Is 9/72 rational or irrational

Answer:

ratio 2 : 3 : 5

size of smallest angle

[tex]180 \times \frac{2}{10} \\ = 36[/tex]

Answer:

The smallest angle of a triangle is 36°.

Step-by-step explanation:

Given, the ratio of angles of a triangle is 2 : 3 : 5

Let the angles of a triangle be ∠A, ∠B and ∠C.

∠A = 2x, ∠B = 3x, ∠C = 5x

∠A+∠B + ∠C= 180°

[sum of all the angles of a triangle is 180°]

2x + 3x + 5x = 180°

10x = 180°

x=180°/10 =18°

∠A=2x=2 x 18° = 36°

∠B = 3x = 3 x 18° = 54°

∠C = 5x = 5 x 18° = 90°

Hence, the smallest angle of a triangle is 36°.

HOPE IT HELPS!!!

Answer:

128 cm^2

Step-by-step explanation:

The area of a trapezoid is given by

A = 1/2 (b1+b2) h

where b1 and b2 are the lengths of the bases and h is the height

A =1/2( 10+22) * 8

A = 1/2 (32)8

  = 128

Answer:

A=128 cm²

Step-by-step explanation:

Hi there!

We are given a trapezoid and we want to find the area of it

The area of a trapezoid is given as [tex]\frac{a+b}{2}h[/tex], where a and b are the bases and h is the height

The bases are the parallel sides

They are the sides marked as 10 cm and 22 cm in this case

The height is the distance between the bases

In this case, it is the side marked as 8 cm

We know everything needed for the area, let's just label everything to avoid any confusion

a=10

b=22

h=8

Now substitute into the formula

A=[tex]\frac{a+b}{2}h[/tex]

A=[tex]\frac{10+22}{2}*8[/tex]

add the numbers on the numerator together

A=[tex]\frac{32}{2}*8[/tex]

Divide 32 by 2

A=16*8

multiply

A=128 cm²

Hope this helps!

Answer:

4.67×10

4

=4.67×10000=46700

[tex]4.67 \times {10}^{4} [/tex]

[tex] = \: 4.67 \times 1000[/tex]

[tex] = \: 46700[/tex]

Answer:

Step-by-step explanation:

Answer:

x = 14

Step-by-step explanation:

x - 42 = 98 - 9x

+42      +42

x = 140 - 9x

+9x       +9x

10x = 140

/10     /10

x = 14

Answer:

[tex]A=60^{\circ}[/tex]

Step-by-step explanation:

Given [tex]2\cos A-1=0[/tex],

Add 1 to both sides:

[tex]2\cos A=1[/tex]

Divide both sides by 2:

[tex]\cos A=\frac{1}{2}[/tex]

Take the inverse cosine of each side (note that the question stipulates that A is acute):

[tex]\arccos(\cos A)=\arccos(\frac{1}{2})[/tex]

[tex]A=\arccos(\frac{1}{2}), A\in (0^{\circ}, 90^{\circ}),\\A=\boxed{60^{\circ}}[/tex]

Answer:

8.37 cm rounded

Step-by-step explanation:

C = 2π r

C = 2π (8)

C = 16 π

C = 50.24

1/6 ( 50.24)= 8.37

Answer:

Q.D.E=(5+2i).(5-2i).i = (25-4i²)i = 25i-4i³

Step-by-step explanation:

Answer:

Since this number is small we know that the exponent will be negative.

In scientific notation the decimal must be between the first two NON zero numbers. So move the decimal and count how many positions it was moved.

1.2 x 10 ^-11

Step-by-step explanation:

Answer:

d = 8t

Step-by-step explanation:

Answer:

A linear equation in the standard form is written as:

y = a*x +b

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

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

a = (d - b)/(c - a)

So we know that our line passes through the points (8, -1) and (2, -5)

then the slope will be:

a = (-5 - (-1) )/(2 - 8) = (-4/-6)  = 2/3

Then our line is something like:

y = (2/3)*x + b

to find the value of b, we can use the fact that we know that our line passes through the point (2, -5)

this means that when x = 2, we must have y = -5

replacing these values in the equation we get:

-5 = (2/3)*2 + b

-5 = 4/3 + b

-5 - 4/3 = b

-15/3 - 4/3 = b

-19/3 = b

then the equation is:

y = (2/3)*x - 19/3

(in the question you wrote the point-slope form, but you can see that it does not work for the second point, so there may be a mistake there, as the slope is missing)

The actual equation in the point-slope form is:

y + 1 = (2/3)*(x - 8)

Answer:

The answer is 2x + -3y = 19

Step-by-step explanation:

I Got It Right Instruction on edge

Answer:

Un número decimal exacto es algo de la forma:

3.27

Para reescribir este número como una fracción, podemos ver que tiene dos dígitos luego del punto.

