Questions on Geometry: Points, lines, angles, perimeter answered by real tutors!

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More information needs to be known. Are you assuming the track is a perfect circle?
Ok, so it is a rectangle with two semicircles in which the width of the rectangle (and thus the diameter of the half circles) is 20 yd. We are still missing that the length of the rectangle is.
I think you're right, something is wrong. I would let your teacher know ASAP.
I'm pretty sure you need to know one of the other angles in order to do this.

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When an equation has the form
, is the slope of the line
is the slope of this line
You are asked to find a line that is perpendicular to this
one. A line that is perpendicular to another line will
have a slope that is , so in your case


Also given is the point (1,-3) that the line must pass through
The general form of the slope-intercept equation is:
, so, filling in the given data:

answer

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First thing is to remember that perpendicular lines have slopes that are negative reciprocals. That is to say that if has a slope and has a slope then is perpendicular to if and only if .

The slope of your given line is already in slope-intercept form, so you can see that the slope of the given line is because is the coefficient on the term. That means that the slope of any line perpendicular to the given line must be .

Knowing the slope and a point, you can use the point-slope form of a line to create the desired equation. The point slope form is: where is the slope and (,) are the coordinates of the given point.

Just plug in the numbers and then solve the resulting equation for to put the equation into slope-intercept form.

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The town of Elena is 24 miles north and 8 miles west of Holberg. A train runs on a straight track between the two towns. How many miles does it cover? Round your answer to the nearest tenth.
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Draw the picture.
distance = sqrt(24^2+8^2) = 25.3 miles
======================
Cheers,
Stan H.

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you mean the diagonals create 4 triangles ....right....anyway it is not clear what you are asking.....please re write and re submit the exact question of what the problem is.... is this a proof of something or finding the length of the diagonals with some givens.......let us know

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Well i think its just simply adding or subtracting to make the question simpler:
Since it goes 90CCW then 30CW it is safe to say that it just goes 60CCW because you are doing one step instead of two. Its like saying: Simplify this pattern. 4 Steps right, 3 Steps left. Instead of going left 4 steps and then BACK 3 steps you can just say take one step right to make it simpler. You would end up in the exact same spot either way.

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I believe the center is Q and the scale factor is 1/3

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(-1,-7)(-1,-6).
slope=(y2-y1)/(x2-x1)
slope=(-6+7)/(-1+1)
slope=1/0 or an undefined slope which is a verticle line through x=-1 ans.

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(6+4,3-2) = (10,1)

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area of a regular pentagon is
:
where x is the length of a side
:
if perimeter is 10000 then one side is
:
10000/5=2000 feet
:

:
sq ft

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6°48'59" + 28°19'36"
.
Adding the "seconds":
59+36 = 95 seconds
Or, 1 min 35 seconds
.
Adding the "minutes" (including the 1 from above)
1 + 48 + 19 = 68 minutes
Or, 1 deg 8 minutes
.
Adding the "degrees" (including the 1 from above)
1 + 6 + 28 = 35 degrees
.
Pulling it all together:
35°8'35"

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The area of the square is double the area of the triangle.
Thus, area of square is 100 square cm.
.
Let x = length of one side of the square
then
x^2 = 100
x = 10 cm
.
Perimeter of any square is four times the length of one side:
perimeter = 4x = 4(10) = 40 cm

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I'm not sure how helpful I can be because I can't see the illustrations or diagrams that you are working with.

What I can do is define the symbols that you have used and discuss the implications somewhat.

Definition of a straight line. A connected set of infinitely many points. It extends infinitely far in two opposite directions. A line has infinite length, zero width, and zero height. Any two points on the line name it. A double-headed arrow over the letter designations of the two points indicates a line.

So, in your first example, AD is a line that passes through points A and D and extends infinitely far in either direction.

Definition of a ray: Just like a line, except that it has one end point and extends infinitely far in the other direction. The symbol above the letter designations of the two points would be a single headed arrow.

Definition of a line segment: Here we have a piece of a line with two end points. The symbol is a bar with no arrowheads.

So, again in your first example, BC is a line segment consisting of the points B and C and all of the infinitely many points between B and C, but not extending in either direction past B or C.

Remember that all of these definitions are ways of describing sets of points. Here is where we are able to apply the ideas of Union and Intersection. Remember from your study of sets: The union of two sets is a set that includes all of the elements that are in either set or both. The intersection of two sets includes those elements that occur in both sets.

Examples:

Consider the sets S1: {A, B, C} and S2: {A, D, E}

The union of S1 and S2 (S1 U S2) would be {A, B, C, D, E}

The intersection of S1 and S2 (denoted with an upside-down U) would be {A} because the element 'A' is the only element both sets have in common.

