Math 9 help??? Can;t solve these problems!!!

1.)2x(5x/2-2x/5)


2.)Solve for x: 2x+3y=81
3x-6y=-57

3.)Find the length of the diagonal, to the nearest tenth of an inch, of a rectangle piece of paper that measures 8 1/2 by 11 inches.


4.)Given triangle ABC with a right angle C. Side AB=30 and side BC=15. Find the measure of angle A.

1) Well, for the first one, you're going to want to solve what's inside the parentheses first. This means finding the most common denominator (remember that?):
2x (5x/2 - 2x/5)
2x (25x/10 - 4x/10)
2x (21x/10)

Now you can multiply:
2x(21x/10)
42x^2/10
4.2x^2


2) To solve for 'x', all you need to apply is a little substitution:
2x+3y=81
3y=81-2x
y=27-2x/3

With this value for 'y' known, you can plug it into the other equation:
3x-6y=-57
3x-6(27-2x/3)=-57
3x-162+4x=-57
7x=105
x=15


3) For this, you apply the Pythagorean Theorem:
√(8.5^2 + 11^2) = diagonal
√(72.25 + 121) = diagonal
√193.25 = diagonal
13.9 = diagonal


4) For this, you need a calculator able to use the inverse-sine function (or you must be familiar with certain right-triangles):
sin^-1(BC/AB) = A
sin^-1(15/30) = A
sin^-1(.5) = A
30°=A

Alright, alright. Just giving you a hard time, is all...

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1.)2x(5x/2-2x/5)
= 2x(5/2x-2/5x)
= 21/5x^2

2) Standard form: 2x+3y=81; 3x-6y=-57;
substitute/eliminate x = -3/2y+81/2
substitute/eliminate y = +17
Solution: x = 15; y = 17;
or (x, y) = (15, 17)




4.)Given triangle ABC with a right angle C. Side AB=30 and side BC=15. Find the measure of angle A.
SSA: Sine Law: Sin(A)/a = Sin(B)/b
sides: 30, 15, 25.9808
angles: 90°, 30°, 60° is a right scalene triangle
area: 194.8557 perimeter: 70.9808
- - - - - -
∠ A = 30°

1.) Perform the addition in parentheses, then multiply by the factor outside.
.. 2x(x(2.5-0.4)) = 2x(2.1x) = 4.2x^2

2.) Double the first equation and add it to the second.
.. 2(2x+3y) + (3x-6y) = 2(81) + (-57)
.. 7x = 105 ... (collect terms)
.. x = 15 ... (divide by 7)
Substitute this value into the first equation.
.. 2(15) + 3y = 81
.. 30 + 3y = 81
.. 3y = 51
.. y = 17
The solution to the system of equations is (x, y) = (15, 17).

3.) sqrt(8.5^2+11^2) = sqrt(72.25+121) = sqrt(193.25) ≈ 13.9
The diagonal is 13.9 inches.

4.) The Law of Sines is helpful.
.. sin(C)/AB = sin(A)/BC
.. sin(A) = (BC/AB)*sin(C)
Since angle C is 90 degrees, its sine is 1. The sine of A is 15/30 = 1/2. Angle A is arcsin(1/2) = 30°.