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Math and Arithmetic

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Blaise Durgan

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Term1/27
Can polymer paint be bought in a paint store or can it be bought from the manufacturer
Definition1/27

Polymer paint can be bought from a paint store, and it can also be purchased from the manufacturer. This paint is extremely durable due to its bond to materials.

Term1/27
You need to cover 512 square feet with two coats of paint if a 1 gallon can of paint covers 220 square feet how many 1 gallon cans of paint do you need
Definition1/27

you will need 5 cans of paint.

Term1/27
A graph of the set of ordered pairs that are solutions of the equation
Definition1/27

Graph of an equation.

Term1/27
How do write an equation of a line when given the slope a point of the line
Definition1/27

if a line has a slope of -2 and a point on the line has coordinates of (3, -5) write an equation for the line in point slope form

Term1/27
Write the equation for the line that passes through -1 0 and 5 0
Definition1/27

Since the slope of the line is 0, then the line is a horizontal line, and since the y-coordinates of the two points are 0, then the line lies on the x-axis.

Thus, the equation of the line is y = 0.

Term1/27
3x plus 2y multiplied by 5x-3y equals
Definition1/27

(3x+2y)*(5x-3y) =3x*5x + 3x*(-3y) + 2y*5x + 2y*(-3y) [This is sometimes called the FOIL method - You multiply the First members of each bracket, then the Outers, Inners, Lasts] = 15x2 - 9xy + 10xy - 6y2 = 15x2 + xy - 6y2

Term1/27
Type the equation that shows the pattern among this set of ordered pairs 0 -5 1 0 2 5 3 10 use y equals mx plus b form
Definition1/27

Ordered pairs are not specified.

if it is like (0,5),(0,1),(0,0),.... then we may find the answer, which then shows the family of different lines according to ordered pairs.

Term1/27
Use addition or substitution to find the value of x for this set of equations 12x-5 equals 30 and y equals 2x-6
Definition1/27

12x - 5 = 30

Add 5 to each side:

12x = 35

Divide each side by 12:

x = 35/12

=======================

y = 2x - 6

Substitute the value of 'x' :

y = 2(35/12) - 6

Clear parentheses:

y = 35/6 - 6

y = 35/6 - 36/6

y = -1/6

Term1/27
What type of graph shows a direct relationship between variables
Definition1/27

type the equation that shows the relationship between the variables in this chart.

Term1/27
Simplifying rational expressions 6x-5y plus -3x-4y
Definition1/27

(6x - 5y) + (-3x - 4y) =

6x - 5y - 3x - 4y =

3x - 9y =

3 (x - 3y)

Term1/27
Use addition or substitution to find the value of x for this set of equations for x - y equals 120 x plus y equals 150
Definition1/27

X = 135 and y = 15

Solved by addition and substitution

Term1/27
Solve for y in the following system of equations-2x - 2y equals -12
Definition1/27
If it's -2x, then -2x-2y=-12, so x+y=6, so y=6-xIf it's 2x, then 2x-2y=-12, so -x+y=6, so y=x+6


Term1/27
Which type of lines pass through the points 5 5 7 1 and 5 5 8 4 on a grid
Definition1/27

neither

Term1/27
Which type of lines pass through the points 1 2 9 9 and 0 12 7 4 on a grid
Definition1/27

perpendicular

Term1/27
What is the common point of these equations x plus y equals 10 x-y equals 6
Definition1/27

16

Term1/27
If y varies directly as x what is the value of y in these ordered pairs
Definition1/27

(4,1) and (20, y)

Term1/27
What is the standard form of the equation y equals -x plus 1
Definition1/27

X-y=1

Term1/27
What is f5 if fx 3x plus 2
Definition1/27

17

Term1/27
Does y vary directly as x in this function y equals x plus 2
Definition1/27

No.

Term1/27
What is the perpendicular distance from the point of 2 and 4 to the line of y equals 2x plus 10
Definition1/27

Straight line equation: y = 2x+10

Perpendicular equation: y = -1/2x+5

Point of intersection: (-2, 6)

Distance: the square root of [(2--2)2+(4-6)2] = 4.472 to 3 decimal places

Term1/27
Is point 1 2 on the line represented by the equation x 2y 5
Definition1/27

If you mean x+2y = 5 then yes

Term1/27
How do you find an ordered pair when given only the data point
Definition1/27

A point, in two dimensional space, is defined as an ordered pair.

Term1/27
If y varies directly as x and y 18 when x 24 find x when y 15
Definition1/27

If y varies directly as x and y is 18 when x is 24, then y is always three fourths of x. So if y is 15, then x is 20.

Term1/27
If y varies directly as x squared find k when x 2 and y 8
Definition1/27

If y varies directly as x and if x = 2 when y = 8 then k = 4.

Term1/27
If y varies directly as x what is the value of y in these ordered pair 8 4 and 4 y
Definition1/27

It is 2.

