Points D, B, and E are collinear. Find the value of a so that points A, B, and C
are collinear.

Answer:

5. x = 25.6

6. x = 11.0

7. x = 41.8°

8. x = 64.2°

9. x = 12.8°

10. x = 51.3°

Step-by-step explanation:

Let's find the x value for each triangle.

For point 5      

We have:

x: is the opposite cathetus to 52°  

20: is the adjacent cathetus to 52°  

52°: is the angle

We can find "x" with the following trigonometric function:

[tex] tan(52) = \frac{x}{20} [/tex]

[tex] x = tan(52)*20 = 25.6 [/tex]

For point 6      

We have:

x: is the hypotenuse  

5: is the opposite cathetus to the given angle  

27°: is the angle

To find "x" we need to use the trigonometric function:

[tex] sin(27) = \frac{5}{x} [/tex]

[tex]x = \frac{5}{sin(27)} = 11.0[/tex]

For point 7

We know:

x°: is the angle

6: is the hypotenuse

4: is the opposite cathetus to x°

Hence, x is:

[tex] sin(x) = \frac{4}{6} [/tex]

[tex] x = sin^{-1}(\frac{4}{6}) = 41.8 [/tex]

For point 8    

We have:

x°: is the angle

14: is the adjacent cathetus to x°

29: is the opposite cathetus to x°

To calculate "x" we need to use the trigonometric function tan(x):

[tex] tan(x) = \frac{29}{14} [/tex]

[tex] x = tan^{-1}(\frac{29}{14}) = 64.2 [/tex]

For point 9    

We have:

x°: is the angle

54: is the hypotenuse

12: is the opposite cathetus to x°

We can use sin(x) to solve for x:

[tex] sin(x) = \frac{12}{54} [/tex]

[tex] x = sin^{-1}(\frac{12}{54}) = 12.8 [/tex]

For point 10  

We have:

x°: is the angle

40: is the hypotenuse

25: is the adjacent cathetus to x°

We need to use cos(x) to solve for x:

[tex] cos(x) = \frac{25}{40} [/tex]  

[tex] x = cos^{-1}(\frac{25}{40}) = 51.3 [/tex]

I hope it helps you!

To solve the given questions, either of the trigonometric functions; sine, cosine and tangent of an angle has to be applied appropriately to either of the questions. The answers to the questions are:

5. x = 25.60

6. x = 11.00

7. x = [tex]41.8^{o}[/tex]

8. x = [tex]64.2^{o}[/tex]

9. x = [tex]12.8^{o}[/tex]

10. x = [tex]51.3^{o}[/tex]

The questions given are right angled triangles which requires the application of trigonometric functions appropriately. A right angle triangle is one that has one of its angles to be [tex]90^{o}[/tex].

So, each of the questions can be solved as follows:

5. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 52 = [tex]\frac{x}{20}[/tex]

⇒  x = Tan 52 * 20

       = 25.5988

x = 25.60

6. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin 27 = [tex]\frac{5}{x}[/tex]

⇒ x = [tex]\frac{5}{Sin 27}[/tex]

       = 11.0134

x = 11.00

7. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin x = [tex]\frac{4}{6}[/tex]

        = 0.66667

x = [tex]Sin^{-1}[/tex] 0.66667

  = [tex]41.8^{o}[/tex]

x = [tex]41.8^{o}[/tex]

8. Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan x = [tex]\frac{29}{14}[/tex]

          = 2.0714

x = [tex]Tan^{-1}[/tex] 2.0714

  = [tex]64.2^{o}[/tex]

x = [tex]64.2^{o}[/tex]

9. Sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

Sin x = [tex]\frac{12}{54}[/tex]

        = 0.22222

x = [tex]Sin^{-1}[/tex] 0.22222

  = [tex]12.8^{o}[/tex]

x = [tex]12.8^{o}[/tex]

10. Cos θ = [tex]\frac{adjacent}{hypotenuse}[/tex]

Cos x = [tex]\frac{25}{40}[/tex]

         = 0.625

x = [tex]Cos^{-1}[/tex] 0.625

  = [tex]51.3^{o}[/tex]

x = [tex]51.3^{o}[/tex]

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According to fraction and ratio, second dog is 3/2 feet long.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

First dog is 5 feet long.

then,

5 feet is equal to 4/5 of the second dog's length.

multiply both sides by 5/4.

5/4 x 5 feet is the second dog's length.

The second dog is 25/4 feet long.

The second dog is 6(1/4) feet long.

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Answer:

Step-by-step explanation:Step 1: Remove parentheses by multiplying factors.

= (x * x) + (1 * x) + (2 * x) + (2 * 1)

Step 2: Combine like terms by adding coefficients.

(x * x) = x2

(1 * x) = 1x

(2* x) = 2x

Step 3: Combine the constants.

(2 * 1) = 2

Step 4: Therefore, Simplifying Algebraic Expression is solved as

= x2 + 3x + 2.

Answer:

2.35 + 0.55 × 15 = 10.6

Therefore, she can go 10.6 miles.

Answer:

10.6

Step-by-step explanation:

2.35 + 0.55 x 15 = 10.6

Answer:

x = 2

y = 4

Step-by-step explanation:

Answer:

0.65

Step-by-step explanation:

The r-value option (B) 0.65 represents the strongest correlation.

The correlation coefficient is a quantitative method of calculating correlation. It is a statistical concept, which helps in establishing a relation between predicted and actual values obtained in a statistical experiment.

