Calculus

There could be a few values. 45 divided by 1 could work, and X=root 45 and Y=1

There are two variables, so two equations would be needed to determine the values. Otherwise, there are many solutions.

2-2/3x = 4/5x

The common denominator of 3x and 5x is 15x so multiply all terms by 15x in order to eliminate the fractions:

30x-10 = 12

30x = 22

Divide both sides by 30 in order to find the value of x:

x = 22/30 = 11/15 in its lowest terms

Substituting the value of x into the original equation: 12/11 = 12/11

Therefore the solution is correct

Full equation is (-b +/- sqrt(b2 - 4ac))/2a.

Try it with x2 - 2x - 3, where a = 1, b = -2 and c = -3...

Range

set to 0

X^2 + 4X = 0

you must complete the square. halve the coefficient of the linear term (4X) and square it and add it to the other side.

(X + 2)^2 = 4

now subtract the 4 from both sides

(X + 2)^2 - 4 = 0

The graph of y = x2 (vertex (0,0) is shifted 2 units to the left, and 4 units down.

the vertex is....

(-2,-4)

my TI-84 confirms this answer

or

Since x = -4/2 = -2 is the equation of the axis of symmetry, and the vertex lies on it, then the x-coordinate of the vertex is -2 and the y-coordinate is f(-2).

f(-2) = (-2)2 + 4(-2) = 4 - 8 = -4

thus, the vertex is (-2, -4)

1500000.00 dollars

3

Most functions are continuous (connected line), and not just two points... 2 points are simply just coordinates on a graph, and would be very hard (perhaps impossible) to make into a function (unless you have a restricted domain)

I may be wrong, but I don't think I am

A function has to be a graph that can be expressed through an equation, and only has a max of one y coordinate for each x coordinate, although it may have zero

-2x=-4x*24

x=12

Take logs of both sides - you can use any base, to give the answer:

10^x = 97

→ log(10^x) = log(97)

→ x log(10) = log(97)

→ x = log(97) ÷ log(10)

If you use common logs (logs to base 10) - highly recommended in this case), then:

lg(10) = 1

→ x = lg(97)

One solution: x = -4

48

Multiply the bottom equation by -1

y2-4y-32 = (y+4)(y-8) when factored

No, (sinx)^2 + (cosx)^2=1 is though

2

Mark a point on the x-axis as 's', then draw a solid line through this point, with a slope of 1. Then shade in the area above this line. The region above the line is shaded because if x-s < y then y > (x-s). The line is drawn as a solid line to represent that it can be equal, as well. At the point x=s, y = 0, which is where you marked s on the x-axis.

5y + x = 0

subtract 5y from each side, then x = -5y

what is frueds rule

geometry, Algebra , trigonometry calculus, physics

Basically, the same way you solve any inequality. However, it may be simpler if you multiply both sides of the inequality by the fraction's denominator first; that way, you will only have integers, and don't need to deal with fractions later on. If you have several fractions, you might multiply both sides of the fraction by the least common denominator.

x2 + 4x + y2 - 6y = 3

You need to be more clear about your question:

Are you trying to find the properties of the curve it defines?

x2 + 4x + y2 - 6y = 3

∴ x2 + 4x + 4 + y2 - 6y + 9 = 16

∴ (x + 2)2 + (y - 3)2 = 42

∴ This describes a circle with a radius of 4, and a center point of (-2, 3)

Did you want to solve for y?

(x + 2)2 + (y - 3)2 = 42

∴ (y - 3)2 = 16 - (x + 2)2

∴ y - 3 = ± [16 - (x + 2)2]1/2

∴ y = 3 ± [16 - (x + 2)2]1/2

Did you want to solve for x?

(x + 2)2 + (y - 3)2 = 42

∴ (x + 2)2 = 16 - (y - 3)2

∴ x + 2 = ± [16 - (y - 3)2]1/2

∴ x = -2 ± [16 - (y - 3)2]1/2

no , since there is a function which lsc but not usc.