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leonid [27]
2 years ago
9

In triangle XYZ, XY = 13, YZ=20, and XZ=25. What is the measure of angle Z to the nearest degree?

Mathematics
1 answer:
anastassius [24]2 years ago
4 0
We can use Law of Cosines to solve for the angle of Z. The solution is shown below:
cos C=(a²+b²-c²)/2ab
cos Z = (yz² + xz² - xy² )/2*yz*xz
cos Z = (20² + 25  - 13²)/2*20*25
cos Z = 856 / 1000
Z=31.13°

The answer is angle 31.13°. 
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vlabodo [156]
<span>A freight train completes its journey of 150 miles 1 hour earlier if its original speed is increased by 5 miles/hour. What is the train’s original speed?
***
let x=original speed
x+5=increased speed
travel time=distance/speed
..
lcd:x(x+5)
150(x+5)-150x=x(x+5)
150x+750-150x=x^2+5x
x^2+5x-750=0
(x-25)(x+30)=0
x=25
What is the train’s original speed? 25 mph</span>
7 0
2 years ago
Conor has a roll of fence that is 25 feet long. He needs 8 yards of fence to go around a flower bed. Does he have enough fence t
vlabodo [156]

Answer:

Yes he has enough fence to go round the flower bed.

Step-by-step explanation:

1 yard = 3 feet

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Yes he has enough fence to go round the flower bed.

8 0
2 years ago
Suppose a1=12−12,a2=23−13,a3=34−14,a4=45−15,a5=56−16. a) Find an explicit formula for an: . b) Determine whether the sequence is
lorasvet [3.4K]

I'm going to assume you meant to write fractions (because if a_n are all non-negative integers, the series would clearly diverge), so that

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and so on.

a. If the pattern continues as above, we would have the general term

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b. Note that we can write a_n as

a_n=\dfrac{n-1}{n+1}=\dfrac{n+1-2}{n+1}=1-\dfrac2{n+1}

The series diverges by comparison to the divergent series

\displaystyle\sum_{n=1}^\infty\frac1n

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2 years ago
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2 years ago
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-4x = -5x - 9
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