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
Dafna1 [17]
3 years ago
7

Justin deposited $54.25 into his bank account after making a $30.00 withdrawl to pay for some school supplies. Represent these s

ituations as signed numbers
a. 45.25, 30.00
b. -45.25, -30.00
c. 45.25, -30.00
d. -45.25, 20.00
Mathematics
1 answer:
Yuri [45]3 years ago
6 0
I believe the answer is c. You had 45.25 so that would be positive then, you withdrew 30 so that would be a negative
You might be interested in
Find the volume of the solid generated when R​ (shaded region) is revolved about the given line. x=6−3sec y​, x=6​, y= π 3​, and
Dmitrij [34]

Answer:

V=9\pi\sqrt{3}

Step-by-step explanation:

In order to solve this problem we must start by graphing the given function and finding the differential area we will use to set our integral up. (See attached picture).

The formula we will use for this problem is the following:

V=\int\limits^b_a {\pi r^{2}} \, dy

where:

r=6-(6-3 sec(y))

r=3 sec(y)

a=0

b=\frac{\pi}{3}

so the volume becomes:

V=\int\limits^\frac{\pi}{3}_0 {\pi (3 sec(y))^{2}} \, dy

This can be simplified to:

V=\int\limits^\frac{\pi}{3}_0 {9\pi sec^{2}(y)} \, dy

and the integral can be rewritten like this:

V=9\pi\int\limits^\frac{\pi}{3}_0 {sec^{2}(y)} \, dy

which is a standard integral so we solve it to:

V=9\pi[tan y]\limits^\frac{\pi}{3}_0

so we get:

V=9\pi[tan \frac{\pi}{3} - tan 0]

which yields:

V=9\pi\sqrt{3}]

6 0
3 years ago
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
I’m about to cry from frustration. Help please before I die
kvv77 [185]

Answer:

\frac{1}{3}x+16=37

63 Jelly Beans

Step-by-step explanation:

The unknown is the number of jelly beans originally in the bag or x

First he had x jelly beans

The he ate one-third of them

\frac{1}{3}x

He then ate 16 more jelly beans

\frac{1}{3}x+16

This was equal to 37 jelly beans

\frac{1}{3}x+16=37

This is the equation

Now solve for x

Subtract 16 from both sides

\frac{1}{3}x=21

Multiply both sides by 3

x=63

63 Jelly Beans

7 0
3 years ago
Read 2 more answers
What is the surface area of a prism that has detentions of: length is 5.5, width is 6, and the hight is 2.4
Alex787 [66]

Answer:

79.2

Step-by-step explanation:

6 0
3 years ago
a pack of toilet paper was originally $4.50 , it now cost $6.75. What is the solution to this problem?
Nitella [24]
2.25 is correct have a good day
5 0
2 years ago
Other questions:
  • Skyler buys 8 T-Shirts and 5 hats for $220. The next day, he buys 5 T-shirts and 1 hat for $112. What is the cost of each T-shir
    15·2 answers
  • 23. Cynthia used some of the ordered pairs from the set below to make a new set.
    7·1 answer
  • What is the unit rate in miles per hour of 8 miles in 45 minutes
    10·1 answer
  • A car is driven on a straight track such that its displacement from the starting point is given as x = t + 2t2. What is the aver
    14·1 answer
  • Helppppppppppppppppppppppppppp
    5·1 answer
  • Help solve this real quick I appreciate it
    9·1 answer
  • 11in 8.1 in 15 in 7 in?
    13·1 answer
  • Find the volume of this.<br> Show work.
    10·1 answer
  • Graph.<br><br> y+4=2/5(x−3)<br> plz help
    14·1 answer
  • 2x+2y=6 3x-y=5 equivalent equation
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!