Answer: Both 14, and 20
Step-by-step explanation:
Draw a triangle with shortest side on the ground (horiz.). The length of this side is 80 feet. Two angles touch the ground: a right angle, and the 70 degree angle.
Then the height of the building is the 2nd shortest side.
The tangent function is the appropriate one to use here:
opp h
tan 70 deg = -------- = ----------
adj 80 ft
h
Since tan 70 deg = 2.75, 2.75 = -------
80 ft
so h = building height = (80 ft)(2.75) = 219.8 ft
Answer:
(x, y) = (2, 5)
Step-by-step explanation:
I find it easier to solve equations like this by solving for x' = 1/x and y' = 1/y. The equations then become ...
3x' -y' = 13/10
x' +2y' = 9/10
Adding twice the first equation to the second, we get ...
2(3x' -y') +(x' +2y') = 2(13/10) +(9/10)
7x' = 35/10 . . . . . . simplify
x' = 5/10 = 1/2 . . . . divide by 7
Using the first equation to find y', we have ...
y' = 3x' -13/10 = 3(5/10) -13/10 = 2/10 = 1/5
So, the solution is ...
x = 1/x' = 1/(1/2) = 2
y = 1/y' = 1/(1/5) = 5
(x, y) = (2, 5)
_____
The attached graph shows the original equations. There are two points of intersection of the curves, one at (0, 0). Of course, both equations are undefined at that point, so each graph will have a "hole" there.
Answer:
Step-by-step explanation:
Discussion
First draw FH
<FOH and <FGH share the end points of the chord FH
<FOH is a central angle.
<FGH touches the circumference of the circle in the on the same side of the point of angle <FOH is closest to
Therefore <FGH is 1/2 <FOH. That is always true of central angles and the smaller angle touching the circumference that <FOH points to
Conclusion
<FGH = 1/2 < FOH
58 = 1/2 <FOH
Therefore <FOH = 2 * 58 = 116
y = < FOH
Answer
y = 116
Answer:
8z - 1
Step-by-step explanation:
Given
3 + 4(2z - 1) ← multiply each term in the parenthesis by 4
= 3 + 8z - 4 ← collect like terms
= 8z - 1