In the case of your first example, I have to assume that one of the endpoints of BC acually lies on the line AD and the other endpoint does not. Given that, the union of line AD and line segment BC describes a pair of supplementary angles, namely angle ABC and angle DBC. On the other hand, if all four points mentioned, namely A, B, C, and D are colinear (that is, they all lie on the same line) then the union of the two lines (more correctly the union of these two sets of points) is simply the line AD because ALL of the elements of segment BC would be already contained in AD.

I hope this at least gets you started.

John

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E=(-4,K) AND F=(K,7) THE SLOPE OF EF IS 2/3, SOLVE FOR K
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slope = (7-K)/(K+4) = 2/3
Cross-multiply to get:
3(7-K) = 2(K+4)
21-3K = 2K+8
5K = 13
K = 13/5
=============
Cheers,
Stan H.

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The basal energy requirement B is the number of calories that a person needs to maintain the life process.
For a 28 year-old female with a height of 160 centimeters and a weight of 45 kilograms(kg), B is 1300 calories. Point (45,1300)
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If her weight increases to 50kg, then B is 1365 calories. There is a linear equation that expresses B in terms of her weight w. Point (50,1365)
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Find the equation and find the basal energy requirement if her weight is 53.2 kg.
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slope = (1365-1300)/(50-45) = 65/5 = 13
----
intercept: 1300 = 13*45 + b
b = 715
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Equation:
B = 13wt. + 715
If wt = 53.2, solve for B
B(53.2) = 13*53.2 + 715
B(53.2) = 1406.6
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Cheers,
Stan H.

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, EQN 1
we get,
---> , EQN 2
Also,
, subst. EQN 2,

--->
---> follows a quadratic eqn:
where ---->
note:


2 values:
, or

Width (either/or)---->
For Length, as per EQN 2:


LENGTH (either/or)---->
We'll check using: & :


, good



, good
*Note: either you use or will just be the same. Same thing on the
Thank you,
Jojo

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First, choose symbols for the width and length
width =
length =
The area of the rectangle is
The problem gives me ft2, so

The formula for the perimeter is obtained by
adding up the lengths of the 4 sides, knowing
that the opposite sides are equal


The problem gives me ft, so

Now I've got 2 equations and 2 unknowns, so they're
solvable

divide both sides by

Now substitute

Multiply both sides by


Use the quadratic equation to solve

where








and also



Now which answer makes sense?
If


Does the perimeter = ?


OK
The other answer works, too, and is more
appropriate since it makes the width shorter

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Formula for area of rectangle is A= a*b
Formula for perimeter of rectangle is P=2a+2b
where a and b are the sides of rectangle
You have given A=35sq ft and P= 27 ft, then
a*b = 35
2a+2b = 27
Now solve system of two equations
From first equation we have a=35/b,
then second equation:
2*(35/b) +2b =27 , now multiply both sides by b
2*35 +2b^2=27b
2b^2-27b+70=0 quadratic equation (Ax^2+Bx+C=0)
A=2, B=-27, C=70
find discriminant B^2-4AC = 169 > 0 equation has 2 solutions

b1=3.5

b2=10

a = 35/b then for b1=3.5 ---> a1=10 and for b2=10---> a2=3.5
We got set of two the same numbers then lets a=10ft and b=3.5ft
Prove : A = 10*3.5 =35 and P= 2*10+2*3.5=27

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inverse proportions take on the form ab=k.......so we have v/p=k....
:
remember when variables are inversely related if one increases the other decreases .that is one way of checking to see if your answer is reasonable.
In our case the pressure is increase therefore the volume must decrease.
:
6(8)=48........so then v(12)=48
:
volume of the gascubic centimeters

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Gas laws. The volume of gas is inversely proportional to the pressure on the gas. If the volume is 6 cubic centimeters when the pressure on the gas is 8 kilograms per square centimeter, then what is the volume when the pressure is 12 kilograms per square centimeter?
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Form: V = kp
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Find "k" for this situation:
6 = k8
k = 3/4
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Situation Equation: V = (3/4)p
So, if the pressure is 12 you can solve for V:
V = (3/4)12
V = 9 cubic cm
===================
Cheers,
Stan H.

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,font size=4>
We know that , EQN 1
But,
Also ----> ---> Angle C is 90 deg larger right?
subst. one of this condition in EQN 1:

Remember too ----> , therefore,


------->

Then,
Check as per EQN 1:


Thank you,
Jojo

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have 2 acute angles and one is 9x and the other is 60+2x how do I get the answer?
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The answer to what? What is your question?

