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Find the greatest common factor of each pair of numbers.
1. 24 and 36

2. 39 and 54

3. 42 and 98

4. 48 and 72

5. 65 and 91

6. 7 and 20

Answer:

245 = 5*7*7

510 = 3*17*2*5

250 = 5*5*5*2

1089 = 3*3*11*11

4725 = 3*3*3*5*5*7

900 = 3*3*5*5*2*2

27000 = 3*3*3*5*5*5*2*2*2

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

[tex] \displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }[/tex]

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

[tex] \displaystyle \large{ {a}^{2} = a \times a = |b| }[/tex]

Where b is the result from a×a. Let's see an example.

Examples

[tex] \displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}[/tex]

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

[tex] \displaystyle \large{ {y}^{2} = - 1}[/tex]

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

[tex] \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }[/tex]

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

[tex] \displaystyle \large{ \sqrt{ {x}^{2} } = |x| }[/tex]

Solving absolute value always gives the plus-minus. Therefore...

[tex] \displaystyle \large{ y = \pm \sqrt{ - 1} }[/tex]

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

[tex] \displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }[/tex]

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

Answer:

Therefore [tex]\sqrt{1} \neq -\sqrt{1}[/tex]

Step-by-step explanation:

[tex]\sqrt{-1} \\[/tex] cannot be calculated as no two identical numbers that are multiplid could give -1. However - [tex]\sqrt{1}[/tex] means -1 x [tex]\sqrt{1}[/tex] = -1 x 1 = -1 . Therefore [tex]\sqrt{1} \neq -\sqrt{1}[/tex]

Answer:0.1  just use a calculator

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Its the best possible answer

Answer:

C

Step-by-step explanation:

The answer is C. All you need to do is check each graph and see if (0,45) (1,70) (2,95) (3,120) are plotted on the graph correctly. And C is correct because each point is plotted on there correctly.

Answer:

a) x= 42 , b) x=(16)/(9) , c) x=60

Step-by-step explanation:

a)

b)

c)

Answer:

The answer will be:

7 2/3

Answer:

The Oringal Answer is 65/8 But In a Simplified Mixed Number the Answer is  8 1/8

Step-by-step explanation:

We need to get rid of parentheses in this term.

All the negative factors will change sign.

In our example, we have only one negative factor.

The sign of the term will change, since there is an odd number of negative factors.

We can reduce this fraction by dividing both numerator and denominator by a common numeric factors.

Step-by-step explanation:

in order of the chart they are in axis number:

3

3

2

2

4

1

4

3

Answer:

b is the correct answer

Step-by-step explanation:

(ii) A perfect cube does not end with two zeros. (iii) If square of a number ends with 5, then its cube ends with 25. (iv) There is no perfect cube which ends with 8.Cube roots of negative numbers are always negative.

Answer:

(85+92+88+98)/4

Step-by-step explanation:

No equal sign because it is a numerical expression.

Answer:   calculdora

5 (x +) + 11 = 25-3x adicionar trabalho

Step-by-step explana

Answer:

1/3 of all of the books

Step-by-step explanation:

5/5 - (2/5 +1/5) =2/5

2/5(1/3) = 2/15 nonfiction mystery books

2/15 + 1/5 = mystery books

1/5 = 3/15

2/15 + 3/15 = 5/15

5/15 = 1/3

Answer:

485 × [tex]10^{-10}[/tex]

Step-by-step explanation:

first we need to convert the number to fraction

0.0000000485

[tex]\frac{0.0000000485}{10000000000}[/tex]

it will be

[tex]\frac{485}{10000000000}[/tex]

or can be written as

[tex]\frac{485}{10^{10} }[/tex]

now we need to convert it to scientific notation

485 × [tex]10^{-10}[/tex]

□X

□X

□V

□V

□X

□V

Answer:

It's the 4th graph on the 1st sheet

Step-by-step explanation:

Answer:

15+24t

Step-by-step explanation:

First, I copied the expression down. Then, I used PEMDAS, so I multiplied 5x3. That left 15 + t(24). I just gave the variable to 24, making 24 t's coefficient. So, the simplified answer would be 15 + 24t.

Answer:

Answer Is B

for every table there 14 napkins

Answer:

43in

Step-by-step explanation:

Perimeter = sum of the sides

Perimeter = 11 + 10 + 10 + 12 = 43

Answer: Therefore,

1 + (-5/8)

Solve it,

= 1-(5/8)

= (8-5)/8

= 3/8

Step-by-step explanation:

Answer:

225

Step-by-step explanation:

Mary = 3x (3 times Carey)

Carey = x

Barry = x/2 (Because Carey read twice as many as Barry, it means he read half the amount Carey did)

3x + x + x/2 = 405

4x + x/2 = 405

8x/2 + x/2 (treat these as fractions) = 405

9x/2 = 405

9x = 810 (cross multiply)

x = 90

Mary = 3(90)      270

Carey =              90

Barry = 90/2      45

Mary - Barry

270 - 45 = 225

Hope this helps! :)

Answer:

h = S/(2 π r) - r

Step-by-step explanation:

Solve for h:

S = 2 π r (r + h)

S = 2 π r (r + h) is equivalent to 2 π r (r + h) = S:

2 π r (r + h) = S

Divide both sides by 2 π r:

r + h = S/(2 π r)

Subtract r from both sides:

Answer: h = S/(2 π r) - r

Answer:

h=s/(2 π r) -r

Step-by-step explanation:

Answer:

Answer:The formula for the area of a parallelogram is A = bh, and the formula for area of a triangle is A = 1/2bh. Since a triangle is half of the area of a parallelogram with the same base and height, the only difference in the formula is 1/2.

Step-by-step explanation:

Maria would determine the height by dividing the area of the garden by the base

From the question, she has the area and the base.

Also, the garden has the shape of a parallelogram

The area of a parallelogram is the product of the base and the height.

So, when the area is divided by the base, she gets the height

Read more about parallelograms at:

https://brainly.com/question/3050890

Answer:

5:6

Step-by-step explanation:

35:42

42/ 6 = 7

35/7 = 5

Answer:

35:42

Step-by-step explanation:

Answer: 3(x+3) = 3X + 3(x-1)

3x + 9 = 3x + 3x - 3

3x + 9 = 6x - 3

0 = 6x - 3 - 3x - 9

0 = 3x - 12

12 = 3x

x=4

Step-by-step explanation:

See the images. I hope it will help you.

Answer:

sure

Step-by-step explanation:

dhdhdhdhdjdrjdhdhhdj

Answer:

I would guess 20%

Step-by-step explanation:

16+30+34)/4)x5   (this is how I think u would get it to be 100)

16/4)x5 = 20

20/100 = 20%

Im less certian about this one than the other but if u think its correct u can try it