Explanation:
Since {v1,...,vp} is linearly dependent, there exist scalars a1,...,ap, with not all of them being 0 such that a1v1+a2v2+...+apvp = 0. Using the linearity of T we have that
a1*T(v1)+a2*T(v1) + ... + ap*T(vp) = T(a1v19+T(a2v2)+...+T(avp) = T(a1v1+a2v2+...+apvp) = T(0) = 0.
Since at least one ai is different from 0, we obtain a non trivial linear combination that eliminates T(v1) , ..., T(vp). That proves that {T(v1) , ..., T(vp)} is a linearly dependent set of W.
The height of the isosceles triangle is 8.49 inches.
<h3>
How to find the height of the triangle?</h3>
Here we have a triangle such that two of the sides measure 9 inches, and the base measures 6 inches.
So this is an isosceles triangle.
We can divide the isosceles triangle into two smaller right triangles, such that the side that measures 9 inches is the hypotenuse, the base is 3 inches, and the height of the isosceles triangle is the other cathetus.
By Pythagorean's theorem, we can write:
(9in)^2 = (3 in)^2 + h^2
Where h is the height that we are trying to find.
Solving that for h we get:
h = √( (9 in)^2 - (3in)^2) = 8.49 inches.
We conclude that the height of the isosceles triangle is 8.49 inches.
If you want to learn more about triangles:
brainly.com/question/2217700
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Answer:
x ≈ 15.9
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
x² + 6² = 17²
x² + 36 = 289 ( subtract 36 from both sides )
x² = 253 ( take the square root of both sides )
x =
≈ 15.9 ( to the nearest tenth )
Let
x-----------> first <span>odd integer
x+2--------> second consecutive odd integer
x+4-------> third consecutive odd integer
we know that
(x+4)</span>²=15+x²+(x+2)²-------> x²+8x+16=15+x²+x²+4x+4
x²+8x+16=19+2x²+4x-------> x²-4x+3
x²-4x+3=0
using a graph tool----------> to calculate the quadratic equation
see the attached figure
the solution is
x=1
x=3
the answer is
the first odd integer x is 1
the second consecutive odd integer x+2 is 3
the third consecutive odd integer x+4 is 5