Calculus

To start with, it is not an equation - there is no equality sign.

You need 2 independent equations to solve when you have two unknowns, x and y.

four consecutive odd, whole numbers cannot have an average of 549. four odd numbers added together would be an even number. an even number divided by another even number (in this case, four) will only yield an even number.

3x² + 10x = 8 Rewrite as: 3x² + 10x - 8 = 0

The only way to get 3x² is 3x and x

(3x + -- ) (x + --)

The factors of 8 are {1 2 4 8} so the answers must be a pair of them.

With 4 factors, and a negative sign (the -8), there are only 8 ways this can be written:

(3x + 1)(x - 8) = 3x² - 23x - 8

(3x + 2)(x - 4) = 3x² -10x - 8 (almost)

(3x + 4 )(x - 2) = 3x² - 8x - 8

(3x + 8)(x - 1) = 3x² +5x - 8

(3x - 1)(x + 8) = 3x² +23x - 8

(3x - 2)(x + 4) = 3x² + 10x -8 ◄ Success!

(3x - 4)(x + 2) = 3x² +2x - 8

(3x - 8)(x + 1) = 3x² -5x - 8

Trial and error, error, error, is the key to this kind of problem. Seeing the -10x early can point you to see that maybe changing the signs can work. ■

7

y = x2 - 4x + 3
y = x -1

Substitute the 2nd equation into the first

x -1 = x2 -4x + 3

Rearranging:

x2 -4x -x +3 +1 = 0
x2 - 5x +4 = 0

Solving this quadratic equation in x by factorising gives 2 values for x
x1 = 4
x2 = 1

Substituting these into the original equation for y (y=x-1) gives
y1 = 3
y2 = 0

So the 2 solutions to the equations are:
x1=4
y1=3

and

x2 = 1
y2 = 0

It could. This is what would happen if it did.

x + 2 = 6.3

Subtract 2 from both sides: x = 6.3 - 2 = 4.3

2x = 2y + 3

So 2y = 2x - 3

and y = x - 1.5

It is not possible to solve a single linear equation in two variables, other than to express one variable in terms of the other.

6.31meters is equal to that

since a=5 you can put that into your equation of a+7=12

a=5

a+7=12

5+7=12

12=12 Correct

So yes the given number is a solution to the given equation

Seven years of bad luck for breaking a mirror !

2x + 3 = 3x - 4

7 = 5x

1.2 = x

* * * * *

Not quite right, I'm afraid:

the correct answer is x = 7.

Here's one way to find it:

2x + 3 = 3x - 4.

Then,

2x + 3 - 3x + 4 = -x + 7 = 0, and

x = 7,

which is the answer we sought.

Checking, we try substituting 7 for x,

in the original equation:

Does 2x + 3 = 3x - 4, when x = 7?

Let's try:

2(7) + 3 = 17, and

3(7) - 4 = 17.

Yes, it does;

thus assuring us that our answer is correct.

There are an infinite number of different quantities to which it could be equal,

depending on what the value of 'X' happens to be at the moment.

7 or -8

72+7 = 56

(-8)2+(-8) = 56

You can solve this using some simple algebra.

Let x be the number you are looking for.

x2 +x-56-0

This can be factored as:

(x-7)(x+8)=0

Now use the zero property that says if AB=0, A=0 or B=0 (or both)

So x-7=0 and x=7 or

x+8=0 and x=-8

It is -15x2 + x - 21.

you have x+9>13

so subtract 9 from both sides to get your answer

(x - 3)(x^2 + 6)

I am not a noob. You are.

x=y is the identity. It is its own inverse.

So the inverse is y=x.

x2-2x+1 = 0

(x-1)(x-1) = 0

x = 1 and also x = 1

Base 10 is based on groupings of 10, and the digits are called 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 11 is based on groupings of 11, and the digits are called 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A. A is used instead of 10 to avoid confusion, because it is a single digit, not two digits that actually have the base 10 value of 11.

Notice in 10 base 10, you are using 2 digits, a 1 in the tens place and a 0 in the ones place. In base 11, you only need 1 digits, an A, which has the same effective value.

140/360 is equivalent to 7/18 in simplest form.

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