Answer:
The solution proves that the equation has a non-trivial solution.
Step-by-step explanation:
We want to show that the equation has nontrivial solutions for which 
Let 
be a set of non-zero numbers such that that 
Because T is a linear solution:
= 
= 
= 
= 
= 0
This shows that 
are linearly independent with the mapping resulting in a non-trivial solution.
The pencil costs $0.25.
One way to deduce this is to divide 1.50 by 2 (equaling 0.75) and then subtracting .5 to get 0.25 because if it's $1 more, then the ruler would cost 0.75 + 0.5 and the pencil would cost 0.75 - 0.5, making a total of $1.50.
Another way is to make it an equation. Let's say the ruler is r dollars and the pencil is p dollars.
r + p = 1.50
r = p + 1.00
If we know these two equations, then you can substitute p + 1.00 in the 1st equation (instead of r). This gets us:
p + 1.00 + p = 1.50
You can simplify this into:
2p + 1.00 = 1.50
Then you subtract 1.00 from both sides:
2p = 0.50
And you divide 2 from both sides:
p = 0.25
Getting you the answer of:
The pencil costs $0.25
Hope this helps! :)
Answer:
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Step-by-step explanation:
<u>Triangle Solving</u>
If we had a triangle will its three sides of known length, we can solve for the rest of the parameters of the triangle, i.e. the area, perimeter and internal angles.
The three circles have diameters 900 m, 700 m and 600 m and are tangent to each other externally. The distances from their centers (where houses are located) are the sum of each pair of the radius of the circles. Thus, the sides of the triangle are
The internal angles can be computed by using the cosine's law
Where \alpha, \beta and \gamma are the opposite angles to x, y and z respectively. Solving for each one of them:
Similarly
The other angle is computed now
The area can be found by
Answer:
The correct answer is Never
