2. Ifj(x) = x2 + 1, find j(a + 1).

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

[tex]\large \mathfrak{Solution : }[/tex]

Common difference of an Arithmetic progression can be found out by subtracting the preceding term from that given term.

i.e

therefore, the common difference of the above Arithmetic progression is -4 .

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: 4 months

Step-by-step explanation:

$75 + $152X = 683

That's the equation you need to set up, with X being the number of months.

To solve, first subtract 75 from both sides.

$152x = 608

Then, divide each side by 152

X = 4

The answer is 4 months.

Answer:

1:23 2:346 3:837

Step-by-step explanation:

it's the right answer

Answer:

the answer of a is 8x+10y

do this by DMAS formula

Answer:

1 [tex]\frac{127}{200}[/tex]

Step-by-step explanation:

512/313

= 1.635

Leave 1 and convert 0.635 to fraction

[tex]\frac{635}{100}[/tex] into simplest form

= [tex]\frac{127}{200}[/tex]

= in mixed fraction

1 [tex]\frac{127}{200}[/tex]

When 512 is divided by 313 using repeated subtraction, the quotient is 1. The answer in mixed form is [tex]1\frac{199}{313}[/tex].

Repeated Subtraction is a method that subtracts the equal number of items from a group, also known as division. Using this method, the same number is subtracted repeatedly from another larger number until the remainder is zero, or smaller than the number being subtracted.

Dividend = 512

Divisor = 313

Subtract 313 from 512 repeatedly.

512 - 313 = 199

Here, 313 is subtracted once from 512 with remainder as 199.

Hence, the quotient = 1, remainder = 199.

Answer in mixed fraction:

[tex]\frac{Dividend}{Divisor} =Quotient \frac{Remainder}{Divisor} = 1\frac{199}{313}[/tex]

Learn more about repeated subtraction here

https://brainly.com/question/190780

#SPJ2

Answer:

B. 2³(3 x 5² + 2²)

Step-by-step explanation:

2³(3 x 5² + 2²)

Step 1. Simplify the exponents

8(3 x 25 + 4)

Step 2. Multiply 3 and 25

8(75 + 4)

Step 3. Add 75 and 4

8(79)

Step 4. Multiply

632

Answer:

Option B. 2³(3 x 5² + 2²) is correct

Step-by-step explanation:

2³(3 x 5² + 2²)

First of all multiply the exponents

8×(3×25+4)

Then do the multiplication of 3 and 25

8×(75+4)

Now add the following numbers in the bracket

8×(79)

And the last multiply the following numbers

8×79

632

[Hence, the expression 2³(3 x 5² + 2²) is equal to 632. ]

Answer:

-20-15=-35

Step-by-step explanation:

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

Answer:

yes

Step-by-step explanation:

the converse is Right

Answer:

B. 14.8

Step-by-step explanation:

In order to find the average, you need to find the mean.

So you add up all the students: [tex]19+13+19+9+14+15=89[/tex].  Then you divide that number by the number of classes she has: [tex]89/6= 14.8333333...[/tex]Finally, you round to the nearest tenth place: 14.8.

[tex]\\ \sf\longmapsto 7(10-2^3)+8\div 2[/tex]

[tex]\\ \sf\longmapsto 7(10-8)+8\div 2[/tex]

[tex]\\ \sf\longmapsto 7(2)+8\div2[/tex]

[tex]\\ \sf\longmapsto 14+8\div 2[/tex]

[tex]\\ \sf\longmapsto 22\div 2[/tex]

[tex]\\ \sf\longmapsto 11[/tex]

Answer:

10.8

Step-by-step explanation:

30％of 180

30/100 = 180

(180x30)/100

5400/100

54

20％ of 54

20/100 = 54

(54x20)/100

1080/100

10.8

Answer:

37

Step-by-step explanation:

LMN is one big line

LM=22

LM=15

LN=22+15=37

Answer:

LN = LM + MN = 37

Step-by-step explanation:

L————————-M———————-N

22. 15

L————————-37———————-N

Answer:

D

Step-by-step explanation:

opposite angles are equal

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

answer

z=50

x=50

y=50

a=130

Answer:

a) 2

b) 38

c) –2

d) – 38

I hope I helped you^_^

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:

14 b^5

Step-by-step explanation:

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

Answer:

Solution,

x/4 = 12/6

or, x/4 = 2

or, x =2×4

or, x = 8

.:. x = 8

Answer:

C as in?

If you expand on the question and make it clear, I can help you!

Step-by-step explanation:

Let the number be x, then

one forth of the number

=

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

Answer:

Step-by-step explanation:

The line parallel to the given has the same slope:

Use the given point to find the y-intercept:

The line is:

Answer:

Accuracy is how close a measured value is to an accepted value. Precision is how close measurements are to one another. To make measurements, you have to evaluate both the accuracy and the precision to get a correct value.