Calculus

This line hits the x axis (y=0) when 4x + 0 = 4 (so x=1) and the y axis (x=0) at 0 + 2y = 4 (so y=2).

3 is the true!

i think its log25

11

53498 x 54590 divided by 65 = 44930089.54

687.84300

4.34684352143

3(2)-9=15 x=2

20

Not necessarily.

1=2x+37

-36=2x

-18=x

It is not an inequality when x=-18

Add the two equations together, notice that the y and -y cancel. You can solve for x. Take your value of x and put it into either equation. Solve for y. Done.

Also, don't mark this question as calculus. This is algebra.

To figure that out, you'll need at least one of the pronumeral's values.

The other thing you could be asking for is a graph. If you go to http://www.calc5.com/ and type in "graph(5x+y=1)", you can see a graph of that equation on a number plane.

The highest common multiple of any set of numbers is infinite.

X = 1

Twenty Million. There are one million per cubic metre.

15x2 - 17x + 4 = 15x2 - 5x - 12x + 4

= 5x(3x - 1) - 4(3x - 1).

= (5x - 4)(3x - 1).

Thus the solution,

when 15x2 - 17x + 4 = (5x - 4)(3x - 1) = 0,

is: x = 4/5 or 1/3.

* * * * *

The technique, in case it is not familiar, is quite simple:

Step 1: Note that the three co-efficients of the given quadratic are 15, -17, and 4.

Step 2: We seek two numbers whose sum and product are -17 and 60.

(Note that 60 is, itself the product of 15 and 4.)

The two numbers we seek are -5 and -12.

Step 3: Replace the middle term, '-17x' with two terms, '-5x' and '-12x'.

Step 4: Continue factorisation easily, as shown. Then, combine like terms.

Step 5: To find solution, apply the following principle: The product of two factors is equal to zero if, and only if, one or other of the two factors is equal to zero.

Add 2x to each side: 4y = 2x

Divide each side by 2: 2y = x

So any two numbers where one is twice the other will be a solution.

Exponential graphs of the form y = bx (if the b >1) have the neg. x axis as an asymptote, pass thru (0,1) and (1,b) and increase toward infinity rapidly. Log graphs of the form y = logb x (if the b >1) have the neg. y axis as an asymptote, pass thru (1,0) and (b,1) and increase slowly toward infinity.

When looking at a sequence, if you divide 2 terms (a2 / a1), (a3 / a2), (an / an-1), you sill get the same answer (b) if it represents an exponential system.

Each angle may be used as a 'reference angle'. A 30 deg. angle in QI will have a sides, x = (sq rt 3)/2 , y= 1/2, r = 1. An angle of 150 deg (180 - 30) will create a triangle in Q2 with the same lengths except x is now negative. So if you know all trig values for 30, then change the signs for cos and tan because x is now negative and you know the values of all. Similarly for 210 deg (180+30) creates the same triangle in Q3 but both x and y values are neg. Sin and cos are neg, but tan (divide 2 neg's) is positive. In Q4 (360 - 30) creates a 330 deg angle for a triangle that is the same shape, but y is neg and x is pos so that sin and tan are neg but cos is pos.

ex: sin 30 = 1/2 (Q1), sin 150 = -1/2 (Q2), sin 210 = -1/2 (Q3), sin 330 = 1/2 (Q4)

notice only the sign (+/-) changes.

Most trig classes teach you that Q1 all trig functions are pos, Q2 sin is pos, Q3 tan is pos, Q4 cos is pos. Remember this and the 1st Quadrant values and then you can get all trig functions using the concept of a reference angle.

a straight 1

Well, if x+3=5 and 2+3=5, I'm guessing x should equal 2

I would not even attempt to factor this, so the quadratic formula.

X = - b (+/-) sqrt(b2 - 4ac)/2a

a = 3

b = - 6

c = - 7

X = - (- 6 ) (+/-) sqrt[(- 6)2 - 4(3)(- 7)]/2(3)

X = 6 (+/-) sqrt(36 + 84)/6

X = 6 (+/-) sqrt(120)/6

X = 6 (+/-) sqrt( 22 * 30)/6

X = [6 (+/-) 2sqrt(30)]/6

----------------------------------------exact answer less clean up

Does this mean w^2 + w -30 = 0 ?

If so, w = 5 or -6