Your
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Aliyah bought a car for $32,000. It is now worth $5000 less than half of what she purchased it for. To the nearest tenth of a pe
rcent , find the percent decrease in the value of the car.
1 answer:
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Answer:
Step-by-step explanation:
Let . We have that
if and only if we can find scalars
such that
. This can be translated to the following equations:
1.
2.
3.
Which is a system of 3 equations a 2 variables. We can take two of this equations, find the solutions for and check if the third equationd is fulfilled.
Case (2,6,6)
Using equations 1 and 2 we get
whose unique solutions are , but note that for this values, the third equation doesn't hold (3+2 = 5
6). So this vector is not in the generated space of u and v.
Case (-9,-2,5)
Using equations 1 and 2 we get
whose unique solutions are . Note that in this case, the third equation holds, since 3(3)+2(-2)=5. So this vector is in the generated space of u and v.
Answer:
Rounded to the nearest tenth, the length of the missing side is 5.4 in.
Step-by-step explanation:
According to the Pythagorean theorem, , where c is the length of the hypotenuse (the longest side), a and b are the lengths of the other two sides. We can use this to solve for the length of the hypotenuse of the right triangle shown in your question (the missing side):
This simplifies to . Now to solve for c (the length of the hypotenuse), we just take the square root of both sides of the equation and solve like so:
This simplifies to c≈5.4 in.