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you know that the sum of the angles of a triangle is equal to 180 degrees. Add the three angles and set them equal to 180.
30+(x+100)+x=180
solve for x. I think you can do this part.
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I hope this helps!
.
Private tutoring is available. Click on my name to go to my website or email me at justin.sheppard.tech@hotmail.com for more information. If you have any other questions you can direct them to me personally and I will answer them for you.

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So you need to know the name for the situation which exists on a cereal box. Take the front top edge of the box and a bottom side edge. The two edges are not parallel, they don't intersect and they are not in the same place. Check on the mathematical meaning of the term "skew".

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Since the equation is in slope intercept form , this means that the equation has the slope and the y-intercept .


Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is .


Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point .


Start with the point slope formula


Plug in , , and


Distribute


Multiply


Add 2 to both sides.


Combine like terms.


So the equation of the line parallel to that goes through the point is .


Here's a graph to visually verify our answer:
Graph of the original equation (red) and the parallel line (green) through the point .

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I have a couple problems I have attempted but not sure if I'm right. Here goes--1) What is the measure of each exterior angle of a regular pentagon? Answer 45 degrees
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A pentagon has 5 sides, so the sum of the interior angles is 3*180 = 540º. Each interior angle is 540/5 = 108º. The exterior angle is 180 - 108 = 72º.
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and 2) The sum of the interior angle of a certain polygon is the same as the sum of its exterior angles. How many sides does the polygon have? Answer 4
--------------------
I think it's 4 also.

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Please solve this question.
Q 1. Write down an equation or equations for each of the following.
a. A plane parallel to xy-plane at a distance of 4 units from origin on negative z-axis.
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z = -4. For all values of x and y, z is 4.
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b. A curve produced due to the intersection of a circular cylinder and yz-plane. Center of this circular cylinder is x-axis (that is, cylinder is around x-axis) and its radius is one.
--------------------------------
The intersection is a circle about the origin.

c. A curve produced due to the intersection of a sphere, center at origin and radius 3, and xy-plane.
----------------
This is also a circle about the origin. Any plane intersecting a sphere will be a circle.

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ok, the first thing that you need to do is get the formula in slope-intercept form. where (x,y) is a coordinate; m=slope; b=the y-intercept
Given: x=1/2y+1
x-1=1/2y subtract 1 from both sides
2(x-1)=y multiply both sides by 2
or y=2(x-1) Identity
y=2x-2 distribute the 2
y=mx+b
now it is in slope-intercept form
so now we know that the slope of the original line is 2 and the y-intercept of the original line is -2
a line that is parallel to this one is going to have the same slope as this line. so the new line will be y=2x+b
We know that the line must go through the points (1,-2)
so plug these points in and solve for b
y =2 x +b
(-2)=2(1)+b plug in points x=1 y=-2
-2 =2+b simplify
-4=b subtract 2 from each side
now plug in the slope(m) and the y-intercept(b) of the new line into the slope intercept form and you get:

.
.
Comments appreciated
donations accepted through PayPal @ justin.sheppard.tech@hotmail.com

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Points, lines and rays have to do with geometry.
Your question is not geometry but algebra.
What do you want us to do with 3x- y + 3 - 0?

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x^2-10=4x+11
----------
x^2-4x-21 = 0
(x-7)(x+3) = 0
x = 7 or x = -3
====================
Cheers,
Stan H.

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parallel lines have the same slope

perpendicular lines have slopes that are negative reciprocals of each other

everything else is neither

slope 1 __ (4-0)/(7-1) __ 4/6 or 2/3

slope 2 __ (6-0)/(3-7) __ 6/(-4) or -3/2

looks like prependicular

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You need to calculate the slope for both lines and compare.
Parallel lines have identical slopes
Perpendicular lines have slopes that are negative reciprocals .
If it meets neither of these, then it fits the neither category.
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.
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First calculate the slopes,

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.
.



.
.
.



.
.
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Looks like they're perpendicular because,

of

.
.
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You can graph the points connect them with lines and check to verify your answer.
.
.
.

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138-90)/12=48/12=4 12 inch increments are required every 3 days. Thus:
3*4=12 days to get the 48inches.
OR:
12/3=4 inches per day.
48/4=12 days.

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I think this is what you mean??
OK, when you look at the pairs of angles, you have two types of angles:linear pairs and vertical angles.
Linear pairs sum to 180 degrees.
Vertical angles are congruent (same measure).
In your diagram, the linear pairs are:
and
and
The vertical angles are :
and
So let's build equations using this information.
1.
1.
.
.
.
2.
2.
2.
.
.
.
3.
3.
.
.
.
Since eq. 2 solved for y, you can use either 1 or 3 to solve for x. You could also add eq. 1 and eq. 3,



.
.
.
So the three angles, given clockwise, are 60 degrees(2x), 120 degrees(y+x), and 60 degrees(y-x).

