Need help with math problem.?

Question

1.Write the EQUATION of the line in slope-intercept form given the slope 7/3 and a point (6,8)

2.Suppose the total price for a television, including 6.5% tax, was $403.64. How much tax was paid?

3.You have a total of $4500 invested in two accounts. One account pays 5% per year; the other pays 6% per year. If you earn a total of $250 this year, how much was invested in each account?

4.x^2 - 18x + 81 factors into (^ means to the power of)

5.Factor by grouping: 15ab + 25a + 27b + 45 factors into

Answer 1

y=mx+b
y=7/3x+b
8=(7/3)6 +b
8=14+b
-6=b
y=7/3x-6


x= cost of Tv
1.065x=403.64
x= 403.64/1.065=$379.00
Tax = 403.64-379=$24.64

x=amount invested at 5%
4500-x = amount invested at 6%
.05 x+.06(4500-x) = 250
.05x+ 270-.06 x=250
-.01x=-20
x= $2,000 invested at 5%
4500-2000= $2500 invested at 6%

4x^2-18x +81
This quadratic equation does not have real roots.
Its 2 imaginary roots are 9/4(1+sqrt3*i) and 9/4(1-sqrt3 i)
the factors are:
{x-9/4(1+sqrt3 i){x-9/4(sqrt3 i}

15ab +25a +27b +45 =
5a(3b+5) +9(3b+5) =
(5a+9)(3b+5)

Answer 2

y-8=(7/3)(x-6)
3(y-8)=7(x-6)
3y-24=7x-42
7x-3y-18=0

2.x*1.065=403.64
x=403.64/1.065
=379
tax paid=403.64-379
=24.64

3.let the investment atb 5% be x
x*0.05+(4500-x)*0.06=250
5x+27000-6x=25000
-x=-200
so $2000 invested @5% and $2500
invested @6%

4.x^2-18x+81
=x^2-2*x*9+(9)^2
=(x-9)^2

5.15ab+25a+27b+45
=5a(3b+5)+9(3b+5)
=(3b+5)(5a+9)

Answer 3

4.) (x-9)(x-9), x=9

Answer 4

2. $24.64