Algebra

Megahertz (MHz) and miles per hour (MPH) cannot be directly converted because they measure completely different, unrelated physical quantities: frequency (cycles per second) and speed (distance per time). MHz measures the speed of an electronic cycle or wave, not physical movement in miles.

An angle consists of two rays or lines having the same endpoint (vertex).

An angle is formed when two rays meet at an endpoint. The endpoint is called the vertex of the angle. The measure of an angle tells how far one side is turned from the other side -0 degrees is no turn and 360 degrees is one full turn. You can name angles by how their measures compare to 90 degrees or 180 degrees. There are 4 types of angles, acute angle, right angle, obtuse angle, and straight angle. An acute angle is an angle that measures less than 90 degrees. A right angle is an angle that measures exactly 90 degrees. A straight angle measures exactly 180 degrees.

Yes!!!

In 2-dimensional polygons, the sum of the internal angles is related to the number of sides.

Hence

3 ; 180

4 ; 360

5 ; 540

6 ; 720

7 ; 900

8 ; 1080

9 ; 1260

10 ; 1440

et seq.,

For each extra side , add 180.

A Square and a Rectangle.

NOT a parallelogram, nor a rhombus, nor a kite. nor a trapezium.

What does the '27 foot circle' represent??? The circumference, Diameter, or Radius. Please clarify.

Remember the equation for the Area of a Circle is

A = pi r^(2)

Since the diameter is 2 ft , then the radius is 1 ft. ( half of the diameter ; 'pi' is a constant at 3.141592.... ~ 3.14

Substituting

A = 3.14 X (1ft)^(2)

A = 3.14 sq.ft.

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.