Sam is saving digital copies of his movies on his computer. Right now, 270 movies take up 486,270 kilobytes. If each movie takes up the same amount of kilobytes, how many kilobytes does each movie take up?
A.
3,602
B.
1,531
C.
2,071
D.
1,801

Step-by-step explanation:

Janyce's rule doesn't work. In the case where n = 3 her rule predicts that there will be 3(3) - 1 = 8 squares but instead, there are 10 squares. Likewise, for n = 4, there are 17 squares instead of 11 that she predicted. Instead, I propose the rule [tex]n^2 + 1.[/tex] It works for all the figures shown and mostly likely, for all other values of n.

2. Part A;

Given that the number of squares obtained using Janyce conjecture for

figures 3 and 4 which are 8 and 11 squares respectively and the number of

squares in the diagram for figures 3 and 4 which are 10 and 17 squares

respectively are not the same, disproves Janyce conjecture

Part B:

The rule for the number of squares in the nth squares is n² + 1

The reasons the above conclusion and rule are correct is as follows:

2. Part A

The given number of squares in each figure are;

[tex]\begin{array}{|c|c|c|}\mathbf{Figure \ number}&\mathbf{Number \ of \ squares} &\mathbf{Janyce \ conjecture \ (3\cdot n - 1)}\\&&\\1&2 \ squares &(3 \times 1 - 1 = 2) \ squares \\2&5 \ squares&(3 \times 2 - 1 = 5) \ squares\\3&10 \ squares &(3 \times 3 - 1 = 8) \ squares\\4&17 \ squares&(3 \times 4 - 1 = 11) \ squares\end{array}[/tex]

Given that the number squares in figure 3, and 4 are;

Figure 3 = 10 squares

Figure 4 = 17 squares

Janyce conjectured number of squares are;

Figure 3 = 8 squares

Figure 4 = 11 squares

The values for the number of squares in the diagram in figures 3 and 4 are different from Janyce conjecture which disproves Janyce's conjecture for the number of squares in the nth figure

Part B

From the diagrams, we have;

The number of squares on the each figure is given by a square shape with a side length equal to the figure number of squares plus one extra square at the top right end corner, we have;

The area of the square part of the shape = n² = The number of squares in the square shape

The number of squares in the nth figure = n² + 1

Verifying, we have;

Figure 1 = (1² + 1) squares = 2 squares (Same as in diagram)

Figure 2 = (2² + 1) squares = 5 squares (Same as in diagram)

Figure 3 = (3² + 1) squares = 10 squares (Same as in diagram)

Figure 4 = (4² + 1) squares = 17 squares (Same as in diagram)

Therefore;

The correct formula for the number of squares in the nth figure = n² + 1

Learn more about the nth term of a sequence here:

https://brainly.com/question/12998719

https://brainly.com/question/15325765

https://brainly.com/question/21493252

Answer:

22 cubes

Step-by-step explanation:

Hi! I'm happy to help!

Perimeter is the total length of all the sides.

Let's start out with the top left corner and work our way counterclockwise.

For our first segment, we start from the top left corner and go to the bottom left corner, this is a length of 3, let's start our equation:

3+

Next, we are at the bottom left corner, let's go to the bottom right corner. This is a length of 5. Let's expand our equation:

3+5+

Now we are at the bottom right corner, let's go to the top right corner. This is also a length of 3. Let's add that to our equation:

3+5+3+

Now we are at the top right corner, lets go to the top middle right corner, which is to the left one unit. Let's add this:

3+5+3+1+

Now, let's head down 2 units to the inside of our shape.

3+5+3+1+2+

Move toward the center one unit:

3+5+3+1+2+1+

Move up one unit:

3+5+3+1+2+1+1+

Move left one unit:

3+5+3+1+2+1+1+1+

Move down one unit:

3+5+3+1+2+1+1+1+1+

Move left another unit:

3+5+3+1+2+1+1+1+1+1+

Start heading back up 2 units towards the top left corner:

3+5+3+1+2+1+1+1+1+1+2+

Finally, reach back 1 unit to the top left corner:

3+5+3+1+2+1+1+1+1+1+2+1=

Let's solve:

3+5+3+1+2+1+1+1+1+1+2+1=

8+3+1+2+1+1+1+1+1+2+1=

11+1+2+1+1+1+1+1+2+1=

12+2+1+1+1+1+1+2+1=

14+1+1+1+1+1+2+1=

15+1+1+1+1+2+1=

16+1+1+1+2+1=

17+1+1+2+1=

18+1+2+1=

19+2+1=

21+1=

22

Our perimeter is 22.

I hope this was helpful,(I think this was longer than it needed to be) keep learning! :D

Answer:

45000rupees

Step-by-step explanation:

cost of 1 litre of petrol=60rupees

cost of 750 litres of petrol=750×60rupees

=45000rupees

Answer:

3x-721/44 over 7

Step-by-step explanation:

1)Combine multiplied terms into a single fraction

2)Multiply the numbers

3)Subtract the numbers

4)Find common denominator

5)Combine fractions with common denominator

6)Multiply the numbers

7)Rearrange terms

Answer:

2

Step-by-step explanation:

Step-by-step explanation:

did you give us all the information ? the equating looks cut off.

so, from what I can see we have

9(y-4) - 3y = 2(3y-2)

let's try :

9y - 36 - 3y = 6y - 4

0 = 32

so, no, this can't be it. this does not have a solution. you must have cut off some additional information.

