Sin θ = 12/37. Find tan θ. Right Triangle Trigonometry.

Answer:

1). Option (b)

2). Option (d)

3). Option (d)

Step-by-step explanation:

Question (1)

For Pythagoras triplet,

(Largest number)² = (Number 1)² + (Number 2)²

a). 5² = 5² + 2²

   25 = 25 + 4

   25 = 29

  Not True.

b). 5² = 3² + 4²

   25 = 9 + 16

   25 = 25

   True.

c). 10² = 1² + 5²

   100 = 1 + 25

   100 = 26

   Not true.

d). 2² = 2²+ 2²

   4 = 4 + 4

   4 = 8

   Not true.

Therefore, Option (b) is correct.

Question (2)

1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{5}{5}-\frac{1}{5}[/tex]

      = [tex]\frac{5-1}{5}[/tex]

      = [tex]\frac{4}{5}[/tex]

Therefore, Option (d) is the answer.

Question (3)

Property of triangle → Sum of lengths of two sides of a triangle should be greater than the measure of third side.

a). 6 + 3 > 2 ⇒ 9 > 2 [True]

    6 + 2 > 3 ⇒ 8 > 3 [True]

    2 + 3 > 6 ⇒ 5 > 6 [False]

    Triangle is not possible.

b). 2 + 8 > 3 → 10 > 3 [True]

    8 + 3 > 2 → 11 > 2 [True]

    2 + 3 > 8 → 5 > 8 [False]

   Triangle is not possible.

c). 5.5 + 2.5 > 2.5 → 8 > 2.5 [True]

   5.5 + 2.5 > 2.5 → 8 > 2.5 [True]

   2.5 + 2.5 > 5.5 → 5 > 5.5 [False]

   Triangle is not possible.

d). 3 + 6 > 7 → 9 > 7 [True]

    3 + 7 > 6 → 10 > 6 [True]

    7 + 6 > 3 → 13 > 3 [True]

   These are the sides of a triangle.

Therefore, Option D is the answer.

We are given:

To Find: ∠E

Concept Used:

Finding the value of 'x':

Since adjacent angles of a parallelogram are Supplementary:

∠D + ∠C = 180

5x + 10 + 13x - 10 = 180              [replacing the values of angle C and D]

18x = 180

x = 10                                          [dividing both sides by 18]

__________________________________________________________

Finding Measure of Angle D:

We are given that:

∠D = 5x + 10

∠D = 5(10) + 10                    [since x = 10]

∠D = 60°

__________________________________________________________

Finding the measure of ∠E:

∠D and ∠E are Adjacent angles

Since Adjacent angles are Supplementary:

∠D + ∠E = 180

60 + ∠E = 180

∠E = 120°                                  [subtracting 60 from both sides]

Hence, the measure of ∠E = 120°

9514 1404 393

Answer:

  1/192

Step-by-step explanation:

The properties of exponents useful here are ...

  a^0 = 1 . . . . for a ≠ 0

  a^-b = 1/a^b

__

  [tex]4^{-2}\cdot 12^{-1}\cdot 12^0=\dfrac{1}{4^2}\cdot\dfrac{1}{12}\cdot 1\\\\=\dfrac{1}{16\cdot12}=\boxed{\dfrac{1}{192}}[/tex]

Answer:

[tex]m∠1 + m∠2 = 180[/tex]

Step-by-step explanation:

[tex]m∠1 = m∠3 \\ m∠2 = m∠4[/tex]

[tex]m∠ 1 = m∠3 \\ 60 = 60[/tex]

[tex]360 - m∠1 + m∠3 = m∠2 + m∠4[/tex]

[tex]360 - 60 + 60 = m∠2 + m∠4[/tex]

[tex]360 - 2(60) = m∠2 + m∠4[/tex]

[tex]360 - 120 = m∠2 + m∠4[/tex]

[tex]240 = m∠2 + m∠4[/tex]

[tex] \frac{240}{2} = m∠2 = m∠4[/tex]

[tex]120 = m∠2 = m∠4[/tex]

[tex]m∠2 = 120 \\ m∠4 = 120[/tex]

[tex]m∠1 = 60 \\ m∠3 = 60[/tex]

[tex]m∠2 = 120 \\ m∠4 = 120[/tex]

[tex]m∠1 + m∠2 + m∠3 + m∠4 { = }^{?} 360[/tex]

[tex]60 + 120 + 60 + 120 { = }^{?} 360[/tex]

[tex]2(60) + 2(120) { = }^{?} 360[/tex]

[tex]120 + 240 { = }^{?} 360[/tex]

[tex]360 = 360[/tex]

[tex]m∠1 + m∠2 [/tex]

[tex]60 + 120 = 180[/tex]

[tex]m∠1 + m∠2 = 180[/tex]

Answer:

22

Step-by-step explanation:

-4(-5)+2

20+2

22

Answer: $‭10,278.9‬0

Step-by-step explanation:

FICA taxes comprise of both the Social Security tax and the Medicare tax rate which in 2017 were 6.2% and 1.45% of income respectively.

