To find the unit rate, divide total miles by number of gallons:
418 miles / 16 gallons = 26.125 miles per gallon
Round the answer as needed.
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:

Step-by-step explanation:
Given



Required
The locus of P

Express as fraction

Cross multiply

Calculate AP and BP using the following distance formula:

So, we have:


Take square of both sides
![4 * [(x +1)^2 + (y +2)^2] = (x - 2)^2 + (y - 4)^2](https://tex.z-dn.net/?f=4%20%2A%20%5B%28x%20%2B1%29%5E2%20%2B%20%28y%20%2B2%29%5E2%5D%20%3D%20%28x%20-%202%29%5E2%20%2B%20%28y%20-%204%29%5E2)
Evaluate all squares
![4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%201%20%2B%20y%5E2%20%2B4y%20%2B%204%5D%20%3D%20x%5E2%20-%204x%20%2B%204%20%2B%20y%5E2%20-%208y%20%2B%2016)
Collect and evaluate like terms
![4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20](https://tex.z-dn.net/?f=4%20%2A%20%5Bx%5E2%20%2B%202x%20%2B%20y%5E2%20%2B4y%20%2B%205%5D%20%3D%20x%5E2%20-%204x%20%2B%20y%5E2%20-%208y%20%2B%2020)
Open brackets

Collect like terms


Divide through by 3

The segment length is 14 (square root)2
Given that Triangle ABC is right angle triangle
The vertex marked is B where side AC is the hypotenuse
The side of AC is at Vertex B is 14
The dash segment from vertex B to point D on side AC
Angle BDA is marked right angle .
Angles A and C both marked 45 degrees.
As shown in diagram
Triangle ABC is drawn according to the statement where B is vertex
The side lengths are 14
Now to find Another side length that is x
So , the equation formed is
x*cos45 = 14
x/√2 = 14
x = 14√2
Hence the length of the segment is 14√2
Learn more about Right angle triangle here brainly.com/question/64787
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30,384 feet difference between the two, since the climber is 29,035 feet above sea level you take a positive 29,035 and a -1,349 due to being below sea level, you add the two together with the equation 29,035+1349=30,384 feet