whats the perimiter of the following rectangle? The side says x - 2 and the bottom says 2x + 1​

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

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Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

Answer:

5 5/8 cups of ketchup

Step-by-step explanation:

1 7/8 x 3

15/8 x 3/1 = 45/8

45/8 = 5 5/8

Answer:

32

Step-by-step explanation:

I don't know if I am correct but if you subtract 32 from 45632 then you will get 45600 which is easily divisible by 100, so your answer is 32

Answer:

The fourth option is the answer.

Step-by-step explanation:

Use distance formula

[tex] {x}^{2} + {y}^{2} = {d}^{2} [/tex]

where x is the distance between the two endpoints of the congruent line segment and y is the distance between the congruent line segment.

[tex] {3}^{2} + {6}^{2} = 45[/tex]

Set 45 equal to d^2.

[tex]45 = {d}^{2} [/tex]

[tex] \sqrt{45} = d[/tex]

[tex]3 \sqrt{5} = d[/tex]

L and M have the same distance between points as well. so they are congruent.

Answer:

Quotient= 70

Remainder=14

Step-by-step explanation:

Do you need explanation?

Answer:

23 goes into 1,624 70 times

Answer:

x = 6

Step-by-step explanation:

Because AB = BC and AB = 4x , AC = 24

=> 4x = 24

      x =6

Answer:

X=3

I hope this helps,

Not the neatest of handwriting though

Answer:

2 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Change the mixed numbers to improper fractions

([tex]\frac{9}{2}[/tex] - [tex]\frac{11}{3}[/tex] ) + [tex]\frac{5}{3}[/tex] ← the LCM of 2 and 3 is 6

= [tex]\frac{9(3)}{2(3)}[/tex] - [tex]\frac{11(2)}{3(2)}[/tex] + [tex]\frac{5(2)}{3(2)}[/tex]

= [tex]\frac{27}{6}[/tex] - [tex]\frac{22}{6}[/tex] + [tex]\frac{10}{6}[/tex]

= [tex]\frac{5}{6}[/tex] + [tex]\frac{10}{6}[/tex]

= [tex]\frac{15}{6}[/tex]

= [tex]\frac{5}{2}[/tex]

= 2 [tex]\frac{1}{2}[/tex]

Answer:

2: B*W=A (Answers)

Step-by-step explanation:

A: A meter of rope should cost $0.8 or 80 cents.

B: It should be 1.20 meters.

Answer:

140 comied

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

40° + 3y + 2y = 180°

↔ 5y = 140°

↔ y =28°

Answer: Should be 8 ,,,,,

Answer:

Step-by-step explanation:

well you want to isolate x so in order to undo multiplication, you divide the 5 on both side that way it cancels on the side with the x.

The answer to that is: X = 8.

40 divided by 5 = 8.

To check we can do 5 x 8 = 40.

X = 8

Answer:

$24

Step-by-step explanation:

h x 5 = 30

h = 6

30 - 6 = 25

Answer:

They are all right

Step-by-step explanation:

all of them are right

Everything is correct except the last one. I have attached the solutions, see them.

Answer:

Step-by-step explanation:

The slope-intercept form:

Use point (5, -3) and m = -4/5:

The line is:

Answer:

b = 1

Step-by-step explanation:

We know that

y = mx + b

-3 = -4/5 × 5 + b

-3 = -20/5 + b

-3 = -4 + b

-3 + 4 = b

1 = b

Answer:

Peter = 6 kg

Mary = 12 kg

Lucy = 8 kg

Step-by-step explanation:

let us take number of kg's peter took as x

then lets form an expression to find x

let us take mary's chestnuts as = 2x (twice as much as peter)

let us take Lucy's chestnuts as = 2 + x (picked 2 kg more than peter)

so

x + 2x + 2+ x = 26

4x + 2 = 26

4x = 26 - 2

4x = 24

x = 24/4

x = 6

now let us see how much each of them picked while replacing 6 by x

Peter = x

         = 6 kg

Mary = 2x

         = 2(6)

         = 12 kg

Lucy = 2+x

        = 2 + 6

        = 8 kg

now let us cross check to see the answer

6 + 12 + 8

18 + 8

= 26

CROSS-CHECKED

Answer:

-6

Step-by-step explanation:

[tex] - \frac{12}{3} \times ( - 8 + ( - 4 {)}^{2} - 6) + 2[/tex]

[tex] (-4)² = 4²= 4×4 =16 [/tex]

[tex] - \frac{12}{3} \times ( - 8 +16 - 6) + 2[/tex]

[tex] -8 + 16-6= -14 + 16 = 2[/tex]

[tex] - 4( - 8 + 16 - 6) + 2[/tex]

[tex] - 4 \times 2 + 2[/tex]

[tex] - 8 + 2[/tex]

[tex] = - 6[/tex]

Explanation:

I'm assuming you meant to say the area is 375 in^2, aka 375 square inches.