Entonces podemos multiplicar y dividir por 100 (misma cantidad de ceros que dígitos luego del punto decimal)

así obtenemos:

3.27*(100)/(100) = 327/100

Entonces la fracción 327/100 genera un decimal exacto.

Así, encontrar 10 fracciones es trivial, 10 ejemplos son:

7/10 = 0.7

314/100 = 3.14

27/10 = 2.7

27/100 = 0.27

2/10 = 0.2

25/100 = 0.25

31/10 = 3.1

12/10 = 6/5 = 1.2

131/10 = 13.1

142/100 = 1.42

Ahora, un decimal inexacto puro es algo de la forma:

3.33...

donde el 3 se repite infinitamente.

Tratemos de reescribir este número como una fracción:

primero debemos ver la cantidad de dígitos que se repiten, en este caso es uno solo, el 3, entonces multiplicamos por 10:

3.33*10 = 33.33...

Ahora, podemos restar el numero original:

33.333... - 3.333... = 30

Entonces tenemos que:

3.33*9 = 30

3.33 = 30/9

La fracción:

30/9 nos da in decimal inexacto puro.

Ahora que sabemos construirlas, 10 ejemplos pueden ser:

30/9 = 3.33....

1/3 = 0.33...

40/9 = 4.44...

50/9 = 5.55...

60/9 = 6.66...

70/9 = 7.77...

20/9 = 2.22...

55/9 = 6.11...

544/99 = 5.5959...

10/9 = 1.11...

Finalmente, un periódico mixto es algo de la forma:

1.2343434...

Es decir, el 34 se repite infinitamente, pero también tenemos un 2 luego del punto decimal, por lo que este número no es puramente periódico.

Para construirlos, podemos tomar una fracción exacta, como

1.1 y una periódica, como 1.11...

Si las sumamos, obtenemos:

1.1 + 1.11... = 2.211...

donde el uno se repetirá infinitamente.

Así, simplemente sumando las fracciones del primer caso con las del segundo, obtendremos decimales periódicos mixtos, por ejemplo:

7/10 + 55/9 = 613/90 = 0.7 +  6.11... = 6.8111....

7/10 +  10/9 = 163/90 = 0.7 + 1.11... = 1.811....

31/10 + 10/9 = 379/90 = 3.1 + 1.11... = 4.2111...

31/10 + 20/9 = 479/90 = 3.1 + 2.22... = 5.322...

31/10 + 30/9 = 579/90 = 3.1 + 3.33... = 6.4333...

27/10 + 20/9 =  443/90 = 2.7 + 2.22... = 4.922...

37/10 + 20/9 =  533/90 = 3.7 + 2.22... = 5.922...

4/10 +  10/9 = 136/90 = 0.4 + 1.11... = 1.511....

3/100 + 10/9 = 1027/900 = 0.03 + 1.11... = 1.14111...

4/10 +  20/9 = 236/90 = 0.4 + 2.22... = 2.622....

Answer:

Below in bold.

Step-by-step explanation:

x^2 - y^2 = 11

2x^2  + y^2 = 97

From the first equation:

y^2 = x^2 - 11

Substituting in the second equation:

2x^2 + x^2 - 11 = 97

3x^2 = 108

x^2 = 36

x = 6, -6.

Substituting  for x in the first equation:

(6)^2 - y^2 = 11

y^2 = 36 - 11 = 25

y = 5, -5.

Answer:

no

Step-by-step explanation:

substitute the x- coordinate 5 into the equation and if the result is equal to the y- coordinate 0 then it is a solution

y = 5 + 5 = 10 ≠ 0

Then (5, 0 ) is not a solution to the equation

9514 1404 393

Answer:

  180 km

Step-by-step explanation:

The Nissan had traveled (120 km/h)(1/3 h) = 40 km when it had the puncture. It started from that location when the puncture was repaired at t = (1/3+1/2) = 5/6, where t is in hours. Then the two vehicles met (again) when ...

  Matatu distance = Nissan distance

  90t = 40+120(t -5/6)

  0 = 40 +30t -100 . . . . . . subtract 90t, eliminate parentheses

  60 = 30t . . . . . . . . . . . add 60

  2 = t . . . . . . . . . . . . . 2 hours after leaving, the cars meet again

That distance from town A is ...

  y = 90t = 90(2) = 180 . . . . km

Answer:

2/5

Step-by-step explanation:

First, we can draw the rectangle out, as shown. The length is twice the width, and the diagonal, y, cuts across the rectangle. This forms a right triangle, and using the Pythagorean Theorem, we can say that

y² = x² + (2x)²

y² = x² + 4x²

y² = 5x²

square root both sides

y=√(5x²)

The diagonal, or y, is equal to √(5x²). This is equal to one side of the square

The area for the rectangle, which we need to find for the ratio, is length * width = x * 2x = 2x²

The area for the square, which we also need to find for the ratio, is (side length)² = √(5x²) = 5x²

The ratio for the area of the rectangle to the area of the square is therefore 2x²/5x² = 2/5 (crossing out the x² in both the numerator and the denominator). We know to put the rectangle on top because of the specific wording of "the ratio of the area of the rectangle to..."

