Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 759141: "When might someone want to figure out the greatest possible area that has a given perimeter?"
What does it mean?
Could you please put it in full sentences and explain it so a me myself a great fiver would understand.
Thank you very much for your time!
Answer by jim_thompson5910(28715)

(Show Source):

You can put this solution on YOUR website!
Say you're given 100 ft of fencing. You want to maximize what you can get out of all that fencing (with minimal waste and redundancy). This means you want to maximize the area that the fence can enclose.

The reason the perimeter is fixed is because you often know how much fencing you have (you can measure it if you don't know) or you can specify how much you are willing to buy (mainly based off a set fixed budget). So knowing how to maximize the area will minimize the cost in a way because you are effectively getting the most out of your money. You also save time because you don't have to construct areas by trial and error if you know the exact shape you want to build before you actually do it.

Question 759136: "When might someone want to figure out the greatest possible area that has a given perimeter?"

What does it mean?
P.S it's a grade five question and email me as fast as you can please and thank you! Explain with full details!
Answer by Alan3354(31529)

(Show Source):

You can put this solution on YOUR website!
"When might someone want to figure out the greatest possible area that has a given perimeter?"
-----------------
If you have a given length of fence and want to enclose the largest possible area with it. eg, to give a dog the greatest area inside it.

Question 759116: 5x to the second power-5x=0
Answer by MathLover1(6812)

(Show Source):

You can put this solution on YOUR website!
5x%5E2-5x=0

solutions:
5x=0

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+5x%5E2-5x%29+

Question 759076: Find a quadratic equation having 3+sqrt3 and 3-sqrt3 as roots.
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(31529)   (Show Source):
You can put this solution on YOUR website!
Find a quadratic equation having 3+sqrt3 and 3-sqrt3 as roots.
--------------

Answer by solver91311(17077)   (Show Source):
You can put this solution on YOUR website!

If is a root of a polynomial equation, then is a factor of the polynomial.

and are the factors of your polynomial. Just multiply them. Hint: Treat as single numbers. Remember the product of a pair of conjugates is the difference of two squares.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 759075: Hello all.I have good questions,it would be great if someone could answer me.
''The two solutions of the quadratic equation 3x^2 - x + k = 0 are p:4 and p+1.Determine the values of k and p.''
Someone can help me with this.??
Answer by solver91311(17077)   (Show Source):
You can put this solution on YOUR website!

What does p:4 mean?

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 755455:
s.s {-3,-1}

Answer by GETASEW(1)   (Show Source):
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s.s {-3,-1}

Question 758870: Factor:
Answer by lenny460(837)   (Show Source):
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Factor:

Answer:
(2m + 3)(3m - 2)

Check:
2m * 3m = 6m^2
2m * -2 = -4m
3 * 3m = 9m
3 * -2 = -6
6m^2 - 4m + 9m - 6
Combine like terms:
-4m + 9m = 5m
6m^2 + 5m - 6

Answer:
(2m + 3)(3m - 2)

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: lennoxobuong@yahoo.com

Question 758808: In which quadrant would these coordinates be located ?
(4,7)
Answer by AmazinglyScherzo(2)   (Show Source):
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Quadrants are divided into four sections:
Upper right (Quadrant 1) = (x,y)
Upper left (Quadrant 2) = (-x,y)
Bottom left (Quadrant 3) = (-x,-y)
Bottom right (Quadrant 4) = (x,-y)
Considering both are positive in your question, it is coated in Quadrant 1, or the upper right quadrant.

Question 758770: 2x^2+6x-10=x^2+6
Answer by MathLover1(6812)   (Show Source):
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.....use quadratic formula

solutions:

or

Question 758729: Find the Vertex of the Parabola:
x=1/3y^3y+19
I have used the -b/2a to get y which gives me -9/2 but when I plug in the -9/2 into the y values into the equation I'm not getting the same answer as they are instead I get -11/8 as the x but it keeps saying that is not the answer.