Term1/27
What is the slope of the line that contains (7,-1) and (-2,-4)
Definition1/27

Step One: Identify two points on the line. Step Two: Select one to be (x1, y1) and the other to be (x2, y2). Step Three: Use the slope equation to calculate slope.

Term1/27
if f(x)=3x^2-2x+4 and g(x)=5x^2+6x-8 find (f+g)(x)
Definition1/27

(f+g)(x)=8x^2+4x-4

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Cards in this guide (27)
Can polymer paint be bought in a paint store or can it be bought from the manufacturer

Polymer paint can be bought from a paint store, and it can also be purchased from the manufacturer. This paint is extremely durable due to its bond to materials.

You need to cover 512 square feet with two coats of paint if a 1 gallon can of paint covers 220 square feet how many 1 gallon cans of paint do you need

you will need 5 cans of paint.

A graph of the set of ordered pairs that are solutions of the equation

Graph of an equation.

How do write an equation of a line when given the slope a point of the line

if a line has a slope of -2 and a point on the line has coordinates of (3, -5) write an equation for the line in point slope form

Write the equation for the line that passes through -1 0 and 5 0

Since the slope of the line is 0, then the line is a horizontal line, and since the y-coordinates of the two points are 0, then the line lies on the x-axis.

Thus, the equation of the line is y = 0.

3x plus 2y multiplied by 5x-3y equals

(3x+2y)*(5x-3y) =3x*5x + 3x*(-3y) + 2y*5x + 2y*(-3y) [This is sometimes called the FOIL method - You multiply the First members of each bracket, then the Outers, Inners, Lasts] = 15x2 - 9xy + 10xy - 6y2 = 15x2 + xy - 6y2

Type the equation that shows the pattern among this set of ordered pairs 0 -5 1 0 2 5 3 10 use y equals mx plus b form

Ordered pairs are not specified.

if it is like (0,5),(0,1),(0,0),.... then we may find the answer, which then shows the family of different lines according to ordered pairs.

Use addition or substitution to find the value of x for this set of equations 12x-5 equals 30 and y equals 2x-6

12x - 5 = 30

Add 5 to each side:

12x = 35

Divide each side by 12:

x = 35/12

=======================

y = 2x - 6

Substitute the value of 'x' :

y = 2(35/12) - 6

Clear parentheses:

y = 35/6 - 6

y = 35/6 - 36/6

y = -1/6

What type of graph shows a direct relationship between variables

type the equation that shows the relationship between the variables in this chart.

Simplifying rational expressions 6x-5y plus -3x-4y

(6x - 5y) + (-3x - 4y) =

6x - 5y - 3x - 4y =

3x - 9y =

3 (x - 3y)

Use addition or substitution to find the value of x for this set of equations for x - y equals 120 x plus y equals 150

X = 135 and y = 15

Solved by addition and substitution

Solve for y in the following system of equations-2x - 2y equals -12
If it's -2x, then -2x-2y=-12, so x+y=6, so y=6-xIf it's 2x, then 2x-2y=-12, so -x+y=6, so y=x+6


Which type of lines pass through the points 5 5 7 1 and 5 5 8 4 on a grid

neither

Which type of lines pass through the points 1 2 9 9 and 0 12 7 4 on a grid

perpendicular

What is the common point of these equations x plus y equals 10 x-y equals 6

16

If y varies directly as x what is the value of y in these ordered pairs

(4,1) and (20, y)

What is the standard form of the equation y equals -x plus 1

X-y=1

What is f5 if fx 3x plus 2

17

Does y vary directly as x in this function y equals x plus 2

No.

What is the perpendicular distance from the point of 2 and 4 to the line of y equals 2x plus 10

Straight line equation: y = 2x+10

Perpendicular equation: y = -1/2x+5

Point of intersection: (-2, 6)

Distance: the square root of [(2--2)2+(4-6)2] = 4.472 to 3 decimal places

Is point 1 2 on the line represented by the equation x 2y 5

If you mean x+2y = 5 then yes

How do you find an ordered pair when given only the data point

A point, in two dimensional space, is defined as an ordered pair.

If y varies directly as x and y 18 when x 24 find x when y 15

If y varies directly as x and y is 18 when x is 24, then y is always three fourths of x. So if y is 15, then x is 20.

If y varies directly as x squared find k when x 2 and y 8

If y varies directly as x and if x = 2 when y = 8 then k = 4.

If y varies directly as x what is the value of y in these ordered pair 8 4 and 4 y

It is 2.

What is the slope of the line that contains (7,-1) and (-2,-4)

Step One: Identify two points on the line. Step Two: Select one to be (x1, y1) and the other to be (x2, y2). Step Three: Use the slope equation to calculate slope.

if f(x)=3x^2-2x+4 and g(x)=5x^2+6x-8 find (f+g)(x)

(f+g)(x)=8x^2+4x-4

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