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sweet-ann [11.9K]
2 years ago
9

Rachel jogged along a trail that was 1/4 of a mile long. She jogged along the trail 8 times. How many miles did Rachel jog?

Mathematics
2 answers:
andre [41]2 years ago
8 0
1/4 multiplied by 8.....
Aliun [14]2 years ago
7 0
The answer would be 8 miles. She jogged 2 miles.
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Becky is using the expression 2z + 3 to represent the number of chairs in her classroom. There are twice as many chairs as table
Sergio039 [100]
It represents the number of tables
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2 years ago
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An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false
asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1) 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 p(\lambda)=\det(B-\lambda I). 0 is a root of p, so we have that p(0)=\det(B-0 I)=\det B=0.

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.      

8 0
3 years ago
Find the square: (5x - 4y)2 <br><br> (and please put the process of solving the equation)
satela [25.4K]
(5x-4y)^2
(5x-4y)(5x-4y)

Multiply each term in one bracket in turn by the terms in the other bracket

(5x)(5x) = 25x^2
(5x)(-4y)=-20xy
(-4y)(5x)=-20xy
(-4y)(-4y)=16y^2

Put them together we have
25x^2-20xy-20xy-16y^2
25x^2-40xy-16y^2
7 0
3 years ago
How many different committees of 4 people can be chosen from a group of 21?
sdas [7]

Answer:

There are 21 ways to choose the first person, 20 ways to choose the second, 19 ways for the third and 18 ways for the fourth so the answer is 21 * 20 * 19 * 18 = 143640.

4 0
3 years ago
Brad has 10 lb of oranges to make 12 bowls of fruit salad. His recipe requires 12 oz of oranges for each bowl. Does Brad have en
Illusion [34]

Answer: Yes, Brad has enough oranges.

Step-by-step explanation:

Given :

The orange required for one bowl = 12 oz

Thus orange required for 12 bowls = \frac{12}{1}\times 12=144oz

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(1lb=16oz)

As organges required is less than oranges available with Brad, thus Brad has enough oranges.

7 0
3 years ago
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