Answer:
Range tells you how high and low the graph of this parabola goes in the “y” (vertical) directions.
1. We can see that the parabola peaks on the y-axis at y = 4. That’s as HIGH as it goes.
2. We also see that both sides of the parabola descend to the level of y = -7. That’s as LOW as it is shown to go.
So putting these together, we say the Range is given by:
-7 <= y <= 3
AMBIGUITY WARNING:
Because the two branches of the parabola go fall right down to the edge of the picture boundary, it’s UNCLEAR whether the parabola truly stops at y = -7 or CONTINUES on (to negative infinity).
In THAT case, the RANGE simplifies to:
Y <= 4
Done.
Step-by-step explanation:
First, you expand it.
2x - 6x + 3 = 3 - 4x
Now, simplify.
-4x + 3 = - 4x
Cancel out the double "4x"
3 = 3
Since both side have an equal answer, there in an infinite number of answers.
Hope this helps! ☺♥
Answer:
Only d) is false.
Step-by-step explanation:
Let 
be the characteristic polynomial of B.
a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)
b) Remember that 
. 0 is a root of p, so we have that 
.
c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.
d) det(B)=0 by part c) so B is not invertible.
e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.
Answer:
Graph C with the green dots.
Step-by-step explanation:
y = 0.5x + 5 is a linear equation, so we can rule out A because it is not straight.
5 represents the y-intercept, so we rule out B because that graph doesn't intercept the y-axis at (0,5).
Graph C represents a straight line that passes through (0, 5) & has a 0.5 slope, so that is our answer.
Hope this helps. :0)