The Social security portion is subject to a limit of $127,200 in income but there is no limit for the Medicare tax.

Franklin FICA = (127,200 * 6.2%) + (165,000 * 1.45%)

= ‭7,886.4‬0 + ‭2,392.5‬0

= $‭10,278.9‬0

Answer:

1460 Days

Step-by-step explanation:

365*4

Answer:

1460 days.

Step-by-step explanation:

Answer:

1 cm = 20 km

so 3.5 cm would equal : 3.5 * 20 = 70 km

hope it helps ;)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

[tex]\frac{f(20)-f(0)}{20-0} = \frac{220.2-175}{20} = 2.26[/tex]

Step-by-step explanation:

as with all functions f(t), the average rate of change on [a.b] is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

Answer:

0.5440

Step-by-step explanation:

Given that ;

          Brand 1 : Couple      Brand 2: Sedan        Total

                           100                            200              300

                           240                              85              325

            Total  :  340                              285             625

The probability that a vehicle selected at random is a couple given that it was brand 1 will be;

The probability that a selected vehicle is a couple is  340/625

=0.5440

Correct Question :-

Given :-

We need to find :-

Solution :-

Using proportion ,

By means & extremes ,

=> - 7x = - 21 × 9

=> x = ( - 21 × 9 ) / - 7

=> x = 3 × 9

=> x = 27

Hence , when y = 9 → x = 27

Answer:

3 gallons

Step-by-step explanation:

as u can travel 32 miles on 1 gallon, 32 x 3 = 96 so 1 x 3= 3

Answer:

that would be true

Step-by-step explanation:

Answer:FALSE

Step-by-step explanation:

Answer:

21 memebers must be present

Step-by-step explanation:

First we have to convert the percent to decimal form for an easier calculation. Do this by taking 60 and dividing by 100.

You should get 0.60, now just multiply .60 by 35 and you'll get the answer of 21.

Answer:

Step-by-step explanation:

2 dollars

Answer:

$2.00

Step-by-step explanation:

Step-by-step explanation:

the 3rd angle = 180 - ( 35+80 ) = 65

Answer:

65

Step-by-step explanation:

let the third angle be y

y+35+80=180

y+115=180

y=180-115

y=65

Step-by-step explanation:

5500×35=192500

/100=1925 $

Answer:

15.625

Step-by-step explanation:

Answer:

4. John drove 25 miles in 1 hour

Step-by-step explanation:

The unit rate is the number of something per unit. There should be a first number and the second number should always be 1.

The statement which best describes a unit rate is John drove 25 miles in 1 hour .

Unit rate can be defined as the ratio between two measurements with the second term as 1. It is considered to be different from a rate, in which a certain number of units of the first quantity is compared to one unit of the second quantity.

According to the question

Best describes a unit rate is that which have second term as 1 unit

So,

Only John drove 25 miles in 1 hour satisfy the condition ,

Hence, The statement which best describes a unit rate is John drove 25 miles in 1 hour .

To know more about unit rate here:

https://brainly.com/question/11258929

#SPJ2

Answer:

third and fifth

Step-by-step explanation:

Answer:

See attached pdf for answer

Step-by-step explanation:

Step-by-step explanation:

Let the width=x

Length =6x-4

As we know that in a rectangle

[tex]{\boxed{\sf Area=LB}}[/tex]

[tex]\hookrightarrow\sf x (6x-4)=20 [/tex]

[tex]\hookrightarrow\sf 6x^2-4x=20 [/tex]

[tex]\hookrightarrow\sf 6x^2-4x-20=0 [/tex]

[tex]\hookrightarrow\sf x=\dfrac {1}{3}+\dfrac {1}{3}\sqrt {31} \quad or \quad \dfrac {1}{3}+\dfrac {-1}{3}\sqrt {31}[/tex]

Answer: $151.20

Step-by-step explanation:  8 percent of 140. Add this number to 140.

[tex]\frac{x}{140} = \frac{8}{100}[/tex]

100x=112

x=11.2

Answer:

28

Step-by-step explanation: