1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
DedPeter [7]
2 years ago
7

For which pair of points can you use this number line to find the distance?

Mathematics
2 answers:
anzhelika [568]2 years ago
8 0
The answer is going to be c
KIM [24]2 years ago
4 0

Answer:

c

Step-by-step explanation:

You might be interested in
a manufacturer uses a mold to make a part in the shape of a triangular prism. The dimensions of this part are shown below. Whic
VMariaS [17]
To estimate the volume of Thai triangular prism you will use the formula for finding the volume.

V=Bh, where B is the area of the base and h is the height of the prism.

V = (1/2 x 12.6 x 1.6) x 10.75
V = 108.36 cubic mm

You answer is approximately 108 cubic millimeters.
8 0
3 years ago
Read 2 more answers
Linear Algebra question! Please help!
kozerog [31]

Answers:

  1. false
  2. false
  3. true
  4. false
  5. True

==================================================

Explanation:

Problem 1

This is false because the A and B should swap places. It should be (AB)^{-1} = B^{-1}A^{-1}.

The short proof is to multiply AB with its inverse (AB)^{-1}  and we get: (AB)*(AB)^{-1} = (AB)*(B^{-1}A^{-1}) = A(B*B^{-1})*A^{-1} = A*A^{-1} = I

The fact we get the identity matrix proves that we have the proper order at this point. The swap happens so that B matches up its corresponding inverse B^{-1} and the two cancel each other out.

Keep in mind matrix multiplication is <u>not</u> commutative. So AB is not the same as BA.

-------------------------

Problem 2

This statement is true if and only if AB = BA

(A+B)^2 = (A+B)(A+B)

(A+B)^2 = A(A+B) + B(A+B)

(A+B)^2 = A^2 + AB + BA + B^2

(A+B)^2 = A^2 + 2AB + B^2 ... only works if AB = BA

However, in most general settings, matrix multiplication is <u>not</u> commutative. The order is important when multiplying most two matrices. Only for special circumstances is when AB = BA going to happen. In general,  AB = BA is false which is why statement two breaks down and is false in general.

-------------------------

Problem 3

This statement is true.

If A and B are invertible, then so is AB.

This is because both A^{-1} and B^{-1} are known to exist (otherwise A and B wouldn't be invertible) and we can use the rule mentioned in problem 1. Make sure to swap the terms of course.

Or you can use a determinant argument to prove the claim

det(A*B) = det(A)*det(B)

Since A and B are invertible, their determinants det(A) and det(B) are nonzero which makes the right hand side nonzero. Therefore det(A*B) is nonzero and AB has an inverse.

So if we have two invertible matrices, then their product is also invertible. This idea can be scaled up to include things like A^4*B^3 being also invertible.

If you wanted, you can carefully go through it like this:

  1. If A and B are invertible, then so is AB
  2. If A and AB are invertible, then so is A*AB = A^2B
  3. If A and A^2B are invertible, then so is A*A^2B = A^3B

and so on until you build up to A^4*B^3. Therefore, we can conclude that A^m*B^n is also invertible. Be careful about the order of multiplying the matrices. Something like A*AB is different from AB*A, the first of which is useful while the second is not.

So this is why statement 3 is true.

-------------------------

Problem 4

This is false. Possibly a quick counter-example is to consider these two matrices

A = \begin{bmatrix}1 & 0\\0 & 1\end{bmatrix} \text{ and } B = \begin{bmatrix}-1 & 0\\0 & -1\end{bmatrix}

both of which are invertible since their determinant is nonzero (recall the determinant of a diagonal matrix is simply the product along the diagonal entries). So it's not too hard to show that the determinant of each is 1, and each matrix shown is invertible.

However, adding those two mentioned matrices gets us the 2x2 zero matrix, which is a matrix of nothing but zeros. Clearly the zero matrix has determinant zero and is therefore not invertible.

There are some cases when A+B may be invertible, but it's not true in general.

-------------------------

Problem 5

This is true because each A pairs up with an A^{-1} to cancel out (similar what happened with problem 1). For more info, check out the concept of diagonalization.

5 0
2 years ago
What is the answer for these questions?
PIT_PIT [208]

Answer:

a.) yes

b.) no

c.) yes

d.) yes

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
What is 1 2/3 multiple 2/3
Flauer [41]

Answer:

1\frac{1}{9}

Step-by-step explanation:

Given the following question:

1\frac{2}{3} \times\frac{2}{3}

In order to multiply the two, we have to convert the mixed number into a improper fraction and then multiply the numerator by the numerator, the denominator by the denominator.

1\frac{2}{3} =3\times1=3+2=\frac{5}{3}
\frac{5}{3} \times\frac{2}{3}
5\times2=10
3\times3=9
=\frac{10}{9}

<u>Convert the improper fraction into a mixed number:</u>

\frac{10}{9}
\frac{10}{9} =10\div9=1\frac{1}{9}
=1\frac{1}{9}

Your answer is "1 1/9."

Hope this helps.

7 0
2 years ago
If a varies directly as b and a=3 when b=12, what is the value of a when b=18?
Zepler [3.9K]

Answer:

a is proportional to b

a=kb

k is proportionality constant

k =a/b =3/12 =1/4

k=1/4 = a/b=a/18

1/4=a/18

a=18/4 =9/2 =4.5 answer

4 0
3 years ago
Other questions:
  • Clara estimates that the length of a hiking trail is 10 km. She later learns that its actual length is 12 km. What is the percen
    10·1 answer
  • Of 70 tosses of a dime, 55 results are heads. Find the empirical probability of tossing heads with this coin. ______ Is this a f
    8·1 answer
  • Write 0.31 Repeating<br> as a fraction in simplest form.
    10·1 answer
  • Last Friday David rented 4 movies from the video store. This Friday he rented 2 movies. Let x represent the cost of renting each
    9·1 answer
  • Describe and correct the error in finding the median of the data 63,55,49,58,50,59,51
    9·2 answers
  • 40 POINTS PLEASE HELP
    14·2 answers
  • Find the surface area of the square pyramid
    9·1 answer
  • Solve for b. 5b + 8 - 2b = 7b. A 2 B.4/5 C.4/7 D.1/2​
    10·2 answers
  • PLEASE ASAP I NEED HELP ON THIS PROBLEM
    7·1 answer
  • A building is acquired on January 1,at a cost of 930,000 with estimated useful life of 8 years and salvage value of 73,700
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!