Answer by John10(267)   (Show Source):
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Hi,
You have a correct way to find the vertex of parabola.
However, your function is not correct. Please check it again.
Thanks! John

Question 758673: in a triangle ABC,if angle A+angle B =150 degree and angle B+angle C=100.find the measure of each angle of the triangle
Answer by Cromlix(741)   (Show Source):
You can put this solution on YOUR website!
If angle A + angle B = 150 degrees
then angle C = 180 - 150 = 30 degrees.
If angle B + angle C = 100 degrees
then angle A = 180 - 100 = 80 degrees.
Then angle B = 180 - (30 + 80)
= 180 - 110
= 70 degrees
Angle A = 80 degrees
Angle B = 70 degrees
Angle C = 30 degrees
Hope this helps.
:-)

Question 758615: How do I solve for x with factoring for the following: 25x^2+16=40x.
I'm not sure but i think that I need to move 40x over to the right side so it looks like this:
25x^2+16-40x=0
But I'm unsure.
Answer by John10(267)   (Show Source):
You can put this solution on YOUR website!
Hi,
Good start!
You have 25x^2 - 40 x + 16 = 0
From there, you will factor the left side:
(5x)^2 - 2(5x)(4) + 4^2 = 0
(5x - 4)^2 = 0
You can solve for x from here.
If you have any questions and need some assistance, please email me.
Thank you!

Question 758405: Complete the Square of:
x^2-6x+y^2+5=0
Thank You :) :)
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
Complete the Square of:
x^2-6x+y^2+5=0
----
x^2 -6x + 9 + y^2 = -5+9
----
(x-3)^2 + (y-0)^2 = 4
----
Circle with center at (3,0) ; radius = 2
==========================================
Cheers,
Stan H.
=========================

Question 758250: can you show me step by step on how Solve the quadratic equation by completing the square -3x^2+7x=-5
Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(6761)   (Show Source):
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Solve the quadratic equation by completing the square
-3x^2+7x=-5
-3x^2+7x+5=0
3x^2-7x-5=0
complete the square
3(x^2-7/3x+49/36)-49/12-5=0
3(x-7/6)^2-49/12-60/12=0
3(x-7/6)^2-109/12=0
x-7/6)^2=109/36
take sqrt of both sides
x-7/6=±√109/6
x=1.17±1.74
x=2.906
or
x=- 0.57

Answer by josgarithmetic(1774)   (Show Source):
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Not exactly to what you ask, but be prepared to draw a picture:

Factor a on the left-hand member; this will make the expression there easier to understand and use.

Thinking about the quadratic expression , you can think of it like a rectangle, build with side lengths and . You could draw this and label the two different sides. The area for this rectangle is the expression, . If you assume the longer side is the binomial ( seems intuitively wrong, but do not worry about that), you can cut it in half and remove the piece and place it along the other direction side of the rectangle ---- forming a square which has a corner square piece missing. THAT is the square which we will ADD to both sides of the equation in order to COMPLETE THE SQUARE. You will find when you analyze the drawing so far made, that is this square piece.

Compute the value of this square piece: .

Now, add this term to both sides:

Note very carefully how accounting for the presence of the -3 factor on the left side and the adjustment for this was made on the righthand side.

SIMPLIFY and put into standard form. As you do this simplifcation, be aware you have created a square trinomial on the left hand side. YOU FACTOR that square trinomial:

Question 757880: 0=4v^2+21v-18
for this quadratic equation why did they have 0=(4v-3)(v+6) instead of (2v-9)(2v+2)?
What determines the factors you use if they equal the same thing? 3*6=18 and so does 2*9. I don't get why it was wrong.
Answer by KMST(1936)   (Show Source):
You can put this solution on YOUR website!
Factoring the quadratic polynomial is one way of solving the equation . Factoring works well for this equation, if not easily.
is not a factorization of
is the factorization of
Not all polynomials can be factorized.
If there is a simple factorization, it is easier if the polynomial starts with .
If there is a leading coefficient in front of , factoring gets complicated, but there is a method to find the four coefficients of the factorization.

THE IDEA:
When you multiply or you get a sum of all possible products (4 products). Teachers tell students to use the acronym "FOIL" to make sure they include the right four products, and do not get mixed up.
They tell you to "FOIL", meaning to write the sum of the four terms. Then you have to add together the two terms in x. They call that "collect like terms".
To factor you have to "un-FOIL", reversing the procedure to get the four "FOIL" terms.
You know that of the four products that make , the first is and the last is .
The trick is to find the other two terms that get collected together to form .

THE PROCEDURE:
Multiply the from and the .
You get a product, , that is also the product of the missing terms' coefficients.
You want to write as the product of two factors thaT ADD UP TO THE in .
Not worrying (for now) about the minus sign, the ways to write as a product are:

and

To multiply to , we need to give one factor a minus sign.
To add to we need to give the minus sign to the smaller factor, and we need oine factor much larger than the other.
does not work. and are not far apart enough.
is the solution.
The FOIL would be .
We write those terms in a tic-tac-toe table, like this:

Then we write the common factors for each row and column:

