57. If you draw a diagram and make a right traveler with the Jacques, the base of the cliff, and the top of the cliff, it should be obvious that tan(35 degrees) = (cliff height)/1200m. Solving, cliff height = 1200 * tan(35 deg) = 840 meters.
59.
Original price = 480
After 20% off, price = 480 - 0.20 * 480 = 384
After 7.5% tax, price = 384 + 0.075 * 384 = 412.80, which is the total desired.
Answer:
a) T
B) WT and TZ
C) ZTU
D) YTX
E) YT and WT
F) Angle 5 - right angle
G) obtuse angle (>90)
H) acute angle (<90)
I) obtuse angle, unless it means the other side which would be a reflex angle instead (>180)
Hope this helped!
Answer:
B.
Step-by-step explanation:
They all have 5 as a multiple in common
Answer:
x = 2![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Step-by-step explanation:
Using the tangent ratio in the right triangle with either of the 2 angles and the exact value
tan60° = ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
tan60° =
=
= ![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
Multiply both sides by x
6 = x
( divide both sides by
)
x =
×
← rationalising the denominator
x =
= 2![\sqrt{3}](https://tex.z-dn.net/?f=%5Csqrt%7B3%7D)
3x + 4y + 3z = 5
2x + 2y + 3z = 5
5x + 6y + 7z = 7
<=> 3( 3x + 4y + 3z) = 5.3
6( 2x + 2y + 3z) = 5.6
2( 5x + 6y + 7z ) = 7.2
<=> 9x + 12y + 9z = 15 (1)
12x + 12y + 18z=30 (2)
10x + 12y + 14z = 14 (3)
<=> 3x +9z =15 [ (2) - (1) ]
2x + 4z = 16. [ (2) - (1) ]
<=> 2(3x +9z) = 15.2
3(2x + 4z) = 16.3
<=> 6x+ 18z = 30
6x + 12z = 48
<=> 6z = - 18 => z = -3 and 6x + 18z = 30 so x = [30 - 18.(-3) ] : 6 = 14
We have 2x + 2y + 3z =5 => 2.14 + 2y + 3.(-3) = 5 ==> y = -7
The answer is x = 14, y = -7, z = -3