Algebra

2x^(3)y + 18xy - 10x^(2)y -90y

Rearrange in ascending powers of 'x' .

Hence

2x^(3)y - 10x^(2)y + 18xy -90y

'2' & 'y' are common factor to all four terms.

Hence

2y[ x^(3) - 5x^(2) + 9x - 45]

Inside the 'square' brackets we factor the first two terms and the last two terms.

Hence

2y[(x^(2){x - 5} + 9{x - 5}]

To the two internal terms 'x - 5' is common. Hence

2y[x^(2) + 9)(x - 5)] Fully factored.

NB 'x^(2) + 9 ' = x^(2) + 3^(2) does NOT factor .

Remember two squared terms with a positive(+) between them does NOT factor. However, two squared terms with a negative(-) between them does factor.

x^(2)y^(2) + 2x^(3) y

To factor

'x^(2) is common to both terms.

Hence

x^(2) [ y^(2) + 2xy]

'y' is common to both terms

Hence

x^(2)y[ y + 2x ] Fully factored.

2x - 3y = 2

3x + 2y = 3

Simultaneous Equations.

Arbitrarily decide which letter to eliminate.

In this case 'y'.

To do this we bring the coefficients of 'y' to the same value. . To do this multiply the top equation by '2' and the bottom eq'n by.3.

Hence

4x - 6y = 4

9x + 6y = 9

We now add the two equations. The addition of '-6y + 6y = 0 ', So 'y' is eliminated.

Hence

13x = 13

x = 1

To find 'y' , we substitute 'x = 1' into either equation.

Hence

4(1) - 6y = 4

4 - 6y = 4

-6y = 0

y = 0

So the answer in ( x,y ) form is ( 1,0 ) .

-3 + 3y = 2y + 5

Add '3' to both sides

Hence

3y = 2y + 8

Subtract '2y' from both sides.

y = 8 The answer!!!!!

(3x + 2y)(5x - 3y)

Apply FOIL.

F(First) ; 3x X 5x = 15x^(2)

O(Outside) ; 3x X -3y = - 9xy

I(Inside) ; 2y X 5x = 10xy

L(Last) ; 2y X - 3y = - 6y^(2)

15x^(2) - 9xy + 10xy - 6y^(2)

Collect 'like' terms

15x^(2) + xy - 6y^(2)

The answer!!!!!!

A square mile is an area measurement, not a specific shape. They could be just about anything, as long as they multiply together to make one square mile.

1 mile by 1 mile is a square mile. Two miles by half a mile is a square mile. 1 foot by 5280 miles is a square mile. This means that 8 square miles can be 2 miles by 4 miles or 1 mile by 8 miles.

If you’re in or near Chicago and you want to meet or connect with foreign exchange (Forex) traders, there are several real-world and community paths you can explore — from local trading groups and educational academies to financial firms and trading hubs. While proprietary trading programs like PAX MARKET FUNDS operate online and globally, Chicago also has a deep financial ecosystem where you can learn from, network with, or even work alongside professional traders.

PAX MARKET FUNDS

To find the equation of a line in slope-intercept form (y = mx + b) that is parallel to the line ( y = 2x + 6 ), we need to use the same slope, which is 2. Using the point (4, -4) to find the y-intercept ( b ), we substitute into the equation:

(-4 = 2(4) + b )

This simplifies to (-4 = 8 + b), so ( b = -12 ). Therefore, the equation of the parallel line is ( y = 2x - 12 ).

Horizontal change refers to the difference in the horizontal position of a point or object, often measured along the x-axis in a coordinate system. It can be calculated by subtracting the initial x-coordinate from the final x-coordinate. This concept is commonly used in mathematics, physics, and engineering to analyze motion, graph functions, or assess distances in a two-dimensional space.

The independent variable is the temperature. In experiments or studies examining the relationship between temperature and pressure, temperature is typically manipulated to observe how it affects pressure, which is the dependent variable. This allows researchers to understand how changes in temperature influence pressure in a given system.

117

The goal in solving equations is to find the value(s) of the variable(s) that make the equation true. This involves manipulating the equation through various algebraic techniques to isolate the variable on one side. Ultimately, solving the equation allows us to understand relationships between quantities and to make predictions based on those relationships.

a2 + 62 = 122

a2 + 62 - 62 = 122 - 62

a2 = 144 - 36

a2 = 108

taking the square root of each side, we get a equal plus or minus the square root of 108, or plus or minus 6 times the square root of 3.

f(x) = (1 - x^(2) ^(1/2)

Let y= (1 - x^(2)) ^(1/2)

Use Chain Rule

dy/dx = dy/du X du/dx

Let u = 1 - x^(2)

Hence y = u^(1/2)

dy/du = (1/2)u^(-1/2)

du/dx = -2x

Hence

dy/dx = dy/du X du/dx = (1/2)u^(-1/2) X ( -2x)

dy/dx = (1/2)u( 1 -x^(2)^(-1/2) X ( -2x)

Tidying up

dy/dx = (-2x/(2(1 - x^(2))^(1/2))

dy/dx = -x/ [(1 - x^(2)]^(1/2)

f(x) = 3x4 - 2x2 + 7

The function

f'(x) = 12x^(3) - 4x

!st Derivative

f''(x) = 36x - 4

2nd derivative. The answer!!!!!

The expression ( y = ax - h + k ) represents a linear equation in slope-intercept form, where ( a ) is the slope, ( -h ) is a horizontal shift, and ( k ) is a vertical shift. The term ( h ) adjusts the x-coordinate of the graph, moving it left or right, while ( k ) adjusts the y-coordinate, moving it up or down. Overall, this equation describes how a line can be transformed from its standard position based on shifts and slope.

The equation ( y = x - 11 ) is in slope-intercept form ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept. Here, the slope ( m ) is 1, and the y-intercept ( b ) is -11. This means the line rises one unit for every unit it moves to the right, and it crosses the y-axis at the point (0, -11).

19

A fractional exponent means the 'root'.

e.g. Square Root (4) = 4^(1/2) = 2

Cube root (8) = 8^(1/3) = 2

Fourth Root (16) = 16^(1/4) = 2

When you have something like

4^(3/2) split it up into (4^(1/2))^(3) =

[2]^(3) =>

8 The answer!!!!!

The rule being [a^(n)]^(m) = a^(nm)

2 ^(1/3) = 125992105.....

(1/216)^(1/3) = 1/6

216^(1/3) = 6

Remember Sin( angle) = opposite / hypotenuse.

Hence

Sin(A) = 30/90

Cancel down by '30'0

Sin(A) = 1/3 = 0.333333.....

A = Sin^(-1) 0.33333.....

A = 19.47122063..... degrees.

NB Careful with your triangle labelling.

Angles are always shown with a CAPITAL letter. 'A'.

The side opposite to the given angle is small/lower case of the same letter 'a'.

Similarly , ;B; & 'b; and 'C' & 'c'.

Sin(Angle) = 0.6329

Tale the ArcSin

Angle - Sin^(-1) 0.6329

Angle = 39.2644.... degrees.

A = pi r^(2)

and 2r = d

Substituting

8pi = pi r^(2)

Cancel down by 'pi'

8 = r^(2) r = 2sqrt(2)

So 2r = d = 2(2sqrt(2) = 4sqrt(2). The answer !!!!

Numerically 4sqrt(2) = 5.656.... units of length .