is the square root of 3 rational?

Answer:

1) Perfect square, 2) Perfect square, 3) Not a perfect square, 4) Perfect square, 5) Perfect square, 6) Not a perfect square, 7) Perfect square, 8) Not a perfect square, 9) Not a perfect square, 10) Not a perfect square.

Step-by-step explanation:

From Algebra we must remember that a trinomial is a perfect square if and only if:

[tex](a+b)^{2} = a^{2}+2\cdot a\cdot b + b^{2}[/tex], [tex]\forall \,a,b\in\mathbb{R}[/tex] (Eq. 1)

Now we proceed to prove each trinomial:

1) [tex]a^{2}+2\cdot a +1[/tex]:

If [tex]a^2 =a^2[/tex] and [tex]b^{2} = 1[/tex], then [tex]a = \pm a[/tex] and [tex]b =\pm 1[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a)\cdot (\pm 1) = \pm 2\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.

2) [tex]4+4\cdot a +a^{2}[/tex]

If [tex]a^{2} = 4[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm 2[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2)\cdot (\pm a) = \pm 4\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.

3) [tex]a^{2}-3\cdot a +9[/tex]

If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = 9[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a)\cdot (\pm 3) = \pm 6\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.

4) [tex]4\cdot a^{2}+24\cdot a + 36[/tex]

If [tex]a^{2} = 4\cdot a^{2}[/tex] and [tex]b^{2} = 36[/tex], then [tex]a = \pm 2\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 2\cdot a)\cdot (\pm 6) = 24\cdot a[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.

5) [tex]a^{4}-10\cdot a +25[/tex]

If [tex]a^{2} = a^{4}[/tex] and [tex]b^{2} = 25[/tex], then [tex]a = \pm a^{2}[/tex] and [tex]b = \pm 5[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm a^{2})\cdot (\pm 5) = \pm 10\cdot a^{2}[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.

6) [tex]25\cdot a^{2}+20\cdot a + 9[/tex]

If [tex]a^{2} = 25\cdot a^{2}[/tex] and [tex]b = 9[/tex], then [tex]a = \pm 5\cdot a[/tex] and [tex]b = \pm 3[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 5\cdot a)\cdot (\pm 3) = \pm 30\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.

7) [tex]a^{2}\cdot b^{2}-14\cdot a \cdot b + 49[/tex]

If [tex]a^{2} = a^{2}\cdot b^{2}[/tex] and [tex]b^{2} = 49[/tex], then [tex]a = \pm a\cdot b[/tex] and [tex]b = \pm 7[/tex]. Therefore, [tex]2\cdot a\cdot b = 2\cdot (\pm a\cdot b)\cdot (\pm 7) = \pm 14\cdot a \cdot b[/tex]. In a nutshell, we conclude that this polynomial is a perfect square.

8) [tex]a^{2}-2\cdot a -1[/tex]

If [tex]a^{2} = a^{2}[/tex] and [tex]b^{2} = -1[/tex], then [tex]a = \pm a[/tex] and [tex]b = \pm i[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot a \cdot i[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.

9) [tex]16\cdot a^{2} + 24\cdot a +36[/tex]

If [tex]a^{2} = 16\cdot a^{2}[/tex] and [tex]b^{2} = \pm 36[/tex], then [tex]a = \pm 4\cdot a[/tex] and [tex]b = \pm 6[/tex]. Therefore, [tex]2\cdot a \cdot b = 2\cdot (\pm 4\cdot a)\cdot (\pm 6) = \pm 48\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.

10) [tex]10+6\cdot a +a^{2}[/tex]

If [tex]a^{2} = 10[/tex] and [tex]b^{2} = a^{2}[/tex], then [tex]a = \pm\sqrt{10}[/tex] and [tex]b = \pm a[/tex]. Therefore, [tex]2\cdot a \cdot b = \pm 2\cdot \sqrt{10}\cdot a[/tex]. In a nutshell, we conclude that this polynomial is not a perfect square.

Answer:

A.

Step-by-step explanation:

Answer:

The answer is the first option.

Step-by-step explanation:

Answer:

#1 and # 3 maybe

Soooooooory if this wrong, This is the type of question I would get stuck on... O////O

Answer:

A. X>-7

Step-by-step explanation:

So the equation is

X-5>-12

You add 5 on both sides to get the X by itself. You add it because you have to get rid of the -5 and to get to 0 you would add 5.

Which leaves you with X>-7

Answer:

A.) [tex]x>-7[/tex]

Step-by-step explanation:

Solve this the way you would solve an equation: isolate the variable.

Use inverse operations. Add 5 to both sides:

[tex]x-5+5>-12+5\\\\x>-7[/tex]

Since this can't be simplified further, x is greater than -7.

:Done

Answer:

This is not possible. Perpendicular lines are opposite but there are no opposites of 0

Step-by-step explanation:

Answer:

21 jk its 19

Step-by-step explanation:

40.0*10 is the answer

actually it is 400 but u want in decimal so it is 40.0*10

Answer:

40.0*10

Step-by-step explanation:

have a good day!

Answer:

Step-by-step explanation:

Given

slope =6/5

point =(5, -4)

So

the equation of the line =

(y-y1)=m(x-x1)

Where X1=5,y1=-4,m=6/5

Put the values

(Y+4)=6/5(x-5)

5(Y+4)=6(x-5)

5y+20=6x-30

5y-6x=-30-20

-6x+5y=-50

6x-5y=50.

So the equation of the line is 6x-5y=50.

Answer:

0.036%

Step-by-step explanation:

Answer:

Step-by-step explanation:

80/100 ⋅ 4.5 = 360% because...

80/100 = 80% ( wait that's not the reason. )

Here, 80/100 = 0.8 ⋅ 4.5 = 3.6 and if you move

the decimal point two times to the left, you get 0.036%

Hope this helps! <3

Answer:

x= 24

Step-by-step explanation:

Quotient means divide, increased means add

x/3 + 12 =20

Subtract 12 from each side

x/3 +12-12 = 20-12

x/3=8

Multiply each side by 3

x/3 * 3 =8*3

x= 24

Answer:700 / n, the quotient of 700 and a number. 2w, two times a ... h - 3, three less than a number ... 20 + m, 20 more than a number. x - 12, a number decreased by 12.

Step-by-step explanation:

Answer:

b = 24/5

General Formulas and Concepts:

Pre-Alg

Step-by-step explanation:

Step 1: Define equation

12 = 5/2b

Step 2: Solve for b

Step 3: Check

Plug in b to verify it's a solution.

Answer:

The amount of money Jake had left after his purchase is $10.85

Step-by-step explanation:

The amount of Fruit Chews Jake selected = 1.6 pounds

The amount of Jelly Beans Jake selected = 2.6 pounds

The sales tax = $0.52

The amount of money Jake had to spend = $25

The table of values are;

Price Per Pound     [tex]{}[/tex]                  

Fruit Chews = $4.70

Jelly Beans = $2.35

Chocolate = $3.50

The amount of money Jake had to spend $25

The total amount of the candies Jake bought = 1.6 × $4.70 + 2.6 × $2.35 = $13.63

The total amount Jake spent = The total amount of the candies Jake bought + The sales tax

The total amount Jake spent = $13.63 + $0.52 = $14.15

The amount of money Jake had left after his purchase = The amount of money Jake had to spend - The total amount Jake spent

The amount of money Jake had left after his purchase =  $25 - $14.15 = $10.85

The amount of money Jake had left after his purchase = $10.85.

9514 1404 393

Answer:

  (x, y) = (-2.5, -4)

Step-by-step explanation:

Since you are given an expression for y, it is convenient to substitute that into the second equation.

  2x -3(6x +11) = 7

  2x -18x -33 = 7

  -16x = 40 . . . . . . add 33

  x = -40/16 = -2.5

Using the equation for y, we find ...

  y = 6(-2.5) +11 = -15 +11 = -4

The solution is (x, y) = (-2.5, -4).

Answer:

y(3x + 4y)(x + 8y)

General Formulas and Concepts:

Alg I

Step-by-step explanation:

Step 1: Define expression

3x²y + 28xy² + 32y³

Step 2: Simplify

SOLVING STEPS...

STEP1

FACTOR OUT y FROM THE EXPRESSION

SO ITS

[tex]y \times (3x {}^{2} + 28xy + 32y {}^{2} )[/tex]

STEP2

WRITE 28y AS A SUM

STEP3

FACTOR OUT 3x2 + 24xy

SO IT'S

[tex]y \times (3x \times (x + 8y) + 4xy + 32y {}^{2} )[/tex]

STEP4

FACTOR OUT 4xy + 32y2

SO IT'S

[tex]y \times (3x \times (x + 8y) + 4y \times (x + 8y) \: )[/tex]

STEP5

FACTOR OUT (3x × ( x + 8y ) + 4y × ( x + 8y ) )

SO THE ANSWER IS

[tex]y \times (x + 8y) \times (3x + 4y)[/tex]

GAVE ME THE BRAINLIEST IF MY ANSWER WAS HELPFUL...

Answer:

1.325 x 10 -2

Step-by-step explanation:

That is the answer and I know 100% that it is correct

Answer:

The two people should stand 40 feet from the center so that they can hear each other whisper

Step-by-step explanation:

From the question

Width of the gallery = 100 feet

Width = 2a

a = Width/2

a = 100/2 = 50 feet

Height of the gallery = b = 30 feet

Hence, the distance is

d² = a² - b²

d = √a² - b²

d = √50² - 30²

d = √2500 - 900

d = √1600

d = 40 feet

Hence, the two people should stand 40 feet from the center so that they can hear each other whisper.

Answer:

Step-by-step explanation:

(B). - 28.7

Answer:

2

Step-by-step explanation:

el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2

Answer: 2

Step-by-step explanation : el 2 al cuadrado es 4 si le restas su mitad(2) tu resultado seria 2    Espero que ayude Ten un día maravilloso :)

Answer:

7.75-10°

Step-by-step explanation:

Answer:

[tex] 2x \sec^2 (x^2 + 5) [/tex]

Step-by-step explanation:

[tex] f(x) = \tan (x^2 + 5) [/tex]

[tex] \dfrac{d}{dx} \tan u = \sec^2 u \dfrac{d}{dx} u [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = \sec^2 (x^2 + 5) \dfrac{d}{dx} (x^2 + 5) [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = [\sec^2 (x^2 + 5)]2x [/tex]

[tex] \dfrac{d}{dx} \tan (x^2 + 5) = 2x \sec^2 (x^2 + 5) [/tex]

Answer:

the answer is equal to 10x+15y

Answer:

Step-by-step explanation:

Busy Village is how many times the population of Boring Town?

Answer:

8x - 3

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define expression

6x + 2x - 3

Step 2: Simplify

Answer:

40

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The speed of the waves on the strings, and the wavelength, determine the frequency of the sound produced. The strings on a guitar have different thickness but may be made of similar material. They have different linear densities, where the linear density is defined as the mass per length,

μ

=

mass of string

length of string

=

m

l

.

In this chapter, we consider only string with a constant linear density. If the linear density is constant, then the mass

(

Δ

m

)

of a small length of string

(

Δ

x

)

is

Δ

m

=

μ

Δ

x

.

For example, if the string has a length of 2.00 m and a mass of 0.06 kg, then the linear density is

μ

=

0.06

kg

2.00

m

=

0.03

kg

m

.

If a 1.00-mm section is cut from the string, the mass of the 1.00-mm length is

Δ

m

=

μ

Δ

x

=

(

0.03

kg

m

)

0.001

m

=

3.00

×

10

−

5

kg

.

The guitar also has a method to change the tension of the strings. The tension of the strings is adjusted by turning spindles, called the tuning pegs, around which the strings are wrapped. For the guitar, the linear density of the string and the tension in the string determine the speed of the waves in the string and the frequency of the sound produced is proportional to the wave speed.

Hope it is helpful to you

Answer: Slope = 5/4

y-intercept = 2

Step-by-step explanation:

We have the table:

Months, m            Plant height in inches, n

0                           2

2                           4.5

4                            7

6                            9.5

We want a linear relationship to represent this table.

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

In this case we can select any pair of points, for example, i will choose the first two:

(0, 2) and (2, 4.5)

Then the slope is:

a = (4.5 - 2)/(2 - 0) = (2.5/2) = 1.25 = 5/4

Then our line can be written as:

y = (5/4)*x + b

To find the value of b, we can replace the values of any of the points in the equation, for example, i will use the point (0, 2) or x = 0, y = 2.

2 = (5/4)*0 + b

2 = b

Then our equation is:

y = (5/4)*x + 2.

Slope = 5/4

y-intercept = 2

Answer:

d

Step-by-step explanation:

I took the k12 test