Algebra Questions.?

Question

I have several math problems that have been troubling me. I have answers for some but Im 100% sure that they are wrong. I've tried tutors but they had trouble with them and their answers were so complex I dont trust them. Any help would be appriciated. ^ = Exponent.

1) Factor y^2 + 8y + 16 - 169t^2

2) Multiply (x^2 + x - 1)(-x^3 + x^2 + 1)

3) The product of the reciprocals of two consecutive integers is 1/90. Find the integers.

4) __6__ - __2__
x^3 - 125 - x^2 - 25

5) One summer, Oscar mowed 4 lawns for every 5 lawns mowed by Luis. Together they mowed 144 lawns. How many did each mow?

6)David can paint a bedroom in 1.75 hr. Jay can paint the same room in 2.5 hr. How long will it take them, working together, to paint the bedroom?

7) Solve 9x^2 + 3x = 0

8) Solve 3x^3 + 4x = -8x^2

9)Left f(x) = 3x2 - 21x + 286. Find a such that f(a) = 286.

10) Find the domain of the function f given by f(x) =
__8-x__
x^2 + 6

Answer 1

1. Looks like you have there:
(y+4)²- (13t)²

Factors to [(y+4)+13t][(y+4)-13t]

2. (a+b+c)(whatever)=a(whatever)+b(whatever)+c(whatever)
3. 1/90 = 1/9 * 1/10 which are reciprocals of 9 and 10
4. find the LCD, multiply to make both fractions over the LCD, subtract the numerators.
5. L=1.25O L+O = 144. 2.25O=144. Divide, then replace to find L
6. 1/[1/a+1/b]
7. 3x(3x+1)=0
8. x(3x²+8x+4)=0
9. a=0. Please tell me you considered sticking in zero. Right?
10. the domain (for real numbers) must be such that x²+6 never equals zero. Fortunately no real number will give this, so the domain is all real numbers.

Answer 2

1.(y+4)^2-(13t)^2
2. -1x^5+2x^3+x-1
3.(1/a)*(1/b)=1/90

thus a*b=90, therefore a =9, b=10

4.Don't understand this questions due to the underscores

5. Say Oscar mowed x lawns, Luis mowed 5/4 times x or 1.25x. Combined x + 1.25 x =144
Solve for x, you get x=64 for Oscar, Luis did 80.
6.(1 room/1.75 hours) is David's rate. (1 room/2.5 hours) is Jay's rate. Combined you get (1/1.75)*t + (1/2.5)*t = 1 bedroom. Solve for t, you get 35/34 = 1.03 hours

7. 9x+3=0
9x= -3
x= -1/3
8. 3x^2+4 = -8x
3x^2 + 8x + 4 = 0
(3x + 2)(x + 2) = 0

Thus, x = -2 or -2/3
9. 3x^2 - 21x = 0
3x - 21 = 0
x = 21/3 or 7

10. Your underscores are confusing. Please rewrite the problem.

Answer 3

1) (y-4-13t))(y-4+13t)
2) -x^5-+2x^3+x-1
3) 9, 10
4) 6/(x^3-125)-2/(x^2-25)= [(6x^2-150)-(2x^3-250)]/ [(x^3-125)(x^2-25)] = (-2x^3+6x^2+100)/ [(x^3-125)(x^2-25)]

-2x^3+6x^2+100
= -----------------------------
(x^3-125)(x^2-25)

5) O=4/5L, O+L=144=9/5L, L=80, O=64
6) D=(1/1.75)t=(4/7)t, J=(1/2.5)t=(2/5)t, D+J=(4/7+2/5)t=(34/35)t=1 thus t=35/34 hrs.
7)3x(3x+1)=0 ==> x=0 or -1/3
8) x(3x^2+8x+4)=0 x=0, -2, or -2/3
9) f(a)=3a^2-21a+286=286 ==>> 3a(a-7)=0 ==>> a=0 or 7
10) x^2+6≥6>0 ==>> domain is all real numbers.

Answer 4

2. (x^2+x-1)(-x^3+x^2+1)
= -x^5+x^4+x^2-x^4+x^3+x+x^3-x^2-1
= -x^5+2x^3+x-1 --use this
=-x(x^4-2x^2-1)-1 or most simply form


exponents are added when multiply ... some are cancel out
I think thats the way

**Teya**

Answer 5

I'm going to guess saying that I haven't done this stuff in years, but was interested to do one of your problems, because I used to love algebra.

2) -x^6+x^2-1

but that's just a guess

Answer 6

The answer is Q.