Evaluate the expression (-243)^2/5

If [tex]k\in\mathbb{Z}[/tex] than [tex]k+1\in\mathbb{Z}[/tex] however any [tex]\mathbb{Z}[/tex] divided by 2 is in [tex]\mathbb{Q}[/tex].

But it is not so simple.

If [tex]k[/tex] is odd then [tex]k+1[/tex] is even but when even number is divided by 2, you get an odd number which is in [tex]\mathbb{Z}[/tex].

However if [tex]k[/tex] is even then [tex]k+1[/tex] is odd and when we divide that by 2, you get a number like for example [tex]\frac{5}{2}[/tex] which is not in [tex]\mathbb{Z}[/tex] but rather inside [tex]\mathbb{Q}[/tex]. There are fortunately no irrational numbers.

There is also a problem with zero, zero is neither odd nor even but still an integer. If your [tex]k[/tex] happens to be -1, [tex]k+1=0[/tex], and zero divided by 2 is still just 0 which is in [tex]\mathbb{Z}[/tex].

So to sum up,

If [tex]k[/tex] is odd and not -1, then [tex]\frac{k+1}{2}\in\mathbb{Z}[/tex].

Or to put it in math [tex]\forall k\in\mathrm{odd}-\{-1\}\cup\{0\}\implies\frac{k+1}{2}\in\mathbb{Z}[/tex].

If [tex]k[/tex] is even or -1, then [tex]\frac{k+1}{2}\in\mathbb{Q}[/tex].

Or to put it in math [tex]\forall k\in\mathrm{even}\cup \{-1\}\implies\frac{k+1}{2}\in\mathbb{Q}[/tex].

Notes:

[tex]\mathbb{Z}[/tex] is a set of integers.

[tex]\mathbb{Q}[/tex] is a set of rational numbers.

[tex]\mathbb{Z}\subset\mathbb{Q}[/tex] means integers are a subset of rational numbers, that is, every integer is a also a fraction, however not every fraction is an integer.

Hope this helps :)

Answer:

Perimeter 18 and area is 9

[tex]6\cdot\square=9\\\\\square=9:6\\\\\square=\frac{9}{6}\rightarrow\square=\frac{3}{2} \ (\text{devide 9 and 6 by 3})[/tex]

If Carmens age is x and Antoine is 5 1/4 years older than Carmen

then Antoine's age is x + 5 1/4

Katy is 11 1/2 years older than Carmen

hence, Katy's age is x + 11 1/2

its visible that Katy is older than Antoine since (x + 11 1/2 ) > (x + 5 1/4)

difference between Antoine's and Katy's age can be found out by subtracting Antoine's age from Katy's age

Difference = Katy's age - Antoine's age

= x + 11 1/2 - (x + 5 1/4)

= x + 11 1/2 - x - 5 1/4

= 6 (1/2 - 1/4)

= 6 1/4

6 1/4 rounded off to the nearest year is 6 years.

Therefore difference is 6 years.

Katy is 6 years older than Antoine

Answer:

8500

Step-by-step explanation:

depreciation=10000×15%=1500

initial cost = 10000

final cost = initial cost- depreciation

=10000-1500

=8500

Answer: 14x+6

Step-by-step explanation:

by using distribution from the ”2” outside the parenthesis, you simply do

2x7= 14 (add the variable x) so 14x

then you do 2x3= 6

Answer:

answer is Afridi.AB=CB

Answer:

18-2x

Step-by-step explanation:

distribute the 2 in 2(9-x) opposite of x is -x

Answer:

Graph copy is needed..

Step-by-step explanation:

Photo cannot be pinned*

Answer:

2.b

Step-by-step explanation:

Answer:

190 Degrees Celsius

Step-by-step explanation:

so first you multiply the

Rate per minute X Minutes

15 X 8 = 120

120 this is the  temperature increase so you add this increase to the initial temperature which was 70 degrees Celsius

temperature Increase + Initial temperature

120 + 70 = 190 degrees Celsius

The temperature of the oven is 8 minutes after being turned on to 190°C.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, the initial temperature of the oven is 70° and the temperature will increase at a rate of 15° per minute after being turned on.

We have to find the temperature of the oven 8 minutes after being turned on.

If, after being turned on, the temperature rises by 15° per minute. By dividing the time by the rate at which the temperature rises each minute, one can calculate the oven's temperature eight minutes after it is turned on.

