Answer:
See below.
Step-by-step explanation:
Problem 1.
1. QU
2. QW
3. UW
Given
4. QUW
Problem 2.
1. CB
2. <1, <2
Given
3. BD, BE
Given
4. ABD, CBE
SAS
Answer:
<em>The helicopter is 27.38 m far off the ground</em>
Step-by-step explanation:
The drawing shown in the image below has all the measures and variables needed to solve the problem.
We need to find R, the height of the helicopter. We'll use the law of sines to find the length of side a.
![\displaystyle \frac{28}{\sin X}=\frac{a}{\sin 54^\circ}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B28%7D%7B%5Csin%20X%7D%3D%5Cfrac%7Ba%7D%7B%5Csin%2054%5E%5Ccirc%7D)
The angle X is the measure needed to complete 180°:
X = 180° - 54° - 62° = 64°
Solving for a:
![\displaystyle a=\frac{28}{\sin 64^\circ}\cdot \sin 54^\circ](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Cfrac%7B28%7D%7B%5Csin%2064%5E%5Ccirc%7D%5Ccdot%20%5Csin%2054%5E%5Ccirc)
Calculating:
a = 31.11 m
Now using the sine ratio in the right triangle to the left side:
![\displaystyle \sin 62^\circ=\frac{R}{a}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%2062%5E%5Ccirc%3D%5Cfrac%7BR%7D%7Ba%7D)
Solving for R:
![R=a\sin 62^\circ](https://tex.z-dn.net/?f=R%3Da%5Csin%2062%5E%5Ccirc)
R=31.11*0.88
R = 27.38 m
The helicopter is 27.38 m far off the ground
Answer:
$3.97
Step-by-step explanation:
Three containers @$2.98 = 3 × 2.98 = $8.94
Less $1 = <u>-1.00
</u>
7.94
Less 50% paid my mom = ½ × 7.94 = <u>-3.97
</u>
Paid by Theresa = $3.97
[(3 × 2.98) - 1] ÷ 2 = (8.94 - 1) ÷ 2 = 7.94 ÷ 2 = 3.97
Answer:
Step-by-step explanation:
Perpendicular lines have negative reciprocal slopes
<u>Given line</u>
<u>In slope-intercept form it is</u>
- - x + 7y = 42
- 7y = x + 42
- y = 1/7x + 6
<u>Perpendicular line has slope - 1/(1/7) = - 7 and its equation is:</u>
<u>Finding b using the point (-2, -1)</u>
- -1 = -7(-2) + b
- -1 = 14 + b
- b = -1 - 14
- b = -15
<u>So the line is</u>
Answer:
Triangle UVT and TSR are isosceles triangles (two equal sides).
Angle WUV = Angle WTV (base angles of isosceles triangle)
Angle RTS = Angle TRS (base angles of isosceles triangle)
Line VW is perpendicular to line UT.
Angle WTV = Angle RTS (vertically opposite angles)
Angle WTR = Angle VTS (vertically opposite angles)