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I got 1920 @SportzGuy2310 when I expanded it using the binomial theorem.

200                  

In ab⁴, the exponent applies only to the b.  

What you're thinking about would be written (ab)⁴.  

_.

One ordered pair (a,b) satisfies the two equations ab^4 = 48 and ab = 72. What is the value of b in this ordered pair?  

To find b, consider                                                  ab⁴  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab⁴         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab⁴ = (ab) * (b³)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b³           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

_.

so we need a common denominator by the ratios meet the requierments so e make variables b and g for boys and girls so we have g/b=3/2 and (g+7)/(b-2)=5/2 so we can Substitute the b into 2/3 g to get (g+7)/(2/3(g-2))=5/2 or we can simplify it into (((3/2)b)+7)/b-2=5/2 so we have g=18 and b=12 so then we have g+7=25 and b-2=10 then we do 25+10=35 and the number of students are in the class after these changes are 35

Let  3x  be the number of girls 

and 2x  be the number of boys.

Seven more girls join the class:  the number of girls is now  3x + 7

Two boys drop the class:            the number of boys is now  2x - 2.

The ratio of girls to boys is now 5:2     --->     (3x + 7) : (2x - 2)  =  5 : 2

         (3x + 7) / (2x - 2)  =  5 / 2

                  2 · (3x + 7)  =  5 · (2x - 2)

                         6x + 14  =  10x - 10

                                 24  =  4x

                                   6  =  x

Current number of girls:  3x + 7   --->   3(6) + 7  =  25

Current number of boys:  2x - 2   --->   2(6) - 2  =  10

-3/2+1/2=-2/2=-1

The answer is -1!

thx!

Love your answer :-)  

you end up with \(10/cos(63)\)

which is equal to about 22.03(to the nearest hundredth)

The rolls must be 1, 2, 5, 5, 6 in some order, so there are 5!/2 = 60 ways.

There are more ways though. For example, there could be:

1, 3, 4, 5, 5

2, 2, 3, 5, 5

This gives another 90 ways:

1, 3, 4, 5, 5: 5!/2 = 60

2, 3, 3, 5, 5: 5!/4 = 30

If you add it with the previous one, we get 60+60+30 = 150

hepl i catn ad them so wht s the anser

Next time before you cheat on your homework think:

Is this a question I really need someone to do for me so my math grade can stay above a C, or is this trivial enough so that even I can solve it?

We use the Binomial Theorem to expand the given expression. We have:

(2u - 3v + u^2 - v^2)^9 = ∑(k=0 to 9) C(9,k)(2u)^(9-k)(-3v)^k(u^2 - v^2)^(9-k)

To find the coefficient of u^2 v^9, we need to choose k such that (9-k) powers of (u^2 - v^2) multiply out to u^2 and k powers of (-3v) multiply out to v^9. From the first term (2u)^(9-k), we need to choose two powers of u to multiply out to u^2. Therefore, we choose (9-k-2) = (7-k) of the remaining terms to be (u^2 - v^2), and the remaining k terms to be (-3v). This gives us the equation:

2^(9-k) * (-3)^k * C(9,k) * (u^2 - v^2)^(7-k) * (-3v)^k = u^2 v^9 * coefficient

We need to find the value of the coefficient that satisfies this equation. Plugging in u^2 = v^9 = 1, we get:

2^(9-k) * (-3)^k * C(9,k) * (-3)^(k) = coefficient

Simplifying, we get:

coefficient = 2^(9-k) * 3^(2k) * C(9,k)

To find the coefficient of u^2 v^9, we need to find k such that (9-k-2) = (7-k) powers of (u^2 - v^2) multiply out to u^2, and k powers of (-3v) multiply out to v^9. This means that:

7 - k = 2
k = 5

Therefore, the coefficient of u^2 v^9 is:

2^(9-5) * 3^(2*5) * C(9,5) = 2^4 * 3^10 * 126 = 2,176,782,080

Therefore, the coefficient of u^2 v^9 in the expansion of (2u - 3v + u^2 - v^2)^9 is 2,176,782,080.

Solve 3a + 4b = 5a - 6b + 24 - 3a for a in terms of b.  

                                                            3a + 4b  =  5a – 6b + 24 – 3a   

You just add up the like terms.  

                                                            3a + 4b  =  2a – 6b + 24  

And subtract 2a from both sides  

                                                              a + 4b  =  – 6b + 24  

And subtract 4b from both sides  

                                                                      a  =  – 10b + 24  

When you get better at it, you  

can combine simple steps like  

addition/subtraction of terms.  

It's conventional to place the  

positive number ahead of the  

negative number.  

                                                                       a  =  24 – 10b  

.

1. 24 \(units^{2}\) bc it is a 6-8-10 Pythagorean triple (6x8/2)=(48/2)=24

2. The interior angles in a triangle sum to 180, so 135+30=165. The remaining angle

( \(degrees\)

Answers: 

1. 24

2. 15 degrees

Let's write d to represent XY's length. Trigonometry can be used to determine the length of XY since triangle PXY is a right triangle. Specifically, we have

tan(30) = XY / PY

Since PY = PQ - QY and PQ = QR = 9, we have PY = 9 - QY. Therefore:

tan(30) = XY / (9 - QY)

Solving for XY, we get:

XY = (9 - QY) tan(30)

QY needs to be located. The Pythagorean theorem can be used to determine QY because triangle QYX is also a right triangle:

QY² + XY² = QX²

Triangle QRX being a 30-60-90 triangle gives us:

QX = QR / 2 = 4.5

Therefore:

QY² + XY² = 4.5²

QY² + (9 - QY)² tan²(30) = 4.5²

The result of simplifying and solving for QY is:

QY = 2.25

Inputting this value into the XY expression yields the following result:

XY = (9 - 2.25) tan(30) = 2.25 × √(3)

Real numbers a and b satisfy  

a + ab = 250  

a - ab = -240  

Enter all possible values of a, separated by commas.  

If you add the two equations together                a + ab  =   250  

                                                                           a – ab  = –240  

                                                                          ———————  

you get                                                              2a         =  10  

from which                                                                  a  =  5  

The problem doesn't ask for b,  

but ... find b by substituting  

a back into a + ab = 250                                    5 + 5b  =  250  

                                                                                5b  =  245  

                                                                                  b  =  49  

check b by substituting  

a back into a – ab = –240                                  5 – 5b  =  –240  

                                                                              –5b  =  –245  

                                                                                  b  =  49  

There are six permutations that work

1 3 2 5 4

1 5 2 3 4

2 3 1 5 4

2 5 1 3 4

3 5 1 4 2

3 5 2 4 1

There are six permutations that work

1 3 2 5 4

1 5 2 3 4

2 3 1 5 4

2 5 1 3 4

3 5 1 4 2

3 5 2 4 1

Your FINAL ANSWER IS 6(Which are mentioned above)

I==V/R
R==V/I

200 milliamps ==200 / 1000 =0.2 amps.
R==60 / 0.2 ==300 ohms.
300 / 2 ==150 ohms - resistance in 1/2 of original wire.

I ==V/R
I==400 / 150 ==2.67 amps.
2.67 x 1,000 ==2,670 milliamps of current.

Cutting the wire in half will increase the amps by a factor of 2   to   400 ma         (because the resistance is halved)

  increasing the voltage ACROSS the wire will increase the amps by  400 / 60    

     400 / 60  *  400 ma = 2666.7 mAmps