Summer study packet for Trigonometry help?

Question

I have school starting on monday and we received a packet for summer studying if we felt neccessary a few days ago at my schools open house. Only problem is, I forgot a lot of the stuff I learned in Geometry and Algebra 2. I get good grades so I'd hate to go in there all confused. I was able to do some of the problems but not all. Here are some sample problems I need to learn how to do...

Solve the following for x:

1.) -17/8x - 4/3 = 1

2.) 51/2x - 23/3x = 6



Solve each system of equations for x and y:

1.) { 4x-3y = -6
{ x+2y = -7

2.) { 19=5x+2y
{ 1=3x-4y


Compute the products:

1.) (3x² - 2a²)²

2.) [(a+b)-4] [(a+b)+4]


Factor the following:

1.) ab-bc+a²-ac

2.) 3x² - 22x - 16



Those are just some random problems I'm having trouble with.

This is not homework, it is only a summer study packet that should get me ready for class on monday.

Answer 1

Solve for x
Problem 1
-17/8x - 4/3 =1
adding 4/3 on both sides
-17/8x - 4/3 + 4/3 = 1 +4/3
-17/8x = 7/3
crossmultiply
56x = -51
x = -51/56

Problem 2
51/2x - 23/3x =6
multiplying botrh sides by 6x
51(6x)/2x - 23(6x)/3x = 6(6x)
51(3) - 23(2) = 36x
(153 -46) = 36x
107 = 36x
divide both sides by 36
x = 107/36
Solve x and y
Problem 1
4x - 3y =-6 ---------------eqn (1)
x + 2y = -7 ---------------eqn (2)
multiply eqn(2) by - 4
-4x -8y = 28 ------------eqn (3)
adding eqn (1) and eqn (3)
--11y = 22
y = - 22/11 = -2
substituting this in eqn (2)
x +2(-2) = -7
x - 4 = -7
x = -7 + 4 = -3

Problem 2
5x + 2y = 19 ------------- eqn (1)
3x - 4y =1 ------------- eqn (2)
multiplying eqn (1) by 2
10x + 4y = 38 ------- eqn (3)
adding eqn (2) and (3)
13x = 39
x = 39/13 = 3
substituting x value in eqn (2)
3(3) - 4y = 1
9 -4y =1
-4y = -8
y =8/4 =2
Compute the products
Problem 1
(3x^2 - 2a^2)^2 = 9x^4 - 12x^2 a^2 + 4a^4
Problem 2
[(a +b) - 4][(a +b) + 4]

using the formula (x + y)(x -y) = x^2 - y^2 , the given expression is

[(a +b)^2 - (4)^2] = a^2 + b^2 +2ab - 16

Factorize
Problem 1
ab - bc + a^2 - ac
rearranging
a^2 + ab - (ac +bc)
a(a + b) - c(a +b)
(a+b)(a -c)

Problem 2
3x^2 - 22x -16
3x^2 - 24x + 2x -16
3x(x -8) + 2(x -8)
(3x +2)(x -8)

Answer 2

In your second problem, if you mean (51/2)*x - (23/3)*x = 6:
(51/2 - 23/3)*x = ((51*3 - 23*2)/6) = (107/6)*x = 6, so
x = (6/107)*6 = 36/107.
But if the problem is 51/(2x) - 23/(3x) = 6, then first multiply both sides by 6x to get 51*3 - 23*2 = 6*(6x) or
107 = 36x, so x = 107/36.

To solve the system 4x - 3y = -6 and x + 2y = -7: from the second equation, we find x = -2y - 7. Putting this into the first equation, we find 4*(-2y - 7) - 3y = -6, or -8y - 28 -3y = -6, so
-11y = 22, and y = -2. Then x = -2 y - 7 = -2*(-2) - 7 = -3. You should check to see that this is the solution.

To factor ab - bc + a^2 - ac, we notice that this is
b*(a - c) + a*(a - c) = (b + a)*(a - c).

You seem pretty rusty. You should get yourself an Algebra 1 text and brush up.

Answer 3

web site 4. 8a) 3(x + 4) - 2(3x - 5) + 4x - a million = 4(2x - a million) - (2x + 5) before everything, improve your brackets: 3x + 12 - 6x + 10 + 4x - a million = 8x - 4 - 2x - 5 Now convey at the same time like words (x with different x's, numbers with different numbers) x +21 = 6x - 9 Take x to a minimum of one area 30 = 5x Divide 30 via 5 x = 6 web site 6. 13a) sin40 = opposite / hypotenuse = x / 10 Rearrange the equation for x (convey 10 up) x = 10sin40 Now, placed it into your calculator x = 6.40 3 b) comparable thought, different than cos40 = x / 10 (cos40 = adjoining / hypotenuse) attempt working the rest out your self :)