Answer:
Step-by-step explanation:
Question 1: Assumption: This is a 30-60-90 triangle.
Remember that the sides of a 30-60-90 triangle are in the ratio 1:√3:2
The side opposite the 90° angle is 16, so the side opposite the 30° angle is 16/2 = 8
x = 8 units.
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Question 2: Assumption: This is an isosceles triangle.
Draw the altitude to the vertex angle and you get a 30-60-90 triangle.
The side opposite the 90° angle has length 22, so the side opposite the 30° angle has length 11.
x/2 = 11
x = 22 units
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Question 3: Assumption: This is a 45-45-90 triangle.
The sides of a 45-45-90 triangle are in the ratio 1:1:√2
The sides opposite the 45° angles are 19 and x.
x = 19
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Question 4: Assumption: This is an isosceles triangle.
x = 13 units
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Question 5: Assumption: This is a right triangle.
sin(54°) = x/45
x = 45sin(54°) ≅ 36.4 units
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Question 6: Assumption: This is a right triangle.
sin(35°) = z/23
z = 23sin(35°) ≅ 13.2 units
Answer:
a. 20°
Step-by-step explanation:
The external angle T is half the difference of the intercepted arcs:
(92° -52°)/2 = 40°/2 = 20°
∠ETR = 20°
Use the y-intercept formula: y=mx+b
Plug in one of the points for x and y
Using that, solve for either x or y
To solve the average rate of change, use the formula of the slope:
m = ( y2 - y1 ) / ( x2 - x1 )
but first we must solve the value of the function when x = 3
f(3) = - log ( 4 * 3 ) + 5
f (3) = 3.92
solve the function when x = 8
f(8) = - log ( 4 * 8) + 5
f(8) = 3.49
so the average rate of change
m = ( 3.49 - 3.92 ) / ( 8 - 3)
m = - 0.09