Please help with algebra problems?

Question

1) Solve: 8/20 = m/250

2) If g(x) = -7x + 2, find g(-6)

3) Simplify: 48b^6 / 12b^2

4) Find (-8x^2y^3 - 3xy^2) + (5x^2y^3 - xy^2)

Answer 1

1) Solve: 8/20 = m/250

8/20 = m/250
==> cross multiply
20m = 2000
==> divide by 20
m = 100 ... ANSWER
_____________________

2 ) If g(x) = -7x + 2, find g(-6).

Just plug in -6 for x and evaluate:

f(-6) = -7(-6) + 2 = 42 + 2 = 44 ... ANSWER
_____________________

3) Simplify: 48b^6 / 12b^2

Divide 48 by 12 to get 4 as the coefficient. When dividing expoents, the subtract. The rule is: x^m / x^n = x^(m-n), so we have b^6 / b^2 = b(6-2) = b^2. So, we get:

4b^4 .... ANSWER
_____________________

4) Find (-8x^2y^3 - 3xy^2) + (5x^2y^3 - xy^2)

Just combine like terms:

(-8x^2y^3 + 5x^2y^3) + (-3xy^2 - xy^2)
==> just add the coefficients of the like terms
-3x^2y^3 - 4xy^2... ANSWER

(Based on your questions, I'm guessing you're not too familiar with factoring. If you are, you could factor that expression into -xy^2(3xy - 4), but the answer I highlighted is probably what you're looking for.)

Answer 2

1) Cross multiply. 8*250 = 20m, which is a simple algebra problem.

2) Just replace the x in (-7x + 2) with a (-6) and evaluate. It's (-7)(-6) + 2, which is simple arithmatic.

3) You can divide the numerator and denominator by a common factor of 12, which leaves 4 in the numerator and 1 in the denominator (which normally wouldn't be written). Then perform division on the two exponents. Remember, b^x / b^y = b^(x - y).

4) Combine like terms. One way to do this is to rewrite the expression by using the distributive property in reverse. You get (-8 + 5)x^2y^3 + (-3 - 1)xy^2, which you can simplify further by performing the addition to get the coefficients.

Answer 3

1. 8/20 = m/250

8*250/20 = m

m = 100

2. If g(x) = -7x + 2 find g(-6)

substitute g(-6) into equation

-6 = -7(-6) + 2

=44

3. 48b^6/12b^2

48/12 = 4

b^6/b^2 = b^4

= 4b^4

4. -3x^2y^3 - 2xy^2

My algebra is a little rusty but I think theyre right

Answer 4

I don't want to just give answers... here's how you solve #1

1. 8/20 = m/250

cross multiply = 8*250 = 20*m
2000=20m
divide both sides by 20
m = 100
plug in your answer to verify answer = 8/20=100/250
.4 = .4

2. For #2, I must be reading the problem differently than others. I read if g is -6, then solve for x. In that case:
(-6)x = -7x + 2
add 7x to both sides to get x by itself
x = 2

If it is saying x is -6, then -7*-6 +2 = 44

Answer 5

1) m = (250*8)/20 =100
2) g(-6) = (-7)*(-6) + 2 = 42+2 = 44
3) 4b^4
4) -3x^2y^3 - 4xy^2

Practice dude.

Answer 6

1.)m = 100
2.)44
3.)4b^4
4.)-3x^2y^3 - 4xy^2

Answer 7

*nods* JP's answers are right to me.

Answer 8

20m=2000
m=2000/20=100
-----------------------------
g(-60=-7*-6+2=42+2=44
------------------------------
4b^4
------------------------
-3x^2y^3-4xy^2