12. Find three consecutive even integers such that
the sum of the smallest integer and twice the
median integer is 20 more than the largest
integer.

Problem 61

Refer to this link where I solved the problem earlier

https://brainly.com/question/24517029

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Problem 62

T(n) = nth triangular number

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

That squares to (0.5n(n+1))^2 = 0.25n^2(n+1)^2

The next triangular number after T(n) is

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

That squares to 0.25(n+1)^2(n+2)^2

Notice how each squared result has 0.25 and (n+1)^2 found buried in them.

Let's say A = 0.25(n+1)^2

That would mean the first result 0.25n^2(n+1)^2 becomes An^2

The second result 0.25(n+1)^2(n+2)^2 becomes A(n+2)^2

Let's add those to see what happens

An^2+A(n+2)^2

An^2+A(n^2+4n+4)

A(n^2+n^2+4n+4)

A(2n^2+4n+4)

0.25(n+1)^2*(2(n^2+2n+2))

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

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

0.5k(k+1)

We see that the result is a triangular number where k = (n+1)^2

This shows that adding the squares of consecutive triangular numbers gets us another triangular number.

A few examples

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Problem 63

I'll borrow some of the ideas from problem 62

We found that after squaring the nth and (n+1)th triangular numbers, we got An^2 and A(n+2)^2 respectively. We let A = 0.5(n+1)^2

Subtract those expressions to get...

A(n+2)^2 - An^2

A(n^2+4n+4)-An^2

A(n^2+4n+4-n^2)

A(4n+4)

4A(n+1)

4*0.5(n+1)^2*(n+1)

(n+1)^3

This proves that the difference between the squares of consecutive triangular numbers is a perfect cube, aka a cube number.

A few examples:

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Problem 64

Refer to this link where I solved the problem earlier

https://brainly.com/question/24517029

Answer:

112 adults

Step-by-step explanation:

2x+504=11x

11x-2x=504

9x=504

x=56

The ratio is 2:11 so we multiply 56 by 2 and 11. The 2 represents the Adults and the 11 represents the students.

56*2=112 adults

56*11 = 616 students

Just to double check if you do 616-112 it is exactly 504, Therefore the amount of adults is 112.

Have a great day!

Answer:

Step-by-step explanation:

Given:

Find h:

Step-by-step explanation:

We know that

Area of triangle = ½ × b × h

39 = ½ × 8 × h

39 = 4h

39/4 = h

9.75 = h

Answer:

$1955.33 left in her account

Step-by-step explanation:

2300+425.33-20-550=2155.33-200=

first integer=x

second integer=x+1

third integer= x+2 (x + 1 + 1)

x + (x + 1) + (x + 2) = 36

Answer

1. f - 3/4

2. 62 + h

Step-by-step explanation:

1. 1/4 of the fish are angelfish, all fish are one whole, one whole - 3/4's = 1/4

2. we dont have the value of H so we in turn have to figure out the equation and 62 + h is the only answer we can come to

Answer:

question 9

92/11 or 8.36

Step-by-step explanation:

angle on straight line is 180

:. 10x+1 + 12x-5 = 180

collect like terms

10x+12x = 180+5-1

22x = 184

divide both sides by the coefficient of x

22x/22 = 180/22

:. x = 180/22(to d lowest form= 92/11)

or 8.36

Answer:

14 b^5

Step-by-step explanation:

you can do all mathmatical operations to same variables with same power

The coordinate (5, - 8) means the diver is 8 feets below sea level after 5 seconds

The average speed of the diver is 1.78 ft/s

(x, y)

X axis = time = 5 seconds

Y axis = Depth = - 8 feets (negative value = below sea level)

The coordinate (5, - 8) : This gives information about the time with respect to position(depth) of the diver. At the coordinate point (5, - 8) it shows that the diver is at a depth of - 8 after 6 seconds

Recall the formular for speed :

Average speed in water = Total distance in water/ total timetaken

Total distance on water = (0 to - 8) + (-8 to 0) = 16 feets

Total time taken = 9 seconds.

Average speed = 16 ft / 9 seconds = 1.78 ft/s

Learn more : https://brainly.com/question/1378025

Step-by-step explanation:

Let the number be x, then

one forth of the number

=

[tex] \frac{x}{4} [/tex]

Answer:

how can i help you and when to help u and where to help you because i don't have much time say me fast what help do you need

Answer:

[tex] \frac{5}{20} = \frac{1}{4} = \frac{10}{40} \\ thank \: you[/tex]

Answer:

4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108...

Step-by-step explanation:

Numbers go on forever. So there is an infinite amount of numbers that are evenly divisible by 4.

-y/3+x/5=1

y=3x/5-3

have a great day

Answer:

ummmmmmmmm it's: 1+1=3

Answer:

- 5 and 12

Step-by-step explanation:

Using the rules

- (-) = + , + (-) = -

- 7 - (- 5) + (- 3)

= - 7 + 5 - 3

= - 2 - 3

= - 5

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

9 - (- 7) + (- 4)

= 9 + 7 - 4

= 16 - 4

= 12

Answer:

-20-15=-35

Step-by-step explanation:

I think this answers your question, sorry if I'm wrong!

Answer:

x and y are coordinates and m is slope

Answer:

I think it -2 then -7

     We will solve this problem by solving the system of equations formed by the statements given in the question.

Number of male and female officers are 200 and 140 respectively.

Statements given in the question,

Let the number of male officers in the police force = m

And the female officers in the police force = f

       "There are 60 male officers than female officers"

m = f + 60 ----- (1)

       "Ratio of male and female officers is 10 : 7"

Therefore, [tex]\frac{m}{f}=\frac{10}{7}[/tex]

[tex]m=\frac{10}{7}f[/tex] ------- (2)

   By substituting the value of 'm' from equation (2) to equation (1),

[tex]\frac{10}{7}f=f+60[/tex]

[tex]\frac{10}{7}f-f=60[/tex]

[tex]\frac{3}{7}f=60[/tex]

[tex]f=140[/tex]

   Substitute the value of 'f' in equation (1),

m = 140 + 60

m = 200

    Therefore, number of male and female officers are 200 and 140 respectively.

Learn more,

https://brainly.com/question/8260974

Answer:

yes

Step-by-step explanation:

the converse is Right

Answer:

Let speed of slower car be xkm/h

Therefore rate of other car=x+20 km/h

After 4 hrs ,

Distance covered by Car A=4x

Distance covered by Car B=4x+80

4x+4x+80=760km

8x=680

x=45

The rate of the slower car=45km/h

Answer:

C=2πr may be i am not sure

Answer:

The circumference of a circle is B

inches. The radius of the same circle

is 4.5 inches. Which expression best

represents the value of it?

c

The Angles (3x - 3)° and 60° forms alternate interior Angle pair. hence,

Answer:

x = 21

Step-by-step explanation:

3x-3 = 60 (congruent angles)

3x = 60+3

x = 63/3

x = 21

Answer:

[tex]\frac{49}{50}[/tex]

Step-by-step explanation:

First, divide it by 100.

[tex]\frac{98}{100}[/tex]

Then, simplify. (They both can be divided by 2 since it is their GCF)

[tex]\frac{49}{50}[/tex]

Answer: [tex]\frac{49}{50}[/tex]

Answer:

x+2

Step-by-step explanation:

Answer:

The answer is x+2

Step-by-step explanation:

Answer:

[tex]60 \frac{152}{101} [/tex]

Answer:

61 80/101

Step-by-step explanation:

Divide 6241 and 101 which equals 61 R80

Answer:

the answer of a is 8x+10y

do this by DMAS formula