Increase in temperature = Number of minutes × Rate of temperature increase

ΔT=8 min × 15° per minute

ΔT=120°

The temperature of the oven 8 minutes after being turned on is,

T = ΔT + initial temperature

T = 70°+ 120°

T=190°

Thus, the temperature of the oven is 8 minutes after being turned on to 190°C.

Learn more about the arithmetic operation here:

brainly.com/question/20595275

#SPJ2

Answer:

square root of 9/64 is a rational number

Step-by-step explanation:

square root of 9/64 =0.046875

Any number which when written as a decimal form which terminates (that is ends with only 0 -value digits following the last digit) or any decimal form number that ends with a sequence which repeats indefinitely is rational.

Therefore square root of 9/64 is a rational number

Hope you got this

If you have any questions just ask me.

Answer:

i belive if not mistaken 6

Step-by-step explanatio

Answer and Step-by-step explanation:

I will replicate what you said into an algebraic equation.

Your number will be represented as x.

(3x + 3) - (2x + 1) = 9

Distribute the negative.

3x + 3 - 2x - 1 = 9

Combine like terms.

x + 2 = 9

Subtract both sides of the equation by 2.

x = 7

Your number is 7.

Checking my answer:

(3(7) + 3) - (2(7) + 3) = 9

(21 + 3) - (14 + 3) = 9

24 - 17 = 9

9 = 9 ✓

So, your number is 7.

#teamtrees #PAW (Plant And Water)

I hope this helps!

Answer:

22, 23, 24, and 25.

Step-by-step explanation:

The sum of four consecutive integers is 94, and we want to determine the integers.

Let x be the first integer. Since they are consecutive, the second will be (x + 1), the third (x + 2), and the fourth (x + 3).

They sum to 94. Hence:

[tex]\displaystyle x + (x+1) + (x+2) + (x+3) = 94[/tex]

Solve for x. Combine like terms:

[tex]4x + 6= 94[/tex]

Subtract:

[tex]\displaystyle 4x = 88[/tex]

And divide. Hence:

[tex]\displaystyle x = 22[/tex]

Therefore, the first term is 22.

Then the four integers are 22, 23, 24, and 25.

Answer:

= -2

Step-by-step explanation:

6t + 3 (1 - 2t) - 5

= 6t + 3 - 6t - 5

6t and -6t cross out as they equal 0, so we are left with only +3 and -5

+3 - 5 = -2

= -2 ---> final solution

Answer:

w = -13

Step-by-step explanation:

4w - 41 = 7(w-2)

Open the bracket

4w -41 = 7w -14

Collect like terms

4w - 7w = 41 - 14

-3w = 27.

Divide both side by -3

w = -9

Answer: w = 5

Step-by-step explanation:

4w-41=-7w+14

4w+7w=14+41

11w=55

W = 55/11

W = 5

Answer:

8a^3b^3

Step-by-step explanation:

Just put same numbers with numbers, same alphabets with same alphabets

(2a^2b) (4ab^2)

2 x 4 x a^2 x a x b x b^2

Answer:

-5-4i is your answer.

[tex] \sf \red {alternate \: angles}[/tex]

[tex] \huge \purple{ \underbrace{ \overbrace{Hope \: it \: helps}}}[/tex]

Answer:

Step-by-step explanation:

4(v+1)+v=5(v-1)+9

distribute

4v+4+v

which is

5v+4=5v-5+9

5v+4=5v+4

No solution is the answer

Step-by-step explanation:

it is shown in the above process.

hope you understand

All they're asking for are your goals.

The best thing to put for 8. would be:

"I'd like to get better at my math so I don't have so much trouble and would have to ask. I'd like to be able to figure my work out myself!" Or something.

9?.

all you need to put (maybe) would be:

"Yes, I usually work on my homework at [the time you usually start your homework], and I usually work alone."

or,

"No, I usually work on my homework when I feel like it, or before I go to bed, and my parent (or guardian, sibling, friend), help me with some of the questions."

I hope that helped.

Answer:

9 and 11

Step-by-step explanation:

9 and 11 are before and after 10. so, 10 lies between them.

Answer: A

Step-by-step explanation:

-5+-5+-5+-5=-20

-4+-4+-4+-4=-16

5+5+5+5+5=25

4+4+4+4+4=20

The questions asks for -5 x 4 = -20