If so, then,

area of rectangle = length*width

A = L*W

A/L = W

W = A/L

W = 375/25

W = 15 inches

As a check,

A = L*W = 25*15 = 375 which helps confirm the answer.

Lois will sell her tee-shirt for $13.20

The percentage profit = [tex]\frac{profit}{cost price}[/tex] × 100

Profit = Selling price - cost price

Cost price is the total amount expended in making the tee-shirts

cost price includes cost of buying blank shirt , cost of fabric paint and amount Lois pay herself

cost of buying blank shirt = $1

cost of fabric paint = $1

amount Lois pay herself = [tex]1\frac{1}{2}[/tex] x $6

[tex]\frac{3}{2}[/tex] x $6 = $9

Total cost price = $1 + $1 + $9 = $11

0.2 = [tex]\frac{profit}{11}[/tex]

profit = 11 x 0.2 = $2.2

$2.20 = selling price - $11

selling price = $11 + 2.20 = $13.20

To learn more about selling price, please check : https://brainly.com/question/15533091?referrer=searchResults

Movie started at 22 : 45 and ended at 01 : 32.

total watching hours :

I hope it helped !!

Answer:

x = 11

Step-by-step explanation:

[tex] \frac{x + 2}{6} - \bigg( \frac{11 -x }{3} - \frac{1}{4} \bigg) = \frac{3x - 4}{12} \\ \\ \frac{2(x + 2)}{2 \times 6} - \bigg( \frac{4(11 - x) - 1 \times 3}{3 \times 4} \bigg) = \frac{3x - 4}{12} \\ \\ \frac{2x + 4}{12} - \bigg( \frac{4 4 - 4x- 3}{12} \bigg) = \frac{3x - 4}{12} \\ \\ \frac{2x + 4}{12} - \bigg( \frac{41 - 4x}{12} \bigg) = \frac{3x - 4}{12} \\ \\ \frac{2x + 4 - 41 + 4x}{ \cancel{12}} = \frac{3x - 4}{ \cancel{12}} \\ \\ 6x - 37 = 3x - 4 \\ \\ 6x - 3x = 37 - 4 \\ \\ 3x = 33 \\ \\ x = \frac{33}{3} \\ \\ \huge \red{ \boxed{ x = 11}}[/tex]

Answer:

(4 , 1 , -5)

Step-by-step explanation:

hopefully it is clear and visible...and also understandable

:)

Answer:

Still C br-uh

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

3x +7 =f(x+1)

3x +7=x+1

3x-x=-7+1

2x=-6

-3

Answer:

18

Step-by-step explanation:

243÷13=18remainder9

mark me brainliest

Answer:

18

Step-by-step explanation:

243/13

Step-by-step explanation:

2^5 > 4^2

32 > 16

hopefully it makes

:)

Answer:

I love these kind of problems (yes I'm kidding,... lol) your answer is below,...

Step-by-step explanation:

To find the area of the whole shape lets view it as three seprate rectangles,... then we will find the area of the three seperate shapes and add the areas together,... (english scholler voice): "Quite simple really"

For "simplicitys sake" lets view the shape as a house blueprint, no house I would want to live in, but a house non-the-less,... you have the main part of the house (the largest rectangle, the 13yd x 24yd one) the hallway in the middle (the 14yd x 6yd rectangle) and finally the really ridiculous sized I-du-know,... kitchen (the 5yd x 17yd one) Sooo,... lets go,...!

First of all if you didn't follow how I got the three rectangles then it's "quite simple really!" all I did is: take the oppposite side of the very far left side (the one that says 24yd) where is says 7yd and 11yd and because we know that the 7yd + 11yd + the-part-that-we-don't-know-how-long-is, is all = to 24yd then we know that the part that is not labled (the "doorway" from the main part of the house to the hallway) has to be 6yd because 7yd + 11yd + 6yd = 24yd,... AND know we know that that side of the "hallway" is 6yd, so the "hallway" is 6yd x 14yd,... So,...

13yd x 24yd = YES!... 312yd

14yd x 6yd = RIGHT again!... 84yd

5yd x 17yd = YOU are SO LIT,... yes it's 85yd

Alright so we have 312yd and 84yd and 85yd,... all we have to do is add 'em all up and you will have the area of your houseprint,... You got it!

312yd + 84yd + 85yd = (drum roll please,...)  481yd,...

The area of you shape is 481yd,...

So glad to have worked with ye and me thinks that that hopefully helped,...

CHOW,...!

Answer:

h(x) = 3x - 2

Step-by-step explanation:

The opposite of division is multiplying and the opposite of addition is Subtraction.

Answer:i i am going to go with h(x)=1/3 x+2

Step-by-step explanation:

Answer:

(-6, 4)

Step-by-step explanation: