Prove that √3 is irrational.

Here , we are going to use Trigonometric ratios.

In given right angled ∆ ;

[tex]{:\implies \quad \sf \dfrac{x}{18}=\sin (60^{\circ}) \quad \bigg\{ \because \sin (\theta)=\dfrac{P}{H}\bigg\}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{18\sqrt{3}}{2} \quad \bigg\{\because \sin (60^{\circ})=\dfrac{\sqrt{3}}{2}\bigg\}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad x=9\sqrt{3} \: units}[/tex]

Also;

[tex]{:\implies \quad \sf \dfrac{y}{18}=\cos (60^{\circ}) \quad \bigg\{ \because \cos (\theta)=\dfrac{B}{H}\bigg\}}[/tex]

[tex]{:\implies \quad \sf x=\dfrac{18}{2} \quad \bigg\{\because \cos (60^{\circ})=\dfrac{1}{2}\bigg\}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad y=9 \: units}[/tex]

Hence , The required values for x and y are 9√3 and 9 units

Answer:

380

Step-by-step explanation:

This is an airthmatic sequence

we can use the following equation to find the nth term

a₁+(n-1)d

where the common difference (d) is 5

and the first term (a₁) is 10

and n is 75

we have

10+(75-1)*5

10+370

380

Answer:

61.25 dollars

Step-by-step explanation:

We can use a ratio to solve

4 yards            7 yards

--------------  = -----------------

35 dollars         x dollars

Using cross products

4x = 35*7

4x =245

Divide each side by 4

4x/4 = 245/4

x =61.25

Answer:

Both the parts of this question require the use of the "Intersecting Secant-Tangent Theorem".

Part A

The definition of the Intersecting Secant-Tangent Theorem is:

"If a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment."

This, when applied to our case becomes, "The length of the secant RT, times its external segment, ST, equals the square of the tangent segment TU".

Mathematically, it can be written as:

Part B

It is given that RT = 9 in. and ST = 4 in. Thus, it is definitely possible to find the value of the length TU and it can be found using the Intersecting Secant-Tangent Theorem as:

Thus,  

Thus the length of TU=6 inches

Answer:

A

Step-by-step explanation:

Answer: a

Step-by-step explanation:

Answer:

discrete. discrete can be used to describe graphs that involve variables such as customers and tickets.

Answer: Just pretend to fall or ask a quenstion then you chould start talking to some one

Step-by-step explanation:

Answer:

Markup    66.6666666......%      =      66 2/3 % (66 and 2/3 percent)

Step-by-step explanation:

The difference in prices is $150-$90=$60. So, we need to find what percentage of 90 is 60. We do this by dividing: 60/90=0.6666...., which is 66.666...%. So, the markup is 66.666...%.    =    66 2/3 %

The answer is a. 864

Step-by-step explanation:

hence, from given solution it is shown that slope is -4/3.

Answer: Fred's Slope

Step-by-step explanation:

Comparing the slope were are looking at the numerator or y of the slope to find which one takes you the highest compared to the others.

Start with Sam who has a slope of 2/11 or rise 2 run 11 which is pretty flat so sam is out

Fred and Anne both have a slope that is a whole number so we're lloking for the bigger number which would be Fred

Anne's slope is 4.75

sams slope is 2/11

and fred’s is 5

Answer:

15 students walk to school

Step-by-step explanation:

42 - total students

42 - 23 = 19

----

23 girl students

19 male students

----

19 - 6 = 13

13 - 2 = 11

--

11 - 7 = 3

3 + 2 = 5

--

10 girls walk to school

5 boys walk to school

--

10 + 5 = 15

Answer:

$535

Step-by-step explanation:  $681 + 2,150 = 2831   $2831- 691 = 2,140  $2,140/4 = 535 which means they need to sell 535 candy more.

Answer: x = 2√3.