Let D denote the region whose boundary is C. By Green's theorem,

[tex]\displaystyle \int_C 8y^2x\,\mathrm dx + 6x^2y\,\mathrm dy = \iint_D \frac{\partial(6x^2y)}{\partial x} - \frac{\partial(8y^2x)}{\partial y} \,\mathrm dx\,\mathrm dy \\\\ = \int_0^3 \int_0^3 (12xy-16yx)\,\mathrm dx\,\mathrm dy \\\\ = -4 \int_0^3 \int_0^3 xy\,\mathrm dx\,\mathrm dy = \boxed{-81}[/tex]

9514 1404 393

Answer:

  10, -1

Step-by-step explanation:

If you assume the numbers are integers, you can look at the factor pairs that make -10:

  -10 = 10(-1) = 5(-2) = 2(-5) = 1(-10)

The sums of these pairs are 9, 3, -3, -9, so the pair of interest is the first one:

  10, -1

Answer:

126720

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

You are given that x - 3 = 8

It's an equation. The first thing you do is add or subtract when you are learning how to handle equations. This is a level 1 equation. That means that the solution is just to add or subtract something.

In this case, x has 3 taken away from it. So you have to get x by  itself. The way to do that is to add 3. Then the -3 on the left disappears.

x - 3 + 3 = 8+3

x = 11

The answer is A

Answer:

don't know actually but I can elaborate the solution

Step-by-step explanation:

x-3=8

x=8+3

9514 1404 393

Answer:

Step-by-step explanation:

Let b and c represent the rates of the boat and current, respectively. Then the upstream rate is ...

  speed = distance/time

  b -c = (116 km)/(4 h) = 29 km/h

  b +c = (164 km)/(4 h) = 41 km/h

Adding these equations gives ...

  2b = 70 km/h

  b = 35 km/h

Substituting into the first equation, we have ...

  35 -c = 29

  c = 6

Rate of the boat: 35 km/h.

Rate of the current: 6 km/h

9514 1404 393

Answer:

  C)  41

Step-by-step explanation:

The angles of the linear pair are supplementary, so you have ...

  (x +16)° +123° = 180°

  x = 41 . . . . . . . . . . . . . . divide by °, subtract 139

Answer:

x = 41

Step-by-step explanation:

The angles shown are supplementary

Supplementary angles add up to equal 180

This means that x + 16 + 123 = 180

x + 16 + 123 = 180

Solve for x

Combine like terms ( add 16 and 123 )

x + 139 = 180

Subtract 139 from both sides

x = 41

Answer:

1/4= 0.5=0.125, 2/4=0.5=0.125, 3/4= 0.75=0.1878

Answer:

z = 2y - 4x

Step-by-step explanation:

[tex]{ \sf{x = \frac{2y - z}{4} }} [/tex]

multiply both sides by 4:

[tex]{ \sf{(4 \times x) = ( \frac{2y - z}{4}) \times 4 }} \\ \\ { \sf{4x = 2y - z}} \\{ \sf{z = 2y - 4x}}[/tex]

Answer:

[-5, 2]

Step-by-step explanation:

We have to find the interval for which f(x) <= 0, the interval is [-5, 2].

Answer:

(0,-5)

Step-by-step explanation:

4x-2(-2x-5)+10

x=0

y=-2*0-5

y=-5

Answer:

place value of 2 is 100

Step-by-step explanation:

please brainleist my answer

Answer:

The place value of 2 in 6.253 is 200

Step-by-step explanation:

Place value of 2 is occurring in hundreds

Answer:

$4, 15 x 2=30

      2 x 2=4

Answer:

4 dollars

Step-by-step explanation:

We can write a ratio to solve

15 stickers       30 stickers

----------------- = -------------

2 dollars           x stickers

Using cross products

15x = 2*30

15x = 60

Divide by 15

15x/15 = 60/15

x = 4

Hey there!

I believe this would be your answer: [tex]\frac{a^2+ab+b^2} {a+b}[/tex]

Hope this helps!

Have a great day!

1.

Paul's present age = x

John's present age = 18

Paul's age 4 years ago = x - 4

John's age 4 years ago = 18 - 4 = 14

Also,

Paul's age four years ago was twice that of John's age four years ago.

Therefore,

Paul's age 4 years ago = 2(14)

= 28

Paul's age 4 years ago = x - 4 = 28

x - 4 = 28

x = 28 + 4

x = 32

Therefore, the present age of Paul is 32.

2.

Cost of one bottle of milk = $3.2

Cost of five bottles of milk = $3.2 × 5 = $15

Cost of four bottles of juice = $15 - $4.4

= $10.6

Cost of one bottle of juice = x

= Cost of four bottles of juice

4

= 10.6

4

= 2.56

Therefore, one bottle of juice costs $2.56.

3.