Answer:

there is no diagram ......

Answer:

its letter a

Step-by-step explanation:

I hope you help

Answer:

100 mm

Step-by-step explanation:

Square root the area to find the length of each side

[tex]\sqrt[]{625} =25[/tex]

Multiply 25 by 4 to get the sum of all four sides for the perimeter

25 x 4 = 100

Answer:

The answer is -13.

Step-by-step explanation:

The formula of the nth term of an AP(arthimetic progression) is a+(n-1)d.

So the 7th term will be a+6d= -1  ---(1)

The 16th term will a+15d=17  ---(2)

Subtract (2) and (1)

a+15d-(a+6d)=17-(-1)

=a+15d-a-6d=17+1

9d=18

d=18/9

d=2.

Substitute d in eq (1)

a+6(2)= -1

a+12=-1

a= -1-12= -13

Thus the general term of the ap is -13

Answer:

LAW 2: The second law of indices tells us that when dividing a number with an exponent by the same number with an exponent, we have to subtract the powers. In algebraic form, this rule is as follows . ... Example: In this example, the powers were multiplied together to give the answer which is 3 to the power of 6.

Answer:

θ = 60.34

Step-by-step explanation:

[tex]\frac{\left(12.8\cdot \:sin\left(90\right)\right)}{sin\left(52.3\right)}[/tex] = 16.177

[tex]\frac{\left(16.177\cdot \:sin\left(90\right)\right)}{18.6}[/tex] =  θ = .869

[tex]arcsin\left(.869\right)[/tex] = 60.34

Answer:

60.4°

Step-by-step explanation:

There are two right triangles.

One right triangle (on the left side) has an acute angle measuring 52.3°.

Its opposite leg measures 12.8 cm.

We can find the length of its hypotenuse, x.

sin 52.3° = opp/hyp

sin 52.3° = 12.8 cm/x

x * sin 52.3° = 12.8 cm

x = 12.8 cm/sin 52.3°

x = 16.2 cm

Now we use the hypotenuse of the left side triangle which is a leg of the right side triangle.

For the right side triangle, we are looking for angle Θ. We know the opposite leg, 16.2 cm and the hypotenuse, 18.6 cm.

sin Θ = opp/hyp

sin Θ = 16.2/18.6

sin Θ = 0.8698

Θ = sin^-1 0.8698

Θ = 60.4°

Answer:

5/12

Step-by-step explanation:

it says in the question that 1/4 +1/3 is used so in order to make it simple we have to find the common denominator that is 12. so converting 1/4 is 3/12 and 1/3 is 4/12.so u add the numerator and u get 7 over 12 .so now the whole container of peanuts is 12/12 but 7/12 is used so 12-7= 5. so ur ans is 5/12

Answer: I dont understand what your saying im sorry, I'd really like to help but I cant :(

Answer:

there is only one way to to roll a 3

1/36 = .044 = 4.4%

Step-by-step explanation:

Answer:

the first one 2/-1, hope it helps...

Answer:

a)2x-3y

b)4(9a-4)

Step-by-step explanation:

we want to expand the following expression:

[tex] \displaystyle - \frac{1}{4} ( - 8x + 12y)[/tex]

well to do so we consider distributive property thus distribute:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y)[/tex]

reduce fraction which yields:

[tex] \displaystyle - \frac{1}{4} (- 8x )+ - \frac{1}{4}( 12y) \\ \\ \displaystyle 2x + ( - 3y)[/tex]

simplify Parentheses:

[tex] \displaystyle \boxed{ 2x - 3y}[/tex]

in the expression there's a common factor of 4 therefore factor it out:

[tex] \displaystyle 9.4a - 4.4 \\ \\ \displaystyle \boxed{4(9a - 4)}[/tex]

Answer:

One

Step-by-step explanation:

Set each equations equal to each other

[tex] {x}^{2} + 4 = 4x[/tex]

[tex] {x}^{2} - 4x + 4[/tex]

Find the discrimant.

[tex]{ - 4 {}^{2} - 4(1)(4) } = 0[/tex]

This means there is one real solution. Since the discramnt equal 0.