Answer:
x=3
z=65
Step-by-step explanation:
6x+97 and 14x+73 are vertical angles which means they are equal
6x+97= 14x+73
Subtract 6x from each side
6x-6x+97= 14x-6x+73
97 = 8x +73
Subtract 73 from each side
97-73 = 8x+73-73
24 = 8x
Divide each side by 8
24/8 = 8x/8
3 = x
Now we need to find z
6x+97 and z are supplementary angles which means they add to 180
6x+97 +z = 180
6(3) +97 +z = 180
18+97+z=180
Combine like terms
115+z = 180
Subtract 115 from each side
115-115 +z=180-115
z = 65
TRUE because 8/15 = 0.53 which is less than 3/5 = 0.60
Answer:
X= 67
Y= 121
Z= 80
Step-by-step explanation:
To find Y:
(y-9) and 112 are congruent so
y-9=112
y=121
To find Z: (consecutive)
180=121+z+3
180=124+z (combine like terms)
subtract 124 to cancel and move to other side of equation
z= 80
To find X: (consecutive)
180=112+x+1
180=113+x (combine like terms)
subtract 113 to cancel out and move to their side of equation
x = 67
Answer: 125.80 ft
Step-by-step explanation:
Asuming the described situation is as shown in the figure below, we need to find the distance 
between the kite and Jacks house, but first we need to find the 
, 
and then 
.
How?
We will use trigonometry, especifically the trigonometric functions sine and cosine:
For :
(1)
Where is the opposite side to the angle and 
the hypotenuse.
Isolating :
(2)
For :
(3)
Where is the adjacent side to the angle.
Isolating :
(4)
Finding :
(5)
(6)
Now that we have found these values, we have to work with a bigger triangle, where the hypotenuse is the distance between the kite and Jack's house and the sides are the values calculated in (4) and (6).
So, in this case we will use the <u>Pithagorean theorem</u>:
(7)
Isolating and writing with the known values:
(8)
(9)
This is the distance between the kite and the house
The inverse version of a number is it's opposite. The opposite of 3 is -3
