Find the trigonometric ratio. Write your answer as a fraction in the simplest form

Here, if you use the law of sines, you cannot find the measure of the required angle. But if you use the law of cosines, you will get the desired result.

The measure of the angle C of the given triangle is 43.61°

According to the law of cosine, the square of any one side of a triangle is equal to the difference between the squares of the other two sides and double the product of the other sides and cosine angle added together between them. If AB, BC, and CA are lengths of the three sides of a triangle, then using the law of cosine, we can write

AB² = BC² + CA² - 2(BC)(CA)cos C.

Here, AB = 16, BC = 22, and AC = 21.

Now, 16² = 22² + 21² - 2 * 22 * 21 * cos C

i.e. 256 = 484 + 441 - 924 * cos C

i.e. 256 - 925 = - 924 * cos C

i.e. - 669 = - 924 * cos C

i.e. cos C = 669/924 = 0.724

i.e. C = cos⁻¹(0.724) = 43.61

Therefore the measure of the angle C of the given triangle is 43.61°

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Answer:

200 vs 230

$30

Step-by-step explanation:

Answer:

1) S.A = 108, V = 72; 2) S.A = 68, V = 60; 3) S.A = 40, V = 58

Step-by-step explanation:

1) Surface area of a cuboid = 2(lb + bh + hl)

                                             = 2(6*4 + 4*3 + 3*6)

                                             = 2(24 + 12 + 18)

                                             = 2*54

                                             = 108 square units ------- (1)

 Volume of a cuboid = lbh

                                   = 6*4*3

                                   = 72 cube units ----------- (2)

2) Surface area = (1) - specific surface area

     Specific surface area

          =2(2*6 + 6*1 + 2*1)

          =2(12 + 6 + 2)

          =2*20

          =40 square units

  Therefore surface area = 108 - 40 = 68 square units  --------- (3)

  Volume = (2) - specific volume

      Specific volume

              =l*b*h

              =2*6*1

             =12 cube units

 Volume = 72 - 12 = 60 cube units ---------- (4)

3) Surface area = (3) - specific surface area

              Specific Surface Area

               2(2*4 +2*1 + 4*1)

               2(8 + 2 + 4)

               2(14)

               28 square units

 Surface area = 68 - 28 = 40 square units

  Volume = (4) - specific volume

         Specific volume

            = 1*2*4

            = 8 cube units

       Volume = 60 - 8 = 52 cube units

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Answer:

write these time in words 3:45

Answer:

A. (3,0)

D. (0,-1)

E. (2, 1)

Step-by-step explanation:

A. (3,0)

B. (1,7)

C. (6,2)

D. (0,-1)

E. (2, 1)

F. (3, 4)

у< x  #############################

A. (3,0)

C. (6,2)

D. (0,-1)

E. (2, 1)

y< 5 ####################

A. (3,0)

C. (6,2)

D. (0,-1)

E. (2, 1)

X<4 ###################

A. (3,0)

D. (0,-1)

E. (2, 1)

[tex]\sf \bf {\boxed {\mathbb {ANSWER:}}}[/tex]

(a) -3 [tex]\boxed{ > }[/tex] -4

(b) 6 [tex]\boxed{ >}[/tex] -20

(c) -8 [tex]\boxed{ < }[/tex] -2

(d) 5 [tex]\boxed{ > }[/tex] -7

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{☂}}}}}[/tex]

Answer:

5x2-7x-1

Step-by-step explanation:

STEP1:Equation at the end of step 1

((5x2 - 7x) - 3) + 2

STEP2:Trying to factor by splitting the middle term

 2.1     Factoring  5x2-7x-1 

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -7x  its coefficient is  -7 .

The last term, "the constant", is  -1 

Step-1 : Multiply the coefficient of the first term by the constant   5 • -1 = -5 

Step-2 : Find two factors of  -5  whose sum equals the coefficient of the middle term, which is   -7 .

     -5   +   1   =   -4     -1   +   5   =   4

Answer:

121 cm^2

Step-by-step explanation:

area of triangle = base*height/2

=11*22/2

=242/2

=121 cm^2

Answer:

Step-by-step explanation:9.5

Step-by-step explanation:

Cog, KY tj, kyzkysiyso6doydi6wkyx co70 kysu5, 5i

Answer:

220

Use PEMDAS

Answer: The answer is the diameter.

Step-by-step explanation:

Answer:

diameter

Step-by-step explanation:

the diameter goes straight through the center of the circle

Answer:

hello

Step-by-step explanation:

I did not known your answer

Answer:

22 hours

Step-by-step explanation:

Old machine produces 36 widgets in 9 hours. The number of widgets produced in an hour can be determined as;

In 1 hour = [tex]\frac{36}{9}[/tex]

              = 4 widgets

New machine can produce 40 widgets in 8 hours. The umber of widgets produced in an hour can be determined as;

In 1 hour = [tex]\frac{40}{5}[/tex]

              = 5 widgets

Thus, let the time required by old machine be represented by s, and that of new machine by y. Working together we have;

4x + 5y = 100

(4 * 10) + (5 * 12) = 100

Thus the old machine would work for 10 hours, while the new machine would work for 12 hours to produce 100 widgets.