For the given situation,

We need to determine the r-value that represents the strongest correlation.

The relationship between two variables is generally considered strong when their r value is larger than 0.7.

Among the options, 0.65 is near to 0.7, so it has strongest correlation.

Hence we can conclude that the r-value option (B) 0.65 represents the strongest correlation.

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Answer: 3150

Step-by-step explanation:

V = lwh

V = 25 x 7 x 18

V = 3150

Answer:

x=78

Step-by-step explanation:

x+x+24=180

2x+24=180

2x=156

x=78

Step-by-step explanation:

For Pythagoras' Theorem to be valid, the triangle must be a right-angled one.

The formula is:

c^2 = a^2 + b^2

Where c is the longest side. While a,b are the side lengths.

Using the above formula and the measurements given in the question, we can find the value of x.

By Pythagoras' Theorem,

26^2 = (5x)^2 + (12x)^2

676 = 25x^2 + 144x^2

169x^2 = 676

x^2 = 676 ÷ 169

x^2 = 4

x = 2

The values of x and y could be 25 and 113

What are parallel lines ?

parallel lines can be stated as , they both are equi distant from each other and which never intersect.

From the given figure,

y+12 = 3x + 50

as both are parallel to each other.

y-3x = 38

and 5x  = y + 12

as vertically opposites are always equal .

y = 3x + 38

y = 5x - 12

hence,

5x - 12 = 3x +38

2x = 50

x = 25

put x = 25 in y = 3x + 38

y = 3 * 25 + 38

y = 113

hence the values of x and y are 25 and 113 respectively.

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The correct representations of the inequality expression are (a) 6x – 15 > -10 + 5x and (c) 3(2x – 5) > -5(2 – x)

From the question, we have the following expression that can be used in our computation:

–3(2x – 5) < 5(2 – x)

Divide bot sides of the inequality by -1

So, we have the following representation

3(2x – 5) > -5(2 – x)

Next, we open the brackets

This gives

6x – 15 > -10 + 5x

Hence, the representation is 6x – 15 > -10 + 5x

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Complete question

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.

(a) 6x – 15 > -10 + 5x

(b) 6x – 15 < -10 + 5x

(c) 3(2x – 5) > -5(2 – x)

(d) 3(2x – 5) < -5(2 – x)

Answer:

C)   1/3

Step-by-step explanation:

3 = 3/1

3/1  x  1/3  = 3/3  = 1

Answer:

Step-by-step explanation:

formula 0.5 x base x height

Answer:

Remember the formula a^2+b^2=c^2

Step-by-step explanation:

This can be used on right triangles. Now your a and b represent the legs of a triangle and the c represents the hypotenuse(the longest side). If you had a leg that was 2 inches and a second leg that was 4 inches you would plug it into the equation so...

2^2+4^2=c^2

Now evaluate

2^2=4

4^4=16

so

4+16=c

20=c

Now take the square root of 20 which is approximately 4.47 or leave it as square root of 20

If you had one leg and a hypotenuse then plug in and solve like any other equation.

Hope this helps!

Answer:

15

Step-by-step explanation:

5 X 10 = 50

170 / 50 = 3 sets  = 15

The answer is 1.57! I hope this helps you!

Answer:

2.5

Step-by-step explanation:

just divide 50 by 20

Answer:

1. a

2. 422

3. 156.06

Step-by-step explanation:

Answer:

x = 16/9

Step-by-step explanation:

9x -16 = 0

9x = 16

x = 16/9

Let's check

9(16/9) -16 = 0

144/9 - 16 = 0

16 - 16 = 0

0 = 0

So, x = 16/9 is correct!

Answer:

Step-by-step explanation:

9x = 16

x = 16/9

Answer:

Step-by-step explanation:

(x+8)(x-1)(x-3)

Answer:

1200

Step-by-step explanation:

Complementary angles add to 90 degrees. This means that 65 + x = 90, so x = 90 - 65 = 25.

Answer:

I think no 3

if wrong correct me please

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9514 1404 393

Answer:

  x ≈ 4.2

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

  tan(72°) = b/x = 13/x

  x = 13/tan(72°) ≈ 4.223956

Rounded to the nearest tenth, x ≈ 4.2.

Answer:

2/3 + 1/6 + 2/8

=(2×8+1×4+2×3)/24

=(16+4+6)/24

=26/24

=13/12

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On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] =>  sinx = 0 and 2 cosx -1 =0

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]

sinx = 0 and 2 cosx -1 =0

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The solution of the given function cosx - √(3 - 3cos³x) = 0 is C. 30° + 360° n, 330° + 360°n

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We are given the function as;

cosx - √(3 - 3cos³x) = 0

cosx = √(3 - 3cos³x)

Taking square root on both sides.

cos ²x = √(3 - 3cos³x) ²

cos ²x = (3 - 3cos³x)

For solving for x in

cos ²x = (3 - 3cos³x)

cos ²x = 3 (1 - cos³x)

(1 - cos³x) = cos ²x/3

x= π/6 + 2πn

or

x=11π/6 + 2πn

where n is an integer.

30° + 360° n, 330° + 360°n

The correct answer is C.

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Answer:

Step-by-step explanation:

Use formula:

Given

Find the amount:

1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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Answer:

Volume of pyramid =1/3× Area of base × height

Since the base is a square

Area of base = l²

l = length

= 6²

= 36ft²

Height of pyramid = 5ft from the diagram above

Volume = 1/3× 36ft² × 5ft

= 60ft³