2 Lines Intersection

Free 2 Lines Intersection Calculator - Enter any 2 line equations, and the calculator will determine the following:

* Are the lines parallel?

* Are the lines perpendicular

* Do the lines intersect at some point, and if so, which point?

* Is the system of equations dependent, independent, or inconsistent

* Are the lines parallel?

* Are the lines perpendicular

* Do the lines intersect at some point, and if so, which point?

* Is the system of equations dependent, independent, or inconsistent

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. Wh

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. What is the length of each of the other two sides?
2 sides * 20 mm each is 40 mm
subtract this from the perimeter of 48:
48 - 40 = 8
Since the remaining two sides equal each other, their length is:
8/2 = [B]4mm[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallel

All squares are rectangles and all rectangles are parallelograms, therefore all squares are parallelograms. Is this true?
[B]Yes.[/B]
This is similar to A implies B and B implies C so A implies C also known as transitive property

Consecutive Interior Angles

Free Consecutive Interior Angles Calculator - Shows you a proof of consecutive interior angles using parallel lines and a transversal

Cross Product

Free Cross Product Calculator - Given two vectors A and B in R^{3}, this calculates the cross product A × B as well as determine if the two vectors are parallel

If the slope is 6 what would the slope of a line parallel to it be?

If the slope is 6 what would the slope of a line parallel to it be?
Our rule for the relation of second lines to first lines with regards to slope is this:
[LIST]
[*]Parallel lines have the [U]same[/U] slope
[*]Perpendicular lines have the [U]negative reciprocal[/U] slope
[/LIST]
So the slope of the line parallel would also be [B]6[/B]

is parallel to the x-axis and has an y-intercept of 3

is parallel to the x-axis and has an y-intercept of 3
Parallel to the x axis means it runs through the y-axis
y-intercept of 3 means our equation is [B]y = 3[/B]

Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Ar

Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Are line m and line n parallel or perpendicular
[U]Slope of line m is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 5)/(9 - 7)
5/2
[U]Slope of line n is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 1)/(7 - 3)
9/4
Run 3 checks on the slopes:
[LIST=1]
[*]Lines that are parallel have equal slopes. Since 5/2 does not equal 9/4, these lines [B]are not parallel[/B]
[*]Lines that are perpendicular have negative reciprocal slopes. Since 9/4 is not equal to -2/5 (the reciprocal of the slope of m), these lines [B]are not perpendicular[/B]
[*][B]Therefore, since the lines are not parallel and not perpendicular[/B]
[/LIST]

Parallel Resistors

Free Parallel Resistors Calculator - Given a set of parallel resistors, this calculates the total resistance in ohms, denoted R_{t}

Plane and Parametric Equations in R

Free Plane and Parametric Equations in R^{3} Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Quadrilateral

Free Quadrilateral Calculator - Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Rectangles and Parallelograms

Free Rectangles and Parallelograms Calculator - Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

The slope of a line is 7/6. What is the slope of any line parallel to this line?

The slope of a line is 7/6. What is the slope of any line parallel to this line?
Parallel lines have the same slope, because they never touch.
So the slope of the parallel line is [B]7/6[/B]

Vectors

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

Which of the following equations represents a line that is parallel to the line with equation y = -3

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4?
A) 6x + 2y = 15
B) 3x - y = 7
C) 2x - 3y = 6
D) x + 3y = 1
Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line.
If we rearrange A) by subtracting 6x from each side, we get:
2y = -6x + 15
Divide each side by 2, we get:
y = -3x + 15/2
This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].