Algebra

3x^(2) +9x - 2x -6

Collect 'like terms'.

Hence

3x^(2) + 7x - 6

Next write down all the factors of '3' and '6'

Hence

3 ; 1' & 3'

6 ; 1,6 ; 2,3.

From these pairs of number we select a pair from each coefficient, that add/multiply to '7' .

Hence

(3' x 3 ) & (1' x 2) ; NB 'dashes' (') to indicate source of numbers.

Write up brackets

(3x 2)(x 3) -2)(x + 3)

Next we notice that the '6' is negative, so the two signs are different (+/-) The '7x' is positive , so the larger number takes the positive sign .

Hence

(3x - 2)(x + 3)

(18x^(2) - 3x)

'3x' is a common factor to both terms , so 'take it out'.

Hence

3x(6x - 1)

Fully factored.

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

Factor the numerator

Hence

3x(x -2) / 3x

Cancel down by '3x'

Hence

x -2 is the answer.

You can see that all the numbers go up by 7. This means that the first part of the nth term rule for this sequence is 7n. Now, you have to find out how to get from 7 to 3, 14 to 10, 21 to 17 ... this is because we are going up in the 7 times table. To get from the seventh times table to the sequence, you take away four. So the answer is : 7n-4

find out what 6 squared equals. which is 6 x 6 and that equals 36

8b - 4b = 4b

Its like sayimg.

b+b+b+b+b+b+b+b-b-b-b-b = b+b+b+b

Remember + b - b = 0

So 4b - 4b = 0

'Root' ??? Which root??? Square Root, Cube root, nth root. Please specify.

90 = 2 x 45 = 2 x 5 x 9 = 2 x 3 x 3 x 5

The sqrt(90) = sqrt(2 x 3 x 3 x 5 )

Hence

sqrt(90) = sqrt(2) X sqrt(9) x sqrt(5)

sqrt(90) = 1.4142.... x 3 x 2.23606....

Since 2, & 5. are prime number then their 'square roots' are irrational.

Hence it follows that sqrt(90) is irrational.

On a grid/graph the horizontal axis is the x-axis. The vertical axis is the y-axis.

So to select any point on the grid is always given by ( x, y). NEVER ( y,x).

The origin of the grid is is where the two axes intersect . It has the coordinates of ( 0 , 0)

A point given by ( 1,2 ) means from the origin, move one place to the right. Then two places up from the 'one'.

A point given by ( -2, -1) means move TWO places to the left of the origin on the x-axis. , then move ONE down from the x-axis .

Similarly for any other given point.

To simplify the expression (3x - 8 - 3(x - 1)x + 19), first distribute (3(x - 1)x) to get (3x^2 - 3x). Then, combine like terms: (3x - 3x + 19 - 8 - 3x^2), which simplifies to (-3x^2 + 11). Thus, the final answer is (-3x^2 + 11).

A(Triangle) = (1/2) base X ( Perpendicular ) height

Simplified to

A = (/1/2)bh

Substitute

A = (1/2) x 15 ins X 4 ins

A = (1/2) X 60 sq.ins.

A = 30 sq. ins. (Note the units).

To solve problems with different units, first identify all the units involved and determine a common unit for comparison. Convert all measurements to this common unit using appropriate conversion factors. Once all values are in the same unit, perform the necessary calculations. Finally, if needed, convert the result back to the desired unit for clarity.

The expression -7x² represents a mathematical operation where -7 is multiplied by the square of a variable x. To find its value, you need a specific value for x. For example, if x = 2, then -7x² = -7(2²) = -7(4) = -28. Without a specific value for x, the expression remains as is: -7x².

The ancient Olympic Games in 776 BC primarily featured competitors from various city-states of Greece, as it was an event exclusive to Greek athletes. Notably, there were no countries in the modern sense; instead, athletes represented their individual city-states, such as Athens, Sparta, and Corinth. The games were a significant cultural event, emphasizing unity among the Greek states through competition.

To multiply the numbers in scientific notation, you multiply the coefficients and add the exponents. Thus, (5e \times 7e = (5 \times 7)e^{(1+1)} = 35e^2). The result is (35e^2).

Since ( y ) varies directly as ( x ), we can express this relationship as ( y = kx ), where ( k ) is the constant of variation. Given that ( y = 75 ) when ( x = 5 ), we can find ( k ) by substituting these values: ( 75 = k(5) ), which gives ( k = 15 ). Thus, the equation is ( y = 15x ). When ( x = 1 ), substituting gives ( y = 15(1) = 15 ).

44/110

Cancel down by '11'

4/10

Cancel down by'2'

2/5 The simplest form

0.75 = 0.75/1.00

Cancel down the decimal point

075/100

Drop the prefix '0'

75/100

Cancel down by '25'

3/4 as a fraction in its simplest form.

Per cent roughly translates to "out of one hundred." To change a percentage to a fraction, just put it over one hundred and reduce it if you can. 47% is 47/100.

46% is 46/100, or 23/50. 25% is 25/100, or 1/4.

1.061208^(1/3) = 1.02

NB THe index number of '1/3' means the 'Cube Root'.

2x^(2) - 5x - 12

First write down all the factors of '2' & '12'

2 = 1,2

12 = 1,12; 2,6; 3,4 .

From this we select two pairs of numbers, one pair from each coefficient, that add/multiply to '5'

They are, 1,2 & 3,4

Hence

-(2 x 4) + (1 x 3) = -8 + 3 = -5

Set up the brackets

(2x 3)(x 4)

Hence the signs are

( 2x + 3)(x - 4)

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

6x^(2) - x

X + X + X + X = 4x

It is the same as 4 x X = 4x

Think numbers .

3 + 3 + 3 + 3 = 12 = 4(3)

or

4 x 3 = 12 = 4(3)

In mathematics instead of writing a 'string of plusses(+), it is easier to write the number of plusses multiplied to the given number.

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