Algebra

To find the solutions for the equation (3x^2 - 9x = 0), we can factor it as (3x(x - 3) = 0). Setting each factor equal to zero gives us the solutions: (3x = 0) or (x - 3 = 0). Thus, the solutions are (x = 0) and (x = 3).

'x' is an unknown but fixed quantity.

'X' is the multiplication sign.

NB Do NOT confuse lower/small case 'x' with capital 'X'.

a^(2) - b^(2) + ac - bc

Factor

( a - b)( a + b) + c(a - b)

Factor further

(a - b)(a + b + c)

Done!!!!!

x^(2) - 10x + 16 = 0

Factors of '16', which are, 1,2,4,8,16. Select two numbers from this list that add/subtract to '10' . They are '2' and '8'.

Setting up brackets

( x 2)(x 8)

Since '16' is positive(+), then both signs must be the same. Since '10x' is negative (-) , then both signs are negative.

Hence

(x - 2)(x - 8 ) = 0

When

x - 2 = 0 x = 2

& when

x - 8 = 0

x = 8

So the two answers are ,2, & ,8, .

-2

If x = 2 , then it is a vertical line, parallel with the y -axis.

The gradient is described as 'undefined'.

3y^(4)- y^(2) = 0

Factor

y^(2) [ 3y^(2) - 1] = 0

Hence

y^(2) = 0

It follows that y = 0

And

3y^(2) - 1 = 0

y^(2) = 1/3

y = +/- sqrt( 1/3) = +/-0.577350269.....

Hence y = 0 or y = +/-0.577350269.... to make the eq'n equal to zero.

Dynamite is an explosive material that was invented by Alfred Nobel in 1867, primarily used for blasting rock and other hard materials in construction, mining, and demolition. It provided a safer and more manageable alternative to earlier explosives, such as nitroglycerin, which were highly volatile and difficult to handle. By enabling more efficient excavation and tunneling, dynamite revolutionized infrastructure projects and facilitated the expansion of railroads, roads, and mines, significantly boosting industrial development.

0.625 = 0.625/1.000

625/1000

Cancel down by '25'

25/40

Cancel down by '5'

5/8 The answer!!!!!

5

4x - y = 1

3x + y = 13

Simultaneous Equations.

Add ; This will eliminate 'y'

Hence

7x = 14

x = 2

When x = 2

3(2) + y = 13

6 + y = 13

y = 13 - 6

y = 7

Hence the solution in ( x,y) form is ( 2, 7).

In similar pyramids, corresponding edges, angles, and faces are proportional and equal in shape, maintaining the same geometric relationship and structure.

1 meter and 100 centimeters are identical lengths.

Its called the product. For example, in the problem 5x3=15, 15 is the product.

51 + 2z + 8z = 23

Collect 'like terms'

51 + 10z = 23

Subtract '51' from both sides

10z = 23 - 51 = -28

z = -28 /10

z = - 2.8

NB However, you have NOT indicated the mathematical signs !!!!!

Three numbers that satisfy the sides of a right angled triangle.

e.g., 3,4,&5. or 5,12, & 13

As per Pythagorean Equation. h^(2) = a^(2) + b^(2)

13^(2) = 12^(2) + 5^(2)

It means 'to the sixth power', essentially you have to multiply the number with the 'little six' by itself six times, for example, if you had three and a small six it would look like this, 3x3x3x3x3x3, which equals 729.

To find the x-intercepts of the quadratic equation (-3x^2 + 6x + 3), set the equation equal to zero: (-3x^2 + 6x + 3 = 0). Dividing the entire equation by -3 simplifies it to (x^2 - 2x - 1 = 0). Using the quadratic formula (x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}) with (a = 1), (b = -2), and (c = -1), we find the x-intercepts to be (x = 1 \pm \sqrt{2}). Thus, the x-intercepts are (1 + \sqrt{2}) and (1 - \sqrt{2}).

In a general context, "dependent" refers to someone or something that relies on another for support or existence. For example, in a family setting, a child is often considered a dependent because they rely on their parents for care and financial support. In a broader sense, the term can also apply to variables in mathematics or statistics, where a dependent variable is one that changes in response to another variable.

To find how many times greater (3 \times 10^{-2}) is than (6 \times 10^{-5}), divide the two numbers:

[ \frac{3 \times 10^{-2}}{6 \times 10^{-5}} = \frac{3}{6} \times \frac{10^{-2}}{10^{-5}} = \frac{1}{2} \times 10^{3} = \frac{1000}{2} = 500. ]

Thus, (3 \times 10^{-2}) is 500 times greater than (6 \times 10^{-5}).

Examples of expressions that are not polynomials include ( \frac{1}{x} ), ( \sqrt{x} ), and ( e^x ). A rational function like ( \frac{x^2 + 1}{x - 2} ) is also not a polynomial because it has a denominator that is a variable expression. Additionally, expressions with negative or fractional exponents, such as ( x^{-1} ) or ( x^{1/2} ), are not polynomials.

10.05 = 10 5/100 = 10 1/20

A linear relationship exists between two variables if, when you plot their values on a coordinate system, you get a straight line, or values that would "average out" to be a straight line. The line cannot be perfectly horizontal or vertical. There are many relationships among variables that give rise to curved plots as well.

The variables in the following example are not independent of one another, but serve as an easy way to imagine the plots described above. The variables are age (our sample will be 1,000 children currently in school ages 7 to 14) and years of school completed. If we plot individuals by age along the X axis, and then go up and plot their completed years of school along the Y axis, we will have 1,000 points on the grid that will be reasonably close to a straight line. Eliminate children who have repeated a grade, and it surely will be very close to a straight line. The variables have a linear relationship.

Re=Write as

16x^(3) + 12x^(2) + 4x

Take out the common factor of '4'

Hence

4(4x^(3) + 3x^)2) + x)

Take out the common factor of 'x'

Hence

4x( 4x^(2) + 3x + 1) The answer!!!!!

In different parts of the world, it goes by different names.

West Indies and Southern U S A ; An Hurricane

Bay of Bengal(India) ; A Cyclone

South China Sea ; A Typhoon

Northern Australia ; A Willy Willy ( Aboriginal name).

Elsewhere in the world, notably S.E. Africa and Brazil(S AMerica), an Hurricane.