Angle 1 and Angle______ are alternate exterior angles.

The angles associated to the trigonometric equation 2 · tan² θ - 7 · sec θ + 8 = 0 are θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°, θ₂₁ ≈ 120° and θ₂₂ ≈ 240°.

In this question we find a trigonometric equation, that is, an equation involving trigonometric functions, that must be solved for the interval between angles of 0° and 360°. This can be done by algebra properties and trigonometric formulas.

First, write the complete expression:

2 · tan² θ - 7 · sec θ + 8 = 0

Second, use trigonometric formulas and algebra properties to reduce the number of trigonometric functions within the equation:

2 · sin² θ / cos² θ - 7 / cos θ + 8 = 0

2 · sin² θ - 7 · cos θ + 8 · cos² θ = 0

2 - 2 · cos² θ - 7 · cos θ + 8 · cos² θ = 0

6 · cos² θ - 7 · cos θ + 2 = 0

Third, use algebraic subtitution and quadratic formula to determine the roots of the quadratic-like equation:

6 · u² - 7 · u + 2 = 0

u = - 7 / (2 · 6) ± [1 / (2 · 6)] · √[(- 7)² - 4 · 6 · 2]

u = - 7 / 12 ± (1 / 12) · 1

u = - 7 / 12 ± 1 / 12

There are two possibilities:

u₁ = - 2 / 3, u₂ = - 1 / 2

Fourth, find the angles associated to roots by inverse trigonometric functions:

u₁ = - 2 / 3

θ₁₁ ≈ 131.810°, θ₁₂ ≈ 228.190°

u₂ = - 1 / 2

θ₂₁ ≈ 120°, θ₂₂ ≈ 240°

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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:

x=78

Step-by-step explanation:

x+x+24=180

2x+24=180

2x=156

x=78

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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i dont see an =, so imma assume u meant

5x - 12 + 3x=28

8x -12 = 28

8x = 40

x=5

The answer is 1.57! I hope this helps you!

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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6*12/2

72/2

36

Ans:36

Your welcome

Answer:

1. a

2. 422

3. 156.06

Step-by-step explanation:

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:

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

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!

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:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

Answer:

x = 2

y = 4

Step-by-step explanation:

Answer:

3: x = 22.5

4: x = 3.75

Step-by-step explanation:

The coordinates of vertex D in the parallelogram ABCD are (7,-3).

In a parallelogram, opposite sides are parallel and congruent. Therefore, the vector that goes from vertex A to vertex B is the same as the vector that goes from vertex C to vertex D, and the vector that goes from vertex B to vertex C is the same as the vector that goes from vertex D to vertex A.

The vector from vertex A to vertex B is [tex]< 5-(-3), 7-1 > = < 8,6 >[/tex]

So, the vector from vertex C to vertex D is also [tex]< 8,6 >[/tex]

The vector from vertex B to vertex C is [tex]< 6-5, 2-7 > = < 1,-5 >[/tex]

So, the vector from vertex D to vertex A is also [tex]< 1,-5 >[/tex]

To find the coordinates of vertex D, we can add the vector from vertex C to vertex D to the coordinates of vertex C.

The coordinates of vertex C are (6, 2)

So, the coordinates of vertex D are [tex](6+1, 2-5) = (7, -3)[/tex]

Therefore, the coordinates of vertex D in the parallelogram ABCD are (7,-3).

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An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

An interval in math is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers.

Interval notation is a simplified way of describing a particular interval. Let’s see how it’s done.

Step 1: We write the first and last number of the interval, which are the endpoints of the interval. For example, if the interval is from 6 to 20, we write 6, 20.

Step 2: We use a round or square bracket on each side of the two numbers. We use:

A square bracket [ ], if we want to include the endpoints

A round bracket ( ), if we don’t want to include the endpoints

So in this example, we use:

So, we can see that some intervals include the endpoints, some partially include them, and some do not include them. Based on this, there are three types of intervals

These are:

This type of interval does not include the endpoints. For example, (5, 10) does not include endpoints 5 and 10.

This type of interval includes the endpoints. For example, [4, 9] includes the endpoints 4 and 9.

This type of interval includes only one of the endpoints.

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Answer:

Step-by-step explanation:

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

We employ the following equation to get the normal monthly cost:

4m - 8 = 64

Regular monthly expenses amount to $18.

Irma paid for her cats' subscription in advance for a 4-month period.

She saved $8 overall when she utilized a one-time discount.

Irma totaled $64 in payment.

We must identify the equation that can be utilized to calculate m, the average monthly cost.

Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.

When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.

Irma paid a total of $64 according to the problem, thus we can create the following equation:

4m - $8 = $64

We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.

4m = $64 + $8

4m = $72

Finally, divide both sides by 4 to solve for m:

m = $72 / 4

m = $18

So, the regular cost per month, m, is $18.

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

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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The table with values for x or y that make this equation true : 3x + y = 15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

What is solving an equation?

One-step equations can be solved in four different ways: by adding, subtracting, multiplying, and dividing. In an equation, both sides will remain equal if we add the same amount to each side.

Consider, the given equation: 3x + y = 15

We have to complete the given table for the values of x and y.

Plug x = 2 in the given equation.

⇒  3(2) + y = 15

        6 + y = 16

              y = 9

Plug y = 3  in the given equation.

3x + 3 = 15

     3x = 12

       x = 4

Plug x = 6  in the given equation.

3(6) + y = 15

 18 + y = 15

        y = -3

Plug x = 0  in the given equation.

3(0) + y = 15

         y = 15

Plug x = 3  in the given equation.

3(3) + y = 15

  9 + y = 15

        y = 6

Plug y = 0  in the given equation.

3x + 0 = 15

     3x = 15

       x = 5

Plug y = 8  in the given equation.

3x + 8 = 15

3x = 7

x = 7/3

Hence, the table with values for x or y that make this equation true : 3x+y=15 are

x       2     4      6      0      3      5      7/3

y       9     3     -3     15      6     0       8      

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Answer:

Step-by-step explanation:

Use formula:

Given

Find the amount:

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:

I think no 3

if wrong correct me please

pls mark me brainliest

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draw a line from the starting point of the segment to the endpoint using the same angle and length.

1. Place a ruler or straightedge on the given segment and draw a line along the length of the ruler.

2. Use a compass to create a line segment equal to the given segment. Set the compass to the length of the given segment, place the point of the compass on one end of the segment, and draw an arc to the other end of the segment.

3. Use a protractor to measure the angle and length of the given segment. Then, draw a line from the starting point of the segment to the endpoint using the same angle and length.

The answer explains three methods for drawing a line segment equal to a given segment: using a ruler or straightedge, using a compass, and using a protractor.

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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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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)