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Sergeeva-Olga [200]
1 year ago
7

How can I find X and Y in this diagram?

Mathematics
1 answer:
Nastasia [14]1 year ago
7 0

Given the figure of a cyclic quadrilateral

The sum of the opposite angles = 180

so, we can write the following equations:

\begin{gathered} x+100=180\rightarrow(1) \\ 2y+102=180\rightarrow(2) \end{gathered}

we will find (x) from equation (1):

x = 180 - 100 = 80

We will find (y) from equation (2):

2y = 180 - 102

2y = 78

y=78/2 = 39

So, the answer will be:

x = 80

y = 39

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A kite is flying 70 feet above the ground and is attached to a string tied to a stake on the ground. The angle of elevation form
frozen [14]
If you draw a diagram of this, your given values of the resulting triangle give you the sides opposite and adjacent of the angle. The formula that uses these sides is tangent.

The tangent of an angle is equal to the ratio of the opposite side over the other non-hypotenuse side (adjacent).

Therefore;

tan(40)=70/x
0.83909963117=70/x
0.83909963117x=70
x=70/0.83909963117
x=83.4227514823

Where x is the length of the string in feet.
3 0
3 years ago
The ratio of the same side angles of two parallel lines is 1:14. Find all angles.
Oksanka [162]
The angles that lie at the same side of parallel lines are known to be always supplement of each other. This means that when we add them together, the value is 180°. If we let x be the common factor for the measures of the angle, the equation that we could use to determine the answer is,
 
                x + 14x = 180°

The value of x from the equation is 12. Hence, the angles are,
       
              x = 12
            14(12) = 168

Answer: 12° and 168°
5 0
3 years ago
The base of a rectangle is 6cm longer than its height. The area of a rectangle is 91cm squared. What is the perimeter of the rec
r-ruslan [8.4K]

Width = 7cm

Length = 13cm

<u>Explanation:</u>

Area of rectangle =  91cm^{2}

Let width of the rectangle = b ,  

So, length = b+6

Area of rectangle = (length X width) - eqn 1

Putting the value of length and width in above equation 1,

91cm^{2} = b  (b+6)\\91 = b^{2}+6b\\b^{2} + 6b-91 = 0\\

On solving the quadratic equation we get,

b = 7cm

So, width (b) = 7cm

and length = 7+6

l = 13cm

Hence,  

Width = 7cm

Length = 13cm

6 0
3 years ago
The volume of a rectangular prism is 420 cubic centimeters. The length, L, is 6 centimeters and the width, W, is 14 centimeters.
Harman [31]

Answer:

5 centimeters

Step-by-step explanation:

We know the equation to find volume is V = B x h, where B is the base of the prism. (It is also known as the simple V = l x w x h.)

No matter what equation you use, you will end up with V = l x w x h, since the base of a rectangular prism is length x width. So, we're going to plug in our known information to get 420 = 6 x 14 x h.

Then, we're going to multiply 6 x 14 to get 84. Now we have 420 = 84 x h. To isolate the h (in order to find what it is), we must divide both sides by 84.

420/84  = 5, so whats left of the equation is 5 = h, meaning your height is 5 centimeters.

4 0
3 years ago
Loto begins at his back door and walk 8 yards east, 6 yards north, 12 yards east, and 5 yards north to the barn door. About how
KonstantinChe [14]

If he could walk directly from the back door to the barn door, he would walk 10.2 yards less.

First, let's define our coordinate axis, I will use north as the y-axis and east as the x-axis.

So let's assume that Loto begins at the point (0, 0).

Then:

  • He moves 8 yards east, to: (8yd, 0)
  • He moves 6 yards north, to: (8yd, 6yd)
  • He moves 12 yards east, to: (20yd, 6yd)
  • He moves 5 yards north, to: (20yd, 11yd)

So he walked a total of 8yd + 6yd + 12yd + 5yd = 33yd

So he just moves from (0, 0) to (20yd, 11yd), thus the displacement is:

D  =\sqrt{(20yd - 0yd)^2 + (11yd - 0yd)^2}  = 22.8ft

So, if he could walk directly he would only walk 22.8 ft

The difference is:

33yd - 22.8yd = 10.2 yd.

He would walk 10.2 yards less if he could walk directly from the back door to the barn door.

If you want to learn more about displacements, you can read:

brainly.com/question/13271165

3 0
3 years ago
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