Savings spent on personal ornaments = 1/8

Savings spent on clothing = 5/6

Total savings spent = 1/8 + 5/6

= 3/24 + 20/24

= (3+20)/24

= 23/24

Savings left = 1/24 = $130

Total amount of savings = x

As 130 is one part of the total savings,

Total amount of savings =

x = 130 × 24

x = 3120

Therefore, original amount of savings is $3120.

Answer:

(3)

x = 0

y = 3/7

(4)

x = 6

y = -11

Step-by-step explanation:

the beginning was right, but get mistake was then to add the 2 equations but the parts with the y terms she suddenly subtracted.

no, one operation for everything. and then maybe another operation (and again for everything present).

so, some would multiply by -2 and then truly add.

or, as we will do it now to refuse as much as possible from your friend's work, we multiply by 2 and then SUBTRACT !

5x + 7y = 3

3x + 14y = 6

multiply the first equation by 2 and then subtract the second one.

10x + 14y = 6

- 3x + 14y = 6

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

7x + 0 = 0

=>

x = 0

then we use this e.g. in the first equation to get y :

5×0 + 7y = 3

7y = 3

y = 3/7

10x + 3y = 27

3x - 5y = 73

let's go e.g. for 15y (multiply the fits by 5 and the second by 3)

50x + 15y = 135

+ 9x - 15y = 219

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

59x + 0. = 354

59x = 354

x = 6

10×6 + 3y = 27

60 + 3y = 27

3y = -33

y = -11

Answer: 7

Step-by-step explanation:

1. multiply both sides by -6 so the -6 on the right side could cancel out and the left side would be -6:  1= a-13/-6 ==> -6=a-13

2. add both sides by 13 so -13 on the right side could cancel out and the left side would be -6+13: -6=a-13 ==> -6+13=a-13+13

3. you know -6+13 equals 7 right? so the answer is a=7

Hey there! I'm happy to help!

We want to get the a all by itself. For me, I always like to have the variable on the left side, so first, let's just flip this around.

[tex]\frac{a-13}{-6} =1[/tex]

What we want to do is get all of the constants (numbers without variables) on the right side. This will leave a all on its own.

We see that the quantity a-13 is being divided by -6. To undo this, we will just multiply both sides by -6. This will cancel out that -6 and get us closer to having the a isolated.

[tex]\frac{a-13}{-6} *-6=1*-6\\\frac{a-13}{1}=-6\\a-13=-6[/tex]

Now we add 13 to both sides to undo the -13 on the left side.

[tex]a-13+13=-6+13[/tex]

[tex]a+0=7\\a=7[/tex]

Have a wonderful day and keep on learning! :D

Answer:

a.36

b.8.5

c.2.5

d.6

e.9

f.8

Answer:

25, 432, 120

Step-by-step explanation:

a. 5 × 5 = 25 ways

b. 2 × 6 × 6 × 6 = 432 ways

c. 2 × 5 × 4 × 3 = 120 ways

Answer:

First question(-14)

Second question(-24)

Step-by-step explanation:

8 x 3 = 24/since the signs are different the number will be negative.

7 x -2 = -14/since the signs are different the number will be negative.

hope this helps!! plz mark as brainly if it helps you<3

Answer:

(-1,-5)

Step-by-step explanation:

To understand where this point was before the transformation you must first understand the transformation itself. Shifting left is a horizontal translation, this means that it will affect the x-coordinate. The x-coordinate is the first digit in the pair. Therefore, in the case of (3,5), 3 would be the x-coordinate. Additionally, moving left is moving towards the negative, so it is the same as subtracting. Thus, to find where you started, work backward. Do this by adding 4 to the x-coordinate. This means the beginning coordinate was (-1,-5).

Answer:

Step-by-step explanation:

Given function:

This is a quadratic function with positive leading coefficient, therefore it is an increasing function with its minimum at vertex. It has no maximum value.

The vertex is at x = -b/2a:

The minimum value is:

The range of the function is:

f(x)=x^2+8x+8

[tex]\\ \sf\longmapsto \dfrac{-b}{2a}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-8}{2(1)}[/tex]

[tex]\\ \sf\longmapsto \dfrac{-8}{2}[/tex]

[tex]\\ \sf\longmapsto -4[/tex]

[tex]\\ \sf\longmapsto f(-4)[/tex]

[tex]\\ \sf\longmapsto (-4)^2+8(-4)+8[/tex]

[tex]\\ \sf\longmapsto 16-32+8[/tex]

[tex]\\ \sf\longmapsto -16+8[/tex]

[tex]\\ \sf\longmapsto -8[/tex]

The range is

[tex]\\ \sf\longmapsto (8,\infty)[/tex]

Step-by-step explanation:

steps are in picture above.

if you need to ask questions I'll give you answers gladly.

Answer:

230cm²

Step-by-step explanation:

We can split the shape into 2 parts - the triangle and the rectangle.

The area of the retangle is 10*17cm = 170cm²

The area of the triangle  = 1/2 * (22-10) * (17-7)

                                         =  1/2 * 12 * 10 = 60

Therefore the total area is equal to 170+60 = 230cm²