Which of the following subsets of vectors x y z are subspaces of R 3 ?
1 answer:
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Answer:
1. x = ±9
2.
3. 12 and -12.
4. Antoine is incorrect. There exists two solutions x=5 and x= -5.
Step-by-step explanation:
According to the questions,
Problem 1. i.e.
i.e. x = ±9.
Problem 2. i.e.
i.e.
i.e.
Problem 3. [tex]f(x)=x^{2}-144[tex]
To find the roots, we take, [tex]x^{2}-144=0[tex] i.e. [tex]x^{2}=144[tex] i.e. x = ±12.
Thus, the options are 12 and -12.
Problem 4. We have [tex]f(x)=x^{2}+25[tex]
For the roots, we take, [tex]x^{2}+25=0[tex] i.e. [tex]x^{2}=25[tex] i.e. x = ±5.
Thus, Antoine is not correct and two solutions namely x=5 and x= -5 exists.
Answer:
y = 2
Step-by-step explanation:
Kindly view the attached image to see the rules when looking for the horizontal asymptote.
In this situation we have 2x² / x²
The powers of both are equal to each other therefore the horizontal asymptote will be at the coefficient of the numerator divided by the coefficient of the denominator.
In other words the horizontal asymptote is at y = 2/1 or just 2
Answer:
An isosceles triangle with angles measuring 20° and 80°
Step-by-step explanation:
Verify each case
case A) Scalene triangle with angles measuring 110° and 35°
Is not a scalene triangle because the third angle is (180-110°-35°=35°), therefore is an isosceles triangle
case B) An obtuse triangle with sides measuring 5,10 and 15
we know that
Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so in this problem
-----> is not true
therefore
with these measurements can not draw any triangle
case C) An isosceles triangle with angles measuring 20° and 80°
we know that
An isosceles triangle has two equal sides and two equal angles
In this problem the third angle is (180-20°-80°=80°),
therefore
is an isosceles triangle and can be drawn as it is described
case D) An acute triangle with sides measuring 7,4 and 2
we know that
Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
so in this problem
-----> is not true
therefore
with these measurements can not draw any triangle