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Advocard [28]
3 years ago
8

Find the m ∠CVU. Show your work

Mathematics
2 answers:
sergey [27]3 years ago
8 0

An outside angle is equal to the sum of the two opposite inside angles:

3x = 63 + x + 13

Simplify:

3x = x + 76

Subtract 1x from both sides:

2x = 76

Divide both sides by 2:

x = 76/2 = 38

Now replace x with 38 and solve for CVU:

CVU = 3x

CVU = 3(38)

CVU = 114 degrees.

lbvjy [14]3 years ago
4 0

Through exterior angle theorem we now that...

x+13+63=3x

2x=76

x=38

m<CVU=3x=114 degrees

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Let x be the distance traveled on the highway and y the distance traveled in the city, so:
\left \{ {{x+y=375} \atop { \frac{1}{65}x+ \frac{1}{25}y =7}} \right.
 
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\left[\begin{array}{ccc}1&1&\\ \frac{1}{65} & \frac{1}{25} &\end{array}\right]   \left[\begin{array}{ccc}x&\\y&\end{array}\right] =  \left[\begin{array}{ccc}375&\\7&\end{array}\right]

Next, we are going to find the determinant:
D=  \left[\begin{array}{ccc}1&1\\ \frac{1}{65} & \frac{1}{25} \end{array}\right] =(1)( \frac{1}{25}) - (1)( \frac{1}{65} )= \frac{8}{325}
Next, we are going to find the determinant of x:
D_{x} =  \left[\begin{array}{ccc}375&1\\7& \frac{1}{25} \end{array}\right] = (375)( \frac{1}{25} )-(1)(7)=8

Now, we can find x:
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Remember that time equals distance over velocity; therefore, the time on the highway will be:
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We can conclude that the bus was five hours on the highway and two hours in the city. 

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