Term
| How do you find the length of a ramp that is "A" feet off the ground and "B" feet from the back of the truck to the ground? |
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Definition
1.)We know the "A" side/leg of the triangle and the "B" side/leg of the triangle, so now we want to find the hypotenuse.
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2.)To calculate the hypotenuse solve this:
hypotenuse=(Square Root of (A^2)+(B^2))
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3.)Round if Requested
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Term
| How do you find the Hypotenuse of a Right Triangle when you know the length of both legs (Leg A and Leg B)? |
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Definition
1.)Solve the following:
hypotenuse=(Square Root of (Leg A^2)+(Leg B^2))
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2.)Round if Requested
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Term
How do you simplify a radical by factoring that is in the following form?
(Squareroot of A) |
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Definition
1.)Factor "A" into two numbers, one of which is a perfect square which we will call "B".
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2.)Separate the Square Root into two Squareroots that are being multiplied together
(Squareroot of B)*(Squareroot of A)
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3.)Simplify Squareroot of B, as it is a perfect square.
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Term
| Do all numbers have a negative and positive squareroot? |
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Definition
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Term
How do you solve for "A" in a problem of this form?
A=BC+DE;C=F,E=G |
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Definition
1.Use the formula and plug in "F" for C and "G" for "E".
A=BF+DG
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2.)Solve for "A".
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Term
How do you solve an inequality of this form?
Ax+B Less Than Cx-D |
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Definition
1.)Subtract "B" from both sides
Ax+(B-B) Less Than Cx-D-B)
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2.)That should Become
Ax Less Than Cx-D-B)
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3.)Subtract "Cx" from Both Sides
Ax-Cx Less Than ((Cx-Cx)-D-B)
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4.)That should become...
(Ax-Cx) Less Than -D-B)
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5.)Write your solution in Interval Notation.
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Term
What is a shortcut to solving an inequality of this form?
(A+1)x+B Less Than Ax-D |
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Definition
1.) The Solution set is
(-Infinity,-D-B)
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Term
| What are the polarities of the Coordinates of Quadrant II? |
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Definition
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Term
| What are the polarities of the Coordinates of Quadrant III? |
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Definition
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Term
| What are the polarities of the Coordinates of Quadrant IV? |
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Definition
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Term
| What are the polarities of the Coordinates of Quadrant I? |
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Definition
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Term
| How are the Quadrants Ordered on the Coordinate Plane? |
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Definition
Quadrant II |Quadrant I
Quadrant III |Quadrant IV |
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Term
| In what quadrants of the coordinate plane are the first coordinates always positive? |
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Definition
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Term
| In which quadrants of the coordinate plane are the first and second coordinates of the same sign? |
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Definition
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Term
| What is Distance Formula? |
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Definition
Distance
=
(Squareroot of ((x2-x1)^2) + ((y2-y1)^2)) |
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Term
| What is Midpoint Formula? |
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Definition
Midpoint
=
(((x1+x2)/2),((y1+y2)/2)) |
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Term
How do you find x, such that the point
(x,A) is B units from (-C,D)? |
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Definition
1.)First Use Distance Formula to Solve for "B"
B=(SquareRoot of ((x-C)^2)+((A-D)^2)
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2.)Simplify the terms under the radical.
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3.)Square Both Sides
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4.)Subtract from Both Sides
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5.)Take the Square Root of Both Sides
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6.)This should Become
+ or minus Square Root ((B^2)-((A-D)^2)
=
x-C
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7.)Solve for "x" and place your solutions in a solution set.
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Term
What is a shortcut to finding x, such that the point
(x,A) is B units from (-C,D)? |
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Definition
1.)This should Become
+ or minus Square Root ((B^2)-((A-D)^2)
=
x-C
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2.)Solve for "x" and place your solutions in a solution set.
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Term
How do you evaluate an expression for the given value of x and y for a problem of this form?
((x^2)+(y^2))
Where
x=(1/A) and y=(1/A) |
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Definition
1.)Set the problem as
((1/(A^2)+(1/(A^2))
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2.)This should become...
(2/(A^2))
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3.)Simplify to
(1/((A^2)/2))
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4.) So "((x^2)+(y^2))" Equals...
(1/((A^2)/2))
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Term
What is a Shortcut to evaluating an expression for the given value of x and y for a problem of this form?
((x^2)+(y^2))
Where
x=(1/A) and y=(1/A) |
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Definition
1.) So "((x^2)+(y^2))" Equals...
(1/((A^2)/2))
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Term
What is a Shortcut to evaluating an expression for the given value of x and y for a problem of this form?
((x^2)+(y^2))
Where
x=((Square Root of A)/2)
and
y=((Square Root of A)/2) |
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Definition
1.)"((x^2)+(y^2))" Equals...
(A/2)
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Term
How do you determine whether point
(A,B)
is on the graph of
y=Cx-D? |
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Definition
1.)Set up your problem as...
B=(C*A)-D
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2.)If you produce a true statement then the point lies on the graph.
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3.)If not then the point does not lie on the graph.
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Term
How do you graph the equation
y=Ax+B? |
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Definition
1.)Make up a value for "x" and solve for "y".
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2.)Do Step One a Second Time
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3.)Now you know "x" values and their corresponding "y" values. These represent ordered pairs.
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4.)Graph points for each ordered pair and connect them as a line.
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Term
What does a graph of this form look like?
y=Square Root of (A-(x^2)) |
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Definition
1.)Half Circle Crossing Through
Quadrant I and II
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Term
How do you find the "x" intercept of a problem in this form?
Ax+By=C |
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Definition
1.)Set the problem as...
Ax=C
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2.)Solve for "x"...
x=C/A
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Term
How do you find the "y" intercept of a problem in this form?
Ax+By=C |
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Definition
1.)Set the problem as...
By=C
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2.)Solve for "x"...
x=C/B
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Term
What is a Shortcut to finding the "x" intercept of a problem in this form?
Ax+By=C |
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Definition
1.)The Solution is...
x=C/A
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Term
What is a Shortcut to finding the "y" intercept of a problem in this form?
Ax+By=C |
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Definition
1.)The Solution is...
x=C/B
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Term
How do you find the "x" intercepts of the graph of an equation of this form?
y=(x^2)-x-A |
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Definition
1.)Use the Quadratic Formula
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2.)Your Solutions are the x-intercepts
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Term
How do you find the "y" intercepts of the graph of an equation of this form?
y=(x^2)-x-A |
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Definition
1.)Your Solution is...
-A
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Term
How do you determine the symmetries if any of a graph of this form
(x^2)+(y^2)=A? |
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Definition
1.)The graph is symmetric with respect to the x-axis, y-axis, and origin.
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2.)This is because if x was replaced with -x, it would still equal (x^2).
Which gives it "y" axis symmetry.
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3.)This is because if y was replaced with -y, it would still equal (y^2).
Which gives it "x" axis symmetry.
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4.)This is because if x was replaced with -x, it would still equal (x^2).
If you changed "y", to -y, it would still equal (y^2).
Which gives it "origin" symmetry.
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Term
How do you determine the center of a circle based on an equation of this form?
((x+A)^2)+((y-B)^2)=C |
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Definition
1.)The center is (-A,B)
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Term
How do you determine the radius of a circle based on an equation of this form?
((x+A)^2)+((y-B)^2)=C |
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Definition
1.)The Radius is the Square Root of "C".
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Term
How do you find the standard form of the equation of a circle with a center of
(A,B) and touching the x-axis? |
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Definition
1.)Put it in this form...
((x-A)^2)+((y-B)^2)=(|B|^2)
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Term
How do you perform the indicated operations of a problem of this form?
((1/A)-(1/A2))/((B/A4)-(-1/A2)) |
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Definition
1.)Multiply Everything by A4
((1/A)-(1/A2))*A4/((B/A4)-(-1/A2))*A4
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2.)This should Become
(4-2)/(B+2)
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3.)Simplify
2/B+2
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Term
What is the shortcut to performing the indicated operations of a problem of this form?
((1/A)-(1/A2))/((B/A4)-(-1/A2)) |
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Definition
1.) The solution is
2/B+2
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