Algebra

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YES!!!!

Any number , however, large or small, that ends in 0,2,4,6, or 8 is an EVEN Number. 100000000000000000000000 is an even number.

Odd numbers ends in 1,3,5,7, or 9. e.g. 1000000000000000000000001 is an ODD Number.

To solve the expression ( 18 - (3 \times 5)5 (x - 1) - 6 ), start by simplifying the multiplication: ( 3 \times 5 = 15 ), so the expression becomes ( 18 - 15 \cdot 5 (x - 1) - 6 ). Next, calculate ( 15 \cdot 5 = 75 ), which gives you ( 18 - 75(x - 1) - 6 ). Finally, combine the constant terms: ( 18 - 6 = 12 ), resulting in ( 12 - 75(x - 1) ).

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Because you are multiplying a negative & A negative. You can fully understand by closing eyes & reopening them. + will mean positive & - will mean negative. ++: Keep your eyes open, then keep your eyes open again. The eyes will be open. So ++=+. +-: Keep your eyes open, then close your eyes. Your eyes will be closed, so +-=-. --: close your eyes, open your eyes. Your eyes will be open so --=+. Think of -2 * -2 as 2 * 2. You know 22=4. So -2-2=4.

169

The answer is an imaginary number, because of the negative under the square root. The same number multiplied together will always be a positive number. For example, if you square negative one, the answer is positive one, because a negative times a negative is a positive. Because a square root undoes a square, there is no solution to the square root of a negative number. That's why your calculator could not compute this problem.

However, there is a way to solve these types of problems by using imaginary numbers. The answer is 13i, where i is the square root of negative one.

No, vertical angles are not a linear pair. Vertical angles are formed when two lines intersect, creating pairs of opposite angles that are equal in measure. A linear pair consists of two adjacent angles that sum to 180 degrees and share a common side. While vertical angles may be supplementary to other angles, they are not adjacent and do not form a linear pair.

In Deals and Maths

Two methods ;-

#1 ; Use Pythagoras, if the lengths of the other two sides are known.

h^(2) = s(1)&(2) + s(2)^(2)

In words, 'The hypotenuse squared is the sum of the squares of the other two sides.

#2 ; Use Trigonometry (trig.) is the length of one side and an angle are known .

Hence

Sin(angle) = opposite / hypotenuse

hypotenuse = opposite / Sin(angle)

or

Cos(angle) = adjacent/hypotenuse

hypotenuse = adjacent/Cos(angle).

The number of combinations of 4 numbers chosen from a set of numbers ranging from 1 to Y is given by the combination formula ( C(n, k) = \frac{n!}{k!(n-k)!} ), where ( n ) is the total number of items to choose from (in this case, Y) and ( k ) is the number of items to choose (4). Thus, the number of combinations is ( C(Y, 4) = \frac{Y!}{4!(Y-4)!} ). This formula is valid when ( Y ) is at least 4; otherwise, the number of combinations is zero.

To factorize ( x^2 - 49 ), you can recognize it as a difference of squares. It can be expressed as ( (x - 7)(x + 7) ), since ( 49 ) is ( 7^2 ). Therefore, the complete factorization is ( (x - 7)(x + 7) ).

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Yes, (2a) and (2) do not have similar terms because they involve different variables. Similar terms must have the same variable raised to the same power. In this case, (2a) is a term with the variable (a), while (2) is a constant without any variable.

Points are plotted on a coordinate system using ordered pairs, typically in the format (x, y) for a two-dimensional Cartesian plane. The x-coordinate indicates the horizontal position from the origin, while the y-coordinate indicates the vertical position. To plot a point, start at the origin (0, 0), move along the x-axis to the x-value, and then move vertically to the y-value. This intersection of the two movements marks the location of the point on the grid.

Sin(Sine) is a cyclic curve.

This cyclic curve(wave) that repeats every 360 degrees ( or 2pi radian).

Its Amplitude ranges from (+)1 to (-)1

When learning about trigonometry(Trig.) you only learn the bit between 0 degrees and 90 degrees.

On extending this learning you will find it to be a cyclic curve.

The word 'Sine'(Sin) is from Latin and means 'curve'.

The word 'Cosine(Cos) means 'complimentary sine' . It is the same curve as Sine but shifted along the x-axis by 90 degrees.

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To solve a linear equation word problem, first, read the problem carefully to identify the variables and the relationships between them. Next, translate the words into a mathematical equation by determining how the quantities relate to each other. Then, solve the equation using algebraic techniques, such as isolating the variable. Finally, interpret your solution in the context of the original problem to ensure it makes sense.

To create a coordinate plane, start by drawing a horizontal line (the x-axis) and a vertical line (the y-axis) that intersect at a point called the origin (0,0). Then, label the axes with evenly spaced numbers, marking positive and negative values on each axis. Next, create a grid by adding additional lines parallel to the axes at regular intervals. Finally, label the quadrants (I, II, III, IV) to indicate the four sections of the plane.

The degree of an expression, particularly in the context of polynomials, refers to the highest power of the variable within that expression. For example, in the polynomial (3x^4 + 2x^2 - x + 5), the degree is 4 because the term with the highest exponent is (3x^4). In general, for expressions that are not polynomials, the concept of degree may vary or not apply in the same way.

NO!!!!

The 'hypotenuse' only refers to the longest side of a Right-Angled triangle.

Depending on the information given;-

If two other(shorter) sides are known, use Pythagoras.

h^(2) = a^(2) + b^(2)

If one angle and one side are given then you use Trigonometry .

Sin(angle) = opposite/ hypotenuse

hypotenuse = opposite/Sin(angle)

or

Cos(angle) = adjacent/hypotenuse

hypotenuse = adjacent/ Cos(Angle).

Apply Pythagoras.

11^(2) = 8^(2) + s^(2)

Algebraically rearrange

s^(2) = 11^(2) - 8^(2)

Factor

s^(2) = ( 11 - 8)(11 + 8)

s^(2) = 3(19)

s^(2) = 57

s = sqrt(57)

s = 7.549834435.... ~ 7.55 (2 d.p.).

NB

You can only factor two squared terms when there is a NEGATIVE (-) between them. You CANNOT factor two squared terms with a positive(+) between them.

The HYPOTENUSE is the side of a Right-Angled Triangle, opposite to the 90 degree angle.

It is the LONGEST side of a right angled triangle.

Impossible to tell from the given information.

You need at least the length of the other side , then apply Pythagoras.

or

An angular value and apply trigonometry.

NB You need the length of TWO sides or TWO angles.