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(-5,9) (-2,-4)
,
(-7/2, 5/2)
:)

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Well, for a person who doesn't know how to do this, you sure got the right answer!
Let's first find the mid-point of the line segment DE.
D(4,2) and E(-8,18)
The coordinates of the mid-point of a line segment are given by:
(,) making the appropriate substitutions:
(,) Simplify.
(,)
(,)
Now we find the slope (m) of the line segment from C(2,2) to the mid-point of DE(-2,10) using the slope formula:
making the appropriate substitutions:
Simplify.


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Well, UV = the sum of the two equal halves UY+YV and UY = 4x-3 and YV = x, so...
UV = (4x-3)+x
UV = 5x-3
So you are correct on both problems!

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If f is the midpoint of eg, then the length ef must be equal to the length fg.

So

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A HORIZONTAL LINE THROUGH (-2,-3) IS:
Y=-3
(graph 300x200 pixels, x from -6 to 5, y from -10 to 10, y = -3).

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solve for x: m < 2=70 and m < 8 = 6 x - 2
-----------------------
That makes no sense.

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This is a line...the definition of a line indicates an infinite length...since your drawing has arrows on both sides...that indicates infinite length as well.
Therefore, your line is a line.
A ray would be an arrow on only one side of the line like this:
----------->
A segment would be no arrows like this:
-----------
So remember:
2 arrows = line
1 arrow = ray
0 arrows = segment

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Write an equation of the line that passes through the point at (4,4) and is perpendicular to the line whose equation is 2x+y=7.


since given line which contains point (,), we will find a line perpendicular to using what we know:
we can write in the slope-intercept form as
the slopes of the perpendicular lines are negative reciprocal; so the slope is negative reciprocal of the slope from the line, or
since , the slope of the unknown line must be;



we also know that line goes through (,), and we can find the equation by plugging in this info into the formula
Point-Slope Formula:
where m is the slope and (,) is the given point(,)
Plug in, and ,





Here is the graph:
and
From the graph you can see that red line contains point (,)

Solved by pluggable solver: Solve the System of Equations by Graphing

Let's look at the first equation Multiply both sides of the first equation by the LCD 2 Distribute --------- So our new system of equations is: In order to graph these equations, we need to solve for y for each equation. So let's solve for y on the first equation Start with the given equation Add to both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets graph (note: if you need help with graphing, check out this solver) Graph of So let's solve for y on the second equation Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce Now lets add the graph of to our first plot to get: Graph of (red) and (green) From the graph, we can see that the two lines intersect at the point (,) (note: you might have to adjust the window to see the intersection)

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Flashback::
Definition of betweeness>>
B is between A and C if
(a) A, B, amd C are collinear, and;
(b) AB+BC=AC
so if E is between D and F, then
DE+EF=DF
but,
DF=15 and DE=6
thus,
6+EF=15
6-6+EF=15-6
EF=9

Power up,
HyperBrain!

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The best way to explain this problem is to plot these 3 points on a graph.
You have 3 points & to make a rectangle you need the 4 th point which is (2,-3) which is the rectangle.
(2,2), (7,2), (7,-3)
THE X DISTANCE=7-2=5
THE Y DISTANCE=2+3=5
THE FOURTH VERTICES=(2,-3)
THIS RECTANCLE IS A 5 UNIT SQUARE.
AREA=5*5=15 ANSWER.
PERIMETER=4*5=20 ANSWER.

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This is equivalent to driving 500 mi south and 500 mi west. There is an isosceles right triangle.
2a^2=c^2
2*250000=500000
sqrt(500000)=707.107 mi (the slow way)
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On the SAT test we know that if both sides are 1 then the hypotenuse is sqrt(2).
So if you multiply the side time sqrt(2) you get the answer the fast way!
500*sqrt(2)=707.107
.
Ed

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Find b such that f(x)=-2x^2+bx-30 has a maximum value of 2 and the vertex is located in the second quadrant.
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You have a quadratic equation with a = -2, b = b, and c = -30
Maximum value for f(x) occurs when x = -b/2a = -b/(-4) = b/4
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Then f(b/4) = -2(b/4)^2 + b(b/4) -30 = 2
-b^2/8 + b^2/4 - 30 = 2
b^2 - 2b^2 + 240 = -16
b^2 = 256
b = +16 or b = -16
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If b = 16 the vertex is at x= b/4 = 16 and x = 64 which is in the 1st quadrant
If b = -16 the vertex is at x=b/4 = -16 and x = -64 which is in the 2nd Quad.
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Answer b = -16
===================
f(x)=-2x^2-16x-30

======================
Cheers,
Stan H.