Calculus

1

*****

1 is not correct.

The correct solution is x = -1 or -6.

You can easily find it this way:

Factorising, we obtain

x2 + 7x + 6 = (x + 1)(x + 6) = 0.

The above is true if, and only if, either,

x + 1 = 0, or, else,

x + 6 = 0; that is, if

x = -1 or -6, which is the answer we sought.

The rule is that two numbers multiply to give a product of zero, if, and only if, one of the two numbers is zero.

To check our answer, let's try substitution into the original equation:

Does (-1)2 + 7(-1) + 6 = 0?

We see that 1 - 7 + 6 = 0.

Does (-6)2 + 7(-6) + 6 = 0?

We see that 36 - 42 + 6 = 0.

The answer is yes, both times, thus assuring us that we have found the correct answer.

The discriminant is.....

b^2 - 4ac

(-2)^2 - 4(3)(3)

4 - 36 = - 32

Less than 1 so no real roots.

2 x 3 x 2 = 12 interactions

There is no solution. Your system looks like this:
x + 7y = 2
x = 9 - 7y

The first can be rewritten as x = 2 - 7y,
and then join the two as 9 - 7y = 2 - 7y

Adding 7y to both yields 9 = 2 which is false, so there's no solution.

You can convert these to slope/intercept form as:
y = -x/7 + 2/7
y = -x/7 + 9/7

These are parallel lines, and will never intersect, so there is no solution that satisfies both equations.

It is not possible to find the expression of 2y if f(x) = 2x - 3x.

If: x-2y+12 = 0 then x = 2y-12

If: x = 2y-12 then x^2 = (2y-12)^2 which is 4y^2-48y+144

If: x^2 +y^2 -x -31 = 0

Then: 4y^2 -48y +144+y^2 -(2y-12) -31 = 0

Removing brackets and collecting like terms: 5y^2 -50y +125 = 0

Divide all terms by 5 and factorize: (y-5)(y-5) = 0 => y = 5

Therefore by substitution solutions are: x = -2 and y = 5

8

4940.

It is: 55.2

It is -13.

10x + y = 67 ( y=17) what does x equal?

Any value of x! Multiplication is commutative, that is, the order of multiplication doesn't matter, so 2x3=3x2, 23x45=45x23, and so on. Hence, 2 times x and x times 2 are the same. Therefore, it doesn't matter what x is!

Area is 8x+16.

Yes

You have enough fingers and toes to figure this one out (unless you are a redneck which might explain the question in the first place). The answer should also be memorized: 15. Please don't make a mockery of the calculus section.

Both the ellipse and the hyperbola has an x squared and a y squared term. In the ellipse, they are both positive. In the hyperbola, one of them is negative.

Example:

3x^2 /36 + 5y^2 / 64 = 1 (ellipse)

3x^2 / 36 - 5y^2 / 64 = 1 (hyperbola)

4245.28

2x-y = 4 and 2y = 4x-6

pick either equation and solve for one of the variables

the first equation: y = -4 + 2x

plug in the value of variable you solved for into the other equation

2(-4 + 2x) = 4x -6

then solve

-8 + 2x = 4x-6

-2 = 2x

x= -1

then plug in the value you have found into either original equation to find the value of the other variable

2(-1) - y = 4

-2 - y = 4

-y = 6

y = -6

28,800

This is a quadratic equation requiring the values of x to be found.

Rearrange the equation in the form of:

-3x2-4x+6 = 0

Use the quadratic equation formula to factorise the equation:

(-3x+2.69041576)(x+2.23013857)

Therefore the values of x are 0.8968052533 or - 2.230138587

An even more accurate answer can be found by using surds instead of decimals.

24 = 3x + 9 -9 -9 Subtract 9 from each side


15 = 3x
/3 /3 Divide 3 from each side


5 = x You are left with five equals X

pi over three is 60 degrees.