Help ASAP Please! Studying for finals and I'm stuck on this question!

Mathematics

1 answer:

Nezavi [6.7K]3 years ago

8 0

First I am going to assume that these are both right triangles based off of look and because it is much easier. Without it you have to use law of sines or law of cosines...
So to find x you must first find y which can be done simply by using the pythagorean theorem. This theorem is defined as the sum of the squared legs is equal to the sum of the hypotenuse or x^2 + y^2 = z^2

If we substitute in the known values 16^2 + y^2 = 20^2 and solve for y we get that y = sqrt(20^2 - 16^2), this then simplifies to y = 12

Finding x is much more annoying, the easiest way I can immediately see is to find the upper angles by doing sin(16/20) and then 90 - sin(16/20) since the complementary angle is the one you want. I don't have a calculator or a trig table with me right now but I will tell you that x will be equal to 12 ÷ the inverse cosine of the angle (90degrees - sin(16/20)).

I am pretty sure the answer is D though because we know for sure y = 12 and x has to be greater than y because the hypotenuse must be larger than both legs. It could be E but you won't know unless you do the math for x. So it is either D or E but I would be surprised if a Professor made you do all of the work just to say it doesn't work...

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Mr Smith's art class took a bus trip to an art museum. The bus averaged 65 miles per hour on the highway and 25 miles per hour i

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Let x be the distance traveled on the highway and y the distance traveled in the city, so:
$\left \{ {{x+y=375} \atop { \frac{1}{65}x+ \frac{1}{25}y =7}} \right.$

Now, the system of equations in matrix form will be:
$\left[\begin{array}{ccc}1&1&\\ \frac{1}{65} & \frac{1}{25} &\end{array}\right] \left[\begin{array}{ccc}x&\\y&\end{array}\right] = \left[\begin{array}{ccc}375&\\7&\end{array}\right]$

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:
$x= \frac{ D_{x} }{D} = \frac{8}{ \frac{8}{325} } =325mi$

Now that we know the value of x, we can find y:
$y=375-325=50mi$

Remember that time equals distance over velocity; therefore, the time on the highway will be:
$t_{h} = \frac{325}{65} =5hours$
An the time on the city will be:
$t_{c} = \frac{50}{25} =2hours$

We can conclude that the bus was five hours on the highway and two hours in the city.

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answer A is correct because the formula of equation in point slope is

y-y1=m(x-x1)

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