Working together, it would take both machines 22 hours.

Answer:

x = 3/4

Step-by-step explanation:

5/2-3x-5+4x=-7/4

Combine  like terms

-10/2 + 5/2 +x = -7/4

-5/2+ x = -7/4

Add 5/2 to each side

-5/2+5/2 +x = -7/4 + 5/2

x = -7/4+5/2

Get a common denominator

x = -7/4 + 10/4

x = 3/4

Answer:

The answer;

C. y>= 2

The choose ( C)

Answer:

x=48

y=50

Step-by-step explanation:

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correct me if im wrong

Answer:

D

Step-by-step explanation:

we have to see the value of y on x=-2

which is 2

so g(-2)=2

Answer:

Let length = x

Let width = x + 5

Let Area = A

A = x(x + 5)

A = x2 + 5x

Answer:

Slope = 3500

Sarah's salary will increase by 3500 per year

Step-by-step explanation:

Given that Sarah's salary after working n years is given as :

S=90000+3500n

The equation given is similar to a linear equation :

y = bx + c ;

Where, b = slope of the linear equation

Therefore, relating the equation to that of a linear model ; the slope, b is equivalent to 3500 in Sarah's salary equation.

Slope is simply described as the rate of change, the change in y per unit change in x ;

Therefore, this means Sarah's salary will increase by 3500 per year

Step-by-step explanation:

the answer is in the above image

Answer:

1. 20

2. 0

Step-by-step explanation:

1. 20

11 -12÷4+3 (6-2)

Brackets first

11-12÷4+3 x 4

Then division and multiplication

11-3+12

Subtraction next

8+12

Now addition

8+12=20

2. Anything divided by 0 is 0

Answer:

93.4 cm²

Step-by-step explanation:

Area of the shaded region = area of the square - area of half of the circle

Area of the shaded region = s² + ½(πr²)

Where,

r = 6.2 cm

s = length of square = diameter of circle = 2*r = 2*6.2

s = 12.4 cm

Plug in the values

Area of the shaded region = 12.4² - ½(π × 6.2²)

= 153.76 - 60.381411

= 93.378589

≈ 93.4 cm² (nearest tenth)

Answer:

(a) The common difference is 4

(b) The 25th term is 108

Step-by-step explanation:

Given

[tex]T_7 = 36[/tex]

[tex]T_{14} = 64[/tex]

Solving (a): The common difference

The nth term of an AP is:

[tex]T_n = a + (n -1)d[/tex]

For the 7th term, we have:

[tex]36 = a + (7 -1)d[/tex]

[tex]36 = a + 6d[/tex]

For the 14th term, we have:

[tex]64 =a + (14 -1)d[/tex]

[tex]64 =a + 13d[/tex]

Subtract both equations

[tex]64 - 36 = a - a +13d-6d[/tex]

[tex]28 = 7d[/tex]

Divide by 7

[tex]d = 4[/tex]

Solving (b): The 25th term

First, we calculate the first term (a)

The 7th term of the progression is:

[tex]36 = a + 6d[/tex]

Substitute [tex]d = 4[/tex]

[tex]36 = a + 6 * 4[/tex]

[tex]36 = a + 24[/tex]

Subtract 24

[tex]a = 36 -24[/tex]

[tex]a = 12[/tex]

The 25th term is:

[tex]T_{25} = a + (25 - 1)d[/tex]

[tex]T_{25} = 12 + (25 - 1)*4[/tex]

[tex]T_{25} = 12 + 24*4[/tex]

[tex]T_{25} = 108[/tex]

Answer:

y = 3

Step-by-step explanation:

y , 2 , 4 , 5 , 7, 9

Mean = 5

[tex]\frac{4+y+9+5+2+7}{6}=5\\\\\frac{y+27}{6}=5\\\\y+27 = 5*6\\y +27=30\\y=30-27\\y = 3[/tex]

Answer:

4/12

Step-by-step explanation:

i am not good at this but i will try☺

Answer:

30%

Step-by-step explanation:

To find the percentage of something we decide the amount of things we want to find the percentage off by the total amount of things and then multiply the product by one hundred.

Apple: 4

Total fruit: 12

So,

4/12 = 0.3

The percentage of apples:

30%

Answer:

No 1

Here,

Let X be age of daughter

and 3X be age of father

Now,x+17+3 = 20 age

and 3x+43-20 = 7point9x

Step-by-step explanation:

So,

20÷7point9 = 2point8 years ago

Hence,

age of father = 48÷2point8 = 21point5 years

age of daughter = 20÷2point8 = 10 years

so, before 2point8 years ago father was as old as his daughter