Answer:
39
Step-by-step explanation:
The short answer is 39.
Every triangle has 180 degrees. There are no exceptions to this rule.
Since a triangle has 3 angles, all three together must add up to 180o
A right angle = 90 degrees always.
You are given 51 degrees as your second angle
The third one is x
x + 51 + 90 = 180 Total of three angles must be 180
x + 141 = 180 The left has been added to give 141
x = 180 - 141 Subtract 141 from both sides
x = 39 The third angle = 39
The red arrows show that the lines are parallel, but using the stuff given you can make an equation.
its hard to explain without drawing but starting from the 60 if you can make a Z you will get alternate angles and that mean that the given equation MUST be equal to 60. So,
8x-4=60
8x=60+4
8x=64
x=64/8
x=8 (is your answer)
hope you understand
Answer:
(a) 
(b) Domain: 
<em>(See attachment for graph)</em>
(c) 
Step-by-step explanation:
Given
Solving (a): A function; l in terms of w
All we need to do is make l the subject in
Divide through by 2
Subtract w from both sides
Reorder
Solving (b): The graph
In (a), we have:
Since l and w are the dimensions of the fence, they can't be less than 1
So, the domain of the function can be
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To check this
When 
When 
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<em>See attachment for graph</em>
<em></em>
Solving (c): Write l as a function 
In (a), we have:
Writing l as a function, we have:
Substitute for l in
becomes
In a full rotation, 360°, a point on the edge of a gear would travel a distance equal to its circumference. The circumference of a circle is:
C=2πr, and since we are only traveling 150°, we need to set up an appropriate ratio for circumference to the distance the point travels:
d/C=150/360
d=5C/12 and since C=2πr
d=10πr/12
d=5πr/12, and since r=4in
d=5*4π/12 in
d=20π/12 in
d=5π/3 in
d≈5.24 in (to nearest hundredth of an inch)
Answer:
Fastest to slowest = 6.08 > 6.4 > 6.72 > 6.75 > 7.03
Step-by-step explanation:
The person who completes the 50-meter race within the shortest possible time is the fastest sprinter. Here, the third sprinter crossed the line in 6.08 seconds, whereas the 4th sprinter crossed the line in 7.03 seconds. That is why the third sprinter has won the race, and he becomes the fastest. On the contrary, the fourth person takes the most time to complete the race, meaning he is the slowest.
