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
rodikova [14]
3 years ago
13

Round to the nearest hundreth

Mathematics
1 answer:
n200080 [17]3 years ago
3 0

Answer:

∠ B ≈ 66.42°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos B = \frac{adjacent}{hypotenuse} = \frac{BC}{AB} = \frac{2}{5}, thus

B = cos^{-1}(\frac{2}{5} ) ≈ 66.42° ( to the nearest hundredth )

You might be interested in
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
R is in the middle of pqs btw
Vlad [161]

Answer:

46

Step-by-step explanation:

5x = 3x - 2 + 34

5x = 3x + 32

2x = 32

x = 16

plug back in

3( 16 ) - 2

48 - 2

46

5 0
3 years ago
The sum of two numbers is 6565. the larger number is fivefive more than threethree times the smaller number. find the two number
Nimfa-mama [501]
~You would set up the equation x+(3x+5)=6565
~Combine like products so 3x+x=4x.
~Now you have 4x+5=6565.
~Isolate the variable by subracting the 5 from both sides, so you have 4x=6560.
~Since you multiply x by 4, divide both sides by 4, and 6560 divided by 4 is 1,640.
*The first number is 1,640.
~Now to find the second number you simply plug in 1,640 to (3x+5), with 1,640 being x.
~That would become [3(1,640)+5].
~3 times 1, 640 is 4,920, and add the 5 so you get 4,925.
*The second and larger number is 4,925.
If you wanna check just add the two numbers, and you get 6565.

3 0
3 years ago
Please please please answer quick! I need an accurate answer
Jet001 [13]

Answer:

c

Step-by-step explanation:

the opposite of division is multiplication

8 0
2 years ago
Read 2 more answers
PLEASE QUICK HELP!!!
Fantom [35]

Answer:

4.5 / B

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
Other questions:
  • Give two ordered pairs from the graph that will support the idea that the graph is not a function. Explain how your ordered pair
    15·1 answer
  • Which two number add up to 6 and multiply to 12
    11·1 answer
  • What is the value of the figure 8 in 1,083,096
    5·1 answer
  • Based on the graph how many real number solutions to the equation X^3+6x^2+12x+8=0have
    10·1 answer
  • 1b. 80 foot-long rope is cut into 3 pieces.
    6·1 answer
  • Given the side lengths, determine whether the triangle is acute, right, obtuse, or not a triangle for 12,13,14,16
    8·1 answer
  • 3/4 empress fraction as decimal
    6·1 answer
  • Solve for x'if3 - 2x 35-*.​
    6·1 answer
  • In a trivia contest, players form teams and work together to earn as many points as possible for their team. Each team can have
    9·1 answer
  • Slope of (1,-4) and (0,-5)
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!