Calculus

x = -2

3x+8 = 5x+10

Take 3x away from both sides: 8 = 2x + 10

Take 10 away from both sides: -2 = 2x

Divide both sides by 2: -1 = x

2 x 6 =12

The answer is 12

x(x + 9)(x + 1)

x+y = 10 and y = x+8

x+x+8 = 10

x+x = 10-8

2x = 2

x = 1

Substitute the value of x into the original equations to find the value of y:

So: x = 1 and y = 9

Yes

For each of the infinite possible vaues of x, there is a different vaue of y. It is not possible to provide a table with an infinite number of entries.

In calculus, the domain refers to the interval that all x values fall on in a graph, equation, etc.

Two ways. You can use a calculator, and............

0.4X - 3 = 1.4

add 3 to each side

0.4X - 3 + 3 = 1.4 + 3

0.4X = 4.4

divide each side by 0.4

(0.4/0.4)X = 4.4/0.4

X = 11

---------------check

0.4(11) - 3 = 1.4

4.4 - 3 = 1.4

1.4 = 1.4

-------------------------checks

Or, without a calculator; use fractions ( keep as 10ths )

4/10X - 30/10 = 1 and 4/10 ( which is 14/10 )

4/10X - 30/10 = 14/10

add 30/10 to both sides

4/10X = 44/10

now, dividing by 4/10 is same as multiplying by 10/4 ( 44/10 *10/4 ) tens cancel. 44/4 is fraction remaining.

X = 11

----------------------same answer ( you try this check )

y=4x-12-3 is the equation of a straight line. It does not have a vertex.

Did you mean y=x squared - 12x - 3 ?

no it is a binomial. it has 2 terms: 2x and 3

Not necessarily.

24" x 28" x 4" = 2,688 cubic inches, or 15/9 cubic feet.

If you want to use a common liquid unit to express the same volume . . .

231 cubic inches = 1 gallon

2,688 cubic inches = 11.636 gallons

35

4x + 3, where x = 7

4(7) + 3 = 28 + 3 = 31

y=5

Subtract 7 from each side: 4x = -7

Divide each side by 4: x = -7/4 or -1¾ or - 1.75

In order for a system to have infinitely many solutions, it must contain an equation that could be solved by any set of variables. In simple terms, a two-variable system can only be solved through two distinct equations; however, if one of these equations becomes meaningless, or could be solved by any set of variables, the other equation becomes meaningless as well because any value of y could match a given value of x.

In terms of linear algebra, or any set or matrices meant to represent a system, infinitely many solutions occur due to an all 0 row. After the system is reduced to row echelon form, an all 0 row indicates that all coefficients in a given equation are equal to 0, so it does not matter what the variables are. This means that the number of equations no longer equals the number of variables and it becomes impossible to solve through cancellation and back-substitution.

It depends on their orientation - back to front (in contact), back to front with a 30 cm gap, or head to toe.

* If the line were 1 cm units the line would be 1,100,000 km long. * The in contact line would then be (at 30 cm/person) 33,000,000 km long * The 30 cm gap line 66,000,000 km * The head to to toe line (80 cm/unit) 88,000,000 km

x + 4x + 3 = 17

(Take 3 from both sides)


x + 4x = 14


= 5x = 14


(divide both sides by 5)


x = 2.8

6x + 8 = x + 6

Subtract x from each side: 5x + 8 = 6

Subtract 8 from each side: 5x = -2

Divide both sides by 5: x = -0.4

x = -0.4

-- Find the point (x = -4) on the x-axis. (It's 4 units to the left of the origin.)

-- Draw a vertical line through that point, as far up and down as you want to go. (Technically, it never ends.)

Find x when y = 0

0 = -3x + 4 so 3x = 4 or x = 4/3

Mark the point (4/3, 0).

Find y when x = 0

y = 0 + 4 so y = 4

Mark the point (0, 4)

Join the above two points and extend the line in both directions.