Calculus

Yes. y + x = 4 is a linear function because the highest order (exponent) on any dependent or independent variable is 1. So if it were y^2 + x = 4 or y + x^3 = 4 or yx + 4 = 0 or anything like that, it would be non-linear. If that doesn't help, if you rearrange y + x = 4 into standard y = mx + b format you get y = -x + 4. So it's a straight line with a slope of -1 and y-intercept of 4. Any time you have an equation that just has the letters in it (x, y, z, etc. any letter) without any exponents, it's a linear equation.

So x2 - 6x + 9 = 0, Factorises as (x - 3)(x - 3) so only solution is x = 3

I'm pretty sure it's undefined meaning it is a vertical line.

* * * * *

No, it is not. It is a horizontal line, 1 unit above the x-axis. Its slope-intercept equation can be written as y = 0x + c : that is, slope = 0, intercept = 1.

-2/(x-5) = 4/(x+2) (from this step you have to cross multiply)

-2(x+2) = 4(x-5) (use the distributive property)

-2x - 4 = 4x - 20 (add like terms)

-6x = -16 (divide)

x = 8/3 (answer)

6x + 10 = 72

6x = 72 - 10

x = 62/6

x = 10.3333

87^x = 0.5

take the log of both sides:

log(87^x) = log(0.5)

according to one of the log laws, you can move exponents to the front of the log function, so:

x(log87) = log(0.5)

so, then you have to get x by itself, so divide...

x = log(0.5)/log(87)

x= -0.1552

so, to prove this:

87^(-0.1552)= 0.499997

(Close enough, I just rounded in the middle, but this answer would be more than acceptable)

2x-5=3x+6

-5-6=3x-2x

-11=x

x=-11

I suppose the full question is:

Given the following system of equations, find the values of x and y.

x+y=2

x+2y=-10

First, you need to isolate the variable y in the equation x+y=2

You do this by subtracting x from both sides of the equation.

x+y-x=2-x

Simplify:

y=2-x

Now you substitute the equation 2-x in the place of y in the equation x + 2y=-10

Like this:

x+2y=-10

x+2(2-x)=-10

Distribute the two:

x+4-2x=-10

Combine like terms:

-x+4=-10

Subtract 4 from both sides:

-x+4-4=-10-4

Simplify:

-x=-14

Divide both sides by negative one to get rid of the negative sign in front of x:

-x/-1=-14/-1

Simplify:

x=14

Plug the value of x (14) into the equation x+y=2:

14+y=2

Subtract 14 from both sides:

14-14+y=2-14

Simplify:

y=-12

Now you are done.

From now on, please pay attention in class.

If you don't even know the basic math skills that this requires then you have no future.

Yes.

(3sin(x)^2)(Cos(x))

121 is the answer

-20

14 plus 34 is 48.

4

Solving the simultaneous equations: x = -237/11 and y = 90/11

C2-4c+4=0

(c-2)(c-2) c-2=0 and c-2=0

C=2 and c=2

Put 2 in place of c and solve the equation

A longer pendulum will have a smaller frequency than a shorter pendulum.

-3x + 1

The factors of 117 are 1, 3, 9, 13, 39, and 117. These are the only numbers that divide into 117 evenly, without a remainder.

3x - y = -4

3x - y = 0

Those lines do not intersect. They are parallel. You can demonstrate by solving either of them for one of the two variables, then plugging it's value into the other:

3x - y = -4

∴y = 3x + 4

Now substitute:

3x - y = 0

∴ 3x - (3x + 4) = 0

∴ 3x - 3x - 4 = 0

∴ -4 = 0

This result is obviously incorrect, indicating that the lines do not intersect.

20x=130

x=130/20

x=6.5 or 13/2

No, it isn't.

pi never ends but we don't know many the there is someone that claims to know 20million digits if he said a number per second it would take about 2 years so examiners say things like 2000-3500 and he says them and he has not been proved wrong yet.

Rate of flow varies as R^4 where R is the radius or

Rate of flow = (k) x (R^4)

It SHOULD always be less than the divisor...

Otherwise your answer is wrong.