is the height)

Given:

⇒ volume = [tex]\pi[/tex] x 24² x 125 = 72000[tex]\pi[/tex] cm³

As there are 1000 cm³ in 1 liter

⇒ volume =  72000[tex]\pi[/tex] ÷ 1000 = 72[tex]\pi[/tex] ltr ≈ 226 ltr (nearest whole number)

(ii)

Surface area of cylinder open at one end = [tex]\pi r^2+2\pi rh[/tex]

Given:

⇒ surface area = [tex]\pi \times24^2+2\pi \times24\times125[/tex]

⇒ surface area = [tex]6576\pi[/tex] cm²

As there are 10000 cm² in 1 m²

⇒ surface area = [tex]6576\pi[/tex] ÷ 10000 = 2.065911... ≈ 2 m²

(iii)

Volume of a rectangular prism = l x w x h

(where l is the length, w is the width and h is the height)

Given:

⇒ 48000 = 150 x 20 x h

⇒ 48000 = 3000h

⇒ h = 48000 ÷ 3000 = 16 cm

(iv)

Difference in capacity is the difference in volume

Volume of cylinder in liters =  226 ltr

Volume of trough in liters = 48000 ÷ 10000 = 48 ltr

⇒ difference = 226 - 48 = 178 ltr

Answer:

Part A the answer is 9cm

Part B the answer is going to be 9cm

Step-by-step explanation: