If the measure of angle AOB = 2x + 4 and the measure of angle COD = 4x - 10, write an equation for solve for x
2 answers:
Answer:
Step-by-step explanation:
We know that ∠AOB is (2x+4) and ∠COD is (4x-10).
Note that ∠AOB and ∠COD both have one arc mark.
In other words, they are congruent. Therefore, their angle measures are the same.
So, we can set the two equations equal to each other:
Now, we can solve for x. Let's add 10 to both sides. This yields:
Now, let's subtract 2x from both sides. This yields:
Finally, divide both sides by 2. Therefore, the value of x is:
And we're done!
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Answer:
Speed of Current = 5 miles per hour
Step-by-step explanation:
We know distance formula,
D = RT
Where
D is distance
R is rate
T is time
If we let speed of boat (assume) to be "x" and speed of current to be "c"
Then downstream rate is (with current) = x + c
Upstream rate is (against current) = x - c
40 mins to go 20 miles downstream, that means:
D = RT
20 = (x + c)(40)
and
60 minutes to go upstream, 20 miles, that means:
D = RT
20 = (x - c)(60)
Simplifying first equation:
40x + 40c = 20
Simplifying second equation:
60x - 60c = 20
Multiplying first equation by 60, we get:
60 * [40x + 40c = 20] = 2400x + 2400c = 1200
Multiplying second equation by 40, we get:
40 * [60x - 60c = 20] = 2400x - 2400c = 800
Now we add up both these equations:
2400x + 2400c = 1200
2400x - 2400c = 800
----------------------------------
4800x = 2000
x = 2000/4800 = 5/12
We need speed of current, that is "c", so we plug in the value of x into first equation and solve for c:
Speed of Current = 1/12 miles per minute
Since there is 60 minutes in an hours, that would be:
(1/12) * 60 = 5 miles per hour
Speed of Current = 5 miles per hour