Find the measure of one interior angle for the following polygon

Answer:

[tex]{ \tt{ \tan(x) = \frac{opposite}{adjacent} }} \\ \\ { \tt{ \tan( \theta) = \frac{30}{16} }}[/tex]

[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

[tex]y=\dfrac{qx}{p}\\\\qx=py\\\\x=\dfrac{py}{q}[/tex]

Answer:

[tex]x = \frac{yp}{q}[/tex]

Step-by-step explanation:

Answer:

j=|x|

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Option B

<F = 26°

<D = 64.01°

FD = 89

Answered by GAUTHMATH

For right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

It is the longest side of the right triangle.

For a right triangle,

[tex]a^{2}+ b^{2} = c^{2}[/tex], where c is hypotenuse and a, b area other two sides of the right triangle

For given example,

We have been given a right triangle EFD with hypotenuse FD.

Also, EF = 80, ED = 39

Using the Pythagoras theorem,

[tex]\Rightarrow FD^{2}= EF^{2} + ED^{2}\\\\ \Rightarrow FD^{2}= 80^{2} + 39^{2}\\\\ \Rightarrow FD^2 = 6400 + 1521\\\\ \Rightarrow FD^2 = 7921\\\\\Rightarrow FD = 89[/tex]

Consider, sin(F)

[tex]\Rightarrow sin(F)=\frac{ED}{FD} \\\\\Rightarrow sin(F)=\frac{39}{89}\\\\ \Rightarrow sin(F)=0.4382\\\\\Rightarrow \angle F=sin^{-1}(0.4382)\\\\\Rightarrow \angle F=25.98^{\circ}\\\\\Rightarrow \angle F\approx 26^{\circ}[/tex]

Now, consider sin(D)

[tex]\Rightarrow sin(D)=\frac{FE}{FD}\\\\ \Rightarrow sin(D)=\frac{80}{89}\\\\ \Rightarrow \angle D = sin^{-1}(0.8988)\\\\\Rightarrow \angle D = 64.009^{\circ}\\\\\Rightarrow \angle D \approx 64.01^{\circ}[/tex]

Therefore, for right triangle EFD,  m ∠F ≈ 26°, m ∠D ≈ 64.01° and FD = 89

The correct answer is an option (B)

Learn more about Pythagoras theorem here:

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Answer:

70. 8x⁴

71. 3n - 10

72. a/5 + 12

Step-by-step explanation:

70. a number "x" raised to the fourth = x⁴

Product of 8 and x⁴ = 8 × x⁴

= 8x⁴

71. 3 times a number "n" = 3 × n = 3n

3n decreased by 10 = 3n - 10

72. Quotient of a number "a" and 5 = a/5

12 more than a/5 = a/5 + 12

Answer:

D. e - 35

Step-by-step explanation:

We have that:

George earned e extra points.

Kate earned k extra points.

Kate earned 35 fewer extra credit points than George.

This means that k is e subtracted by 35, that is:

k = e - 35

So the correct answer is:

D. e - 35

Step-by-step explanation:

We found that the height of the short wall "x" is 162.6 ft, the height of the tall wall "y" is 221.8 ft, and the distance between the canyon walls "z" is 162.6 ft.

To find the x, y, and z values we need to denote the right triangles from top to bottom as triangles 1, 2, and 3.

1. Finding the height of the short wall "x"

We can find the height of the short wall "x" (in triangle 3) with the following trigonometric function:

[tex] cos(\theta) = \frac{x}{H} [/tex]

Where:

H: is the hypotenuse = 230 ft

θ: is the angle between x and H.

Knowing that the sum of θ and the angle 45° must be equal to 90°, θ is:

[tex] \theta = 90 - 45 = 45 [/tex]

Hence, the height of the short wall "x" is:

[tex]x = cos(\theta)*H = 230cos(45) = 162.6 ft[/tex]                

2. Finding the height of the tall wall "y"  

The height of the tall wall "y" is given by the sum of the bases of the two first right triangles (the right triangles 1 and 2):

[tex] y = y_{1} + y_{2} [/tex]        

Where y₁ and y₂ can be calculated with the tangent and sine trigonometric functions.  

[tex]y_{1} = A*tan(20)[/tex]        

[tex] y_{2} = 230sin(45) [/tex]

Where A is the adjacent side to the angle 20°.

[tex] y = A*tan(20) + 230sin(45) [/tex]      

Since the right triangles 2 and 3 form a square, with all the sides equals to x, we have:        

[tex] A = z = y_{2} = x = 230cos(45) [/tex]        

We can use 230cos(45) or 230sin(45) to calculate y₂, so the height of the tall wall "y" is:      

[tex] y = y_{1} + y_{2} = A*tan(20) + 230cos(45) = 230cos(45)tan(20) + 230cos(45) = 221.8 ft [/tex]                        

3. Finding the distance between the canyon walls "z"

As we said above, the "z" value is the same as "x", then:

[tex]z = x = 230cos(45) = 162.6 ft[/tex]

Learn more about trigonometric functions here: https://brainly.com/question/14272510?referrer=searchResults

I hope it helps you!                                        

Answer:

The speed is 20.8  m/s

Step-by-step explanation:

If a projectile ascends vertically, and after 3 seconds it reaches its maximum height, calculate the velocity that it carries to the middle of its downward trajectory

Let the maximum height is h and initial velocity is u.

From first equation of motion

v = u + at

0 = u - g x 3

u = 3 g.....(1)

Use third equation of motion

[tex]v^2 = u^2 - 2 gh \\\\0 = 9 g^2 - 2 gh \\\\h = 4.5 g[/tex]

Let the speed at half the height is v'.

[tex]v^2 = u^2 + 2 gh \\\\v'^2 = 0 + 2 g\times 2.25 g\\\\v'^2 = 4.5\times 9.8\times9.8\\\\v' = 20.8 m/s[/tex]

Answer:

just add a small amount to the 2.8 and square the result

Step-by-step explanation:

x x^2

2.8 7.84

2.81 7.8961

2.82 7.9524

2.83 8.0089

2.84 8.0656

2.85 8.1225

2.86 8.1796

2.87 8.2369

Answer:

Step-by-step explanation:

it is a function because if you look on the x side 3 is repeating

i think 51 is answer......

Answer:

hope it helps you........

Answer:

x = 5

Step-by-step explanation:

1. Subtract 22 from both sides.

15x = 7x + 62 - 22

2. Simplify 7x + 62 - 22 to 7x + 40.

15x = 7x + 40

3. Subtract 7x from both sides.

15x - 7x = 40

4. Simplify 15x - 7x to 8x.

8x = 40

5. Divide both sides by 8.

x = [tex]\frac{40}{8}[/tex]

6. Simplify [tex]\frac{40}{8}[/tex] to 5.

x = 5

Answer:

Answer is derived according to the procedure of calculating LCM of any two numbers

Step-by-step explanation:

If you have any other questions

ask in comments

[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]

[tex]x^2-y^2-1-2y \\\\x^2-(y^2+2y+1)\\\\x^2-(y+1)^2\\\\(x)^2-(y+1)^2\\\\(x+y+1)(x-y-1)[/tex]

[tex]\\\\[/tex]

[tex] y^2-1-x^2-2x\\\\y^2-(x^2+2x+1)\\\\y^2-(x+1)^2\\\\(y)^2-(x+1)^2\\\\(y+x+1)(y-x-1) [/tex]

According to the question,

we have to find the LCM