Answer:
5/6, 5/8, 5/11, 5/19
Step-by-step explanation:
The larger the denominator, the smaller the sections
We'll use standard labeling of right triangle ABC, C=90 degrees, legs a, b, hypotenuse c.
11.
Right triangle, cliff peak A, boat B, angle opposite cliff is B=28.9 deg. adjacent leg a=65.7 m, cliff height is leg b.
tan B = b/a
b = a tan B = 65.7 tan 28.9° = 36.3 m
12.
Similar story, boat at B, opposite b=3.5 m, rope c=12 m
sin B = b/c
B = arcsin b/c = arcsin (3.5/12) = 17.0°
13.
c=124 m, A=58°
sin A = a/c
a = c sin A = 124 sin 58 = 105.2 m
14.
That's a hypotenuse c=4-1.2 = 2.8 m to a height b=1.8m so
cos A = b/c
A = arccos b/c = arccos (1.8/2.8) = 50.0°
15.
Not a right triangle, an isosceles triangle. Half of it is a right triangle with hypotenuse one arm, c=9.8 cm and angle opposite half the base of B=62/2=31°. We're after d=2b:
sin B = b/c
b = c sin B
d = 2b = 2 c sin B = 2(9.8) sin 31 = 10.1 cm
Almost equilateral
Answer:
(a) (6, 2)
Step-by-step explanation:
The system of equations has one of them in y= form, so it lends itself to solution by substitution.
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Using the equation for y to substitute into the first equation, we have ...
2x -y = 10
2x -(-1/2x +5) = 10 . . . . . substitute for y
2x +1/2x -5 = 10 . . . . . eliminate parentheses
5/2x = 15 . . . . . . . . . add 5, collect terms
x = 6 . . . . . . . . . . . multiply by 2/5
Using the equation for y, we have ...
y = -1/2(6) +5 = -3 +5
y = 2
The solution is (x, y) = (6, 2).
Answer:4
Step-by-step explanation:2x+y+z=2(-2)+3+5=(-4)+3+5=(-1)+5=4