Step-by-step explanation:

[tex]x^{2} +6^{2} =(2x)^{2}\\\\x^{2} +36=4x^{2} \\\\4x^{2}-x^{2} -36=0\\\\3x^{2} -36=0\\\\3(x^{2} -12)=0\\\\x^{2} -12=0\\\\x^{2} =12\\\\x=\sqrt{12} =2\sqrt{3}[/tex]

Answer:

negative 9 I think

Step-by-step explanation:

it's making me right more what

Answer:

It is dilated by the scale factor

Step-by-step explanation:

For example is one line is 2 units long and  the image of that line was 4 units long the scale factor would be 2. (2 x 2 = 4.) If it was the other way around with the 4 as the original line and the 2 as the image line the scale factor would be 1/2. (1/2 x 4 = 2)

Answer:

260 units

explanation:

A dilation with a scale factor is noting but an increase in size of geometrical figure by a certain value.in the circumstances the line AB is 5 units. being a line AB has no width, so it only increases in length. if you want new length, it's simple.all that's nessary multiply the orgin length by the scale factor.

5.52=260

the solution is 260 units.

Answer:

180+54sqrt3

You have to use the formula that is contained within the lessons, the answer you should have before you format it like this is: 273.530743609

Answer:

16.5 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x be the other leg, then

x² + 13² = 21²

x² + 169 = 441 ( subtract 169 from both sides )

x² = 272 ( take the square root of both sides )

x = [tex]\sqrt{272}[/tex] ≈ 16.5 cm ( to the nearest tenth )

Answer:

20m

Step-by-step explanation:

A=s^2

root 25=s

s=5m

so to find perimeter we will use the formula 4s

P=4×5

P=20m

please mark as brainliest

Answer:

The perimeter of the square must be 20m

Step-by-step explanation:

•Area of a square = side²

25m² = side²

5 m = side (square root)

•Perimeter of a square = 4 x side

4 x 5m

20m

Answer:

Each group received 3.75 pounds

You divide 15 by 4 and get 3.75

Answer:

your answers will be

<E=25

M<F=65

M<G=90

Step-by-step explanation:

i hope it helps

have a nice day!!

Answer:

Exact Form:

2 √ 34

Decimal Form:

11.66190378

The distance between points (-7, 8) and (2, 8) is 9 units.

The distance d between two points [tex](x_{1},y_{1}),(x_{2},y_{2})[/tex] is,[tex]d=\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2} }[/tex]

For given question,

Let [tex](x_{1},y_{1}) = (-7,8),(x_{2},y_{2})=(2,8)[/tex]

Let d be the distance between two points.

Using distance formula,

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+ (y_{2}-y_{1})^{2}[/tex]

[tex]d=\sqrt{(2-(-7))^{2}+ (8-8)^{2} }[/tex]

[tex]d=\sqrt{(2+7)^{2}+0^{2}[/tex]

[tex]d=\sqrt{9^{2}+0 }[/tex]

[tex]d=9[/tex]  units

Hence, the distance between points (-7, 8) and (2, 8) is 9 units.

Learn more about distance between two points here:

https://brainly.com/question/4385475

#SPJ2

Answer:

3/2 pages per hour

Step-by-step explanation:

1 : 2/3

= 3/2 : 1

Answer:

. g(x)=2x^2+10x+12=2x²+6x+4x+12=2x(x+3)+4(x+3)

=(x+3)(2x+4)=2(x+2)(x+3)

Answer:

2(x + 3)(x + 2)

Step-by-step explanation:

All three terms of g(x)=2x^2+10x+12 have the factor 2, so

g(x)=2x^2+10x+12 = 2(x^2 + 5x + 6).

This can be factored further, into:

                                 2(x + 3)(x + 2)

Answer:

580 girls and boys

Step-by-step explanation:

Answer:

(6, -30) ⇒ A

(-3, 15) ⇒ D

(1, -5) ⇒ E

Step-by-step explanation:

Answer: It’s A

Step-by-step explanation: