You can put this solution on YOUR website!

Let number of
if there are twice as many women as men, number of

Fraction that are

You can put this solution on YOUR website!
post your question here and you will get an answer

You can put this solution on YOUR website!
your matrix is:


Row operation
1:

....add times the 1st row to the 2nd row =>
Row operation
2:
.........add times the 1st row to the 3rd row...=>

Row operation
3:
..............multiply the 2nd row by ...=>...
Row operation
4:
....add times the 2nd row to the 3rd row..=>...
Row operation
5:
...........add times the 3rd row to the 2nd row...=>...
Row operation
6:
.....add times the 3rd row to the 1st row...>...

Row operation
7:
....add times the 2nd row to the 1st row...=>...

You can put this solution on YOUR website!

if t shirts cost then t shirt cost
and you would spend if you bought

You can put this solution on YOUR website!

...first factor completely (or use quadratic formula) to find roots
.....write as
........group



roots:
if ...=>..
if ...=>..

so, your answer is: They are both positive.

You can put this solution on YOUR website!
The standard equation of a circle with center C(,) and radius is as follows:

so, we need to find ,, and
since the circle that contains P and Q , the distance between them is equal to diameter of the circle:

Solved by pluggable solver: Distance Formula

The first point is (x1,y1). The second point is (x2,y2) Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6) So , Since the second point is (10, 1), we can also say (x2, y2) = (10, 1) So , Put this all together to get: , , , and -------------------------------------------------------------------------------------------- Now use the distance formula to find the distance between the two points (-3, 6) and (10, 1) Plug in , , , and ========================================================== Answer: The distance between the two points (-3, 6) and (10, 1) is exactly units The approximate distance between the two points is about 13.9283882771841 units So again, Exact Distance: units Approximate Distance: units

so, diameter ...=>......=>...
now find midpoint:

Solved by pluggable solver: Midpoint

The first point is (x1,y1). The second point is (x2,y2) Since the first point is (-3, 6), we can say (x1, y1) = (-3, 6) So , Since the second point is (10, 1), we can also say (x2, y2) = (10, 1) So , Put this all together to get: , , , and ---------------------------------------------------------------------------------------- Finding the x coordinate of the midpoint: Add up the corresponding x coordinates x1 and x2 and divide that sum by 2 X Coordinate of Midpoint = X Coordinate of Midpoint = X Coordinate of Midpoint = X Coordinate of Midpoint = So the x coordinate of the midpoint is 3.5 ---------------------------------------------------------------------------------------- Finding the y coordinate of the midpoint: Add up the corresponding y coordinates y1 and y2 and divide that sum by 2 Y Coordinate of Midpoint = Y Coordinate of Midpoint = Y Coordinate of Midpoint = Y Coordinate of Midpoint = So the y coordinate of the midpoint is 3.5 =============================================================================== Summary: The midpoint of the segment joining the two points (-3, 6) and (10, 1) is (3.5, 3.5). So the answer is (3.5, 3.5)

center is (, )=(,)...so and
...plug in ,, and
your equation is:

You can put this solution on YOUR website!
......here you missing to have a circle
I guess should be , but it also might be
let's do it with
....write it in the standard form
The standard equation of a circle with center C(,) and radius is as follows:

..put all terms with and together and all terms with and together using brackets
......complete the square within each bracket



....both sides divide by




so,the center and radius of the circle are:
C(,)

You can put this solution on YOUR website!
given:
whose graph passes through the points of
(,) and (, )
Make a system of equations with the points by substituting them for and :
.........1
.................2
.........1
.................2
take
.........1 and solve for
..........substitute in
.................2 solve for






now find



The exponential function is .

You can put this solution on YOUR website!
Types of Triangles:
: The Isosceles triangle shown on the left has two equal sides and two equal angles.
: The Equilateral triangle shown on the left has three equal sides and three equal angles. Each angle is °
: The Scalene Triangle has no congruent sides. In other words, each side must have a different length.
: The Obtuse Triangle has an obtuse angle (an obtuse angle has more than °).
: The Acute Triangle has three acute angles (an acute angle measures less than °)
: A right triangle has one °.
you are given: the sides of a triangle measure , , and
as you can see, all sides are different in length; so, your triangle is NOT an Isosceles nor Equilateral triangle
it could be Scalene (because has no congruent sides), could be Obtuse (might have an obtuse angle),could be Acute (might have an Acute angle), or could be Right Triangle (might have an right angle angle).
let's check first is it Right Triangle because we can do it using Pythagorean theorem:
let's sides and be legs, and hypotenuse
then we have if this true, we have a Right Triangle

...so, this is true and your triangle IS
but, it is also a scalene triangle with a right angle

You can put this solution on YOUR website!

You can put this solution on YOUR website!

You can put this solution on YOUR website!
....in base
=
=
=
=
=

You can put this solution on YOUR website!

A function is a quadratic function if where , , and are real numbers and not equal to .
The graph of a quadratic function is a . The most basic aid in graphing a parabola is knowing whether (the graph opens ) or (the graph opens ).
The two simplest quadratic functions are and .
a word problem involving a quadratic function:
An inquiry shows that students will attend a theater play in one week if the ticket price is dollars. Suppose that for every dollars added to the ticket price, fewer students will attend the play.
1. What ticket price will give the for the week?
2. what is the approximate for the week if the theater play spends approximately million dollars to have the play showed for one week?
answer:
1. Let be the number of times $ is added to the ticket price (and fewer students attend).
Revenue for the week is
=
=
=
Thus the greatest revenue is given by the maximum of function . It is a quadratic function with a maximum of where is the value of for which the revenue will be greatest.
To answer the question, calculate the corresponding ticket price by adding $ to the original $.
2.
Since spendings are fixed, maximum profit is obtained when maximum revenue is obtained as above, for .

=$

You can put this solution on YOUR website!
......first multiply
....eliminate parentheses, both have negative sign in front of them, so you will change signs inside of them

You can put this solution on YOUR website!
and a half hours is at
equal to distance
as you know the distance is
plug in given values

You can put this solution on YOUR website!


so, in you will have


But if you want to find out an exact number you must do some research, I might be wrong here, but a year with 1 extra day occurs once every 4th year, so:
1000/4 = 250 this is 250 years with 1 extra day, which changes the math into making us take into account that 250 years of those 1000 has 366 days instead of 365


Or, you can forget leap years and use a more sane representation of years such Julian years ( days, exactly) or tropical years ( days at the epoch J2000.0)

so in years will be days

You can put this solution on YOUR website!
recall the distance formula where , and
solve for

so,to drive at will take

You can put this solution on YOUR website!
Equation of a circle whose center is at (,) is:
....This referrers to the "center-radius form". It may also be referred to as "standard form".
given:
center is at (,) = (,)
and
plug given values in formula

You can put this solution on YOUR website!

factor ....both and are divisible by , so factor out

You can put this solution on YOUR website!
The form of the circle equation is in the format , with the center being at the point (, ) and the radius being "".

....both sides divide by


....compare to and you see that (, )=(, ) and

You can put this solution on YOUR website!

Solved by pluggable solver: Graphing Linear Equations

In order to graph we only need to plug in two points to draw the line So lets plug in some points Plug in x=-1 Multiply Add So here's one point (-1,-6) Now lets find another point Plug in x=0 Multiply Add So here's another point (0,0). Add this to our graph Now draw a line through these points So this is the graph of through the points (-1,-6) and (0,0) So from the graph we can see that the slope is (which tells us that in order to go from point to point we have to start at one point and go up 6 units and to the right 1 units to get to the next point) the y-intercept is (0,)and the x-intercept is (,0) We could graph this equation another way. Since this tells us that the y-intercept (the point where the graph intersects with the y-axis) is (0,). So we have one point (0,) Now since the slope is , this means that in order to go from point to point we can use the slope to do so. So starting at (0,), we can go up 6 units and to the right 1 units to get to our next point Now draw a line through those points to graph So this is the graph of through the points (0,0) and (1,6)

You can put this solution on YOUR website!



The domain is all real numbers equal to or smaller than , (, ]
The range is all real numbers equal to or smaller than , (, ]

You can put this solution on YOUR website!

You can put this solution on YOUR website!

....group

You can put this solution on YOUR website!

You can put this solution on YOUR website!

a.
the equation of the line passes through the points (,) and (,)

Solved by pluggable solver: FIND EQUATION of straight line given 2 points

hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (2, 9) and (x2, y2) = (9, 2). Slope a is . Intercept is found from equation , or . From that, intercept b is , or . y=(-1)x + (11) Your graph:

b.

the equation of the parallel to line going through the origin (,)

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Since any two parallel lines have the same slope we know the slope of the unknown line is (its from the slope of which is also ). Also since the unknown line goes through (0,0), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Combine like terms So the equation of the line that is parallel to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)

c.
the equation of the perpendicular to line through (,)

Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line

Remember, any two perpendicular lines are negative reciprocals of each other. So if you're given the slope of , you can find the perpendicular slope by this formula: where is the perpendicular slope So plug in the given slope to find the perpendicular slope When you divide fractions, you multiply the first fraction (which is really ) by the reciprocal of the second Multiply the fractions. So the perpendicular slope is So now we know the slope of the unknown line is (its the negative reciprocal of from the line ). Also since the unknown line goes through (2,9), we can find the equation by plugging in this info into the point-slope formula Point-Slope Formula: where m is the slope and (,) is the given point Plug in , , and Distribute Multiply Add to both sides to isolate y Combine like terms So the equation of the line that is perpendicular to and goes through (,) is So here are the graphs of the equations and graph of the given equation (red) and graph of the line (green) that is perpendicular to the given graph and goes through (,)

...given line
...parallel line
...perpendicular

let's graph them all together:

You can put this solution on YOUR website!

..... as a fraction is

You can put this solution on YOUR website!

You can put this solution on YOUR website!


.......

You can put this solution on YOUR website!
By the number of sides they have:
• - all sides have lengths
• - sides have lengths
• - sides are

type of triangle has the side lengths of ,, is triangle
type of triangle has the side lengths of ,,is triangle
type of triangle has the side lengths of ,, is triangle
What type of triangle has the side lengths of ,, is triangle

You can put this solution on YOUR website!
Let .
Express in terms of .