The first row and the first column are the factors , and

Question 758235: find the ordered pair for the vertex f(x)= -(x+5)^2 +9
Answer by stanbon(57967)   (Show Source):
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find the ordered pair for the vertex f(x)= -(x+5)^2 +9
------
The equation is already in vertex form.
------
Vertex: (-5,9)
-------------------
Cheers,
Stan H.
-------------------

Question 758193: A rectangular park is 6 miles long and 3 miles wide. How long is a pedestrian route that runs diagonally across the park?
Answer by lwsshak3(6761)   (Show Source):
You can put this solution on YOUR website!
A rectangular park is 6 miles long and 3 miles wide. How long is a pedestrian route that runs diagonally across the park?
use pythagorean theorem to solve:

length of pedestrian route≈6.7 mi

Question 758133: find the value of k in 2x^2 - 3(k^2)x = 8 - 6kx if one root is negative of the other.
Answer by htmentor(808)   (Show Source):
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If the roots are negatives of each other, then the quadratic can be factored as
(x+r)(x-r) = 0 with roots r, -r
The quadratic is a difference of squares:
x^2 - r^2 = 0
The standard form for a quadratic is ax^2 + bx + c = 0
In this case the linear term, b = 0
Combining like terms in the equation gives
2x^2 - x(3k^2+6k) - 8 = 0
For the linear term to be zero, 3k^2 + 6k must equal zero:
3k^2 + 6k = 0
3k(k+2) = 0
This gives k=0, k=-2
Check:
k = 0,2 -> 2x^2 - 8 = 0 -> x = 2, -2

Question 758129: A rectangular corral needs to be built using 200feet of fencing. The formula for the corral area is A=100w-w^2 where A is the area and w is the width of the rectangle. Find the maximum possible area of the corral.
HELP! I need the answer please and thank you (:
Answer by Cromlix(741)   (Show Source):
You can put this solution on YOUR website!
A = 100w - w^2
Differentiate
A' = 100 - 2w
A' = 0
100 - 2w = 0
- 2w = - 100
2w = 100
w = 50
Using a nature table.
50 feet is the maximum width
Given 200 feet of fencing
Length = 50 feet
Width = 50ft
Area = length x width
50 x 50
2500 ft^2
Hope this helps.
:-)

Question 757853: 4y^2+12y+5=0

How did they factor and get
(2y+1)(2y+5)=0? How did they get 1 and 5 in factoring from the equation at the top? help please
Answer by stanbon(57967)   (Show Source):
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4y^2+12y+5=0
-----
You would have to use the Quadratic Formula:
y = [-12 +-sqrt(144-4*4*5)]/(2*4)
etc.
Cheers,
Stan H.

Question 757744: A rectangular portrait is 3 inches longer than it is wide. A 3 inch frame of uniform width is to be placed around the portrait. The area of the portrait and frame is 108in^2. Find the dimensions of the portrait without the frame.
Answer by sachi(463)   (Show Source):
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letbthe width is x" then the length is x+3"
A 3 inch frame of uniform width is to be placed around the portrait i.e on both length & width will increase by 3"
so the dimension of the portrait with frame will be L=x+3+3" & W=x+3"
so the area=(x+3)(x+6)=108
or x^2+9x+18=108
or x^2+9x-90=0
or x^2+15x-6x-90=0
or x(x+15)-6(x+15)=0
or (x+15)(x-6)=0
or x=6 or -15
so x= 6 rejecting -ve value
so the dimensions of the portrait without the frame w=6" & l=6+3=9"

Question 757206: Hello
I have absolutely struggled to find somewhere online that I can ask a question for free with no loopholes.
Perhaps you would be able to help me with my small problem …
I need to factorise the following quadratic
10sin^2 x (that is, 10 sin squared x) - 4sinx -5
I would really appreciate any help you could offer, as soon as possible.
Thanking you
Answer by KMST(1936)   (Show Source):
You can put this solution on YOUR website!
does not factorize into factors with rational coeficients.
can be solved using the quadratic formula to find

Since those results satisfy ,
<--> would give you
as the two solutions for

On the other hand, since
you can factorize as

Question 757114: Ok, I have 4 more problems on my Graphing Quadratics worksheet. And it's just factoring the equation. Here's one I don't understand:
7x^2 - 43x - 42 = 0
I forget how to factor that problem, and a few of these:
7a^2 - 59a + 24 = 0
5n^2 + 31n - 28 = 0
5v^2 - 8v - 21 = 0
Help me with this, and more tips to factor faster? Thanks so much! I need it for my Algebra 1 class.
Answer by josgarithmetic(1774)   (Show Source):
You can put this solution on YOUR website!
Just helping with this one:

Requiring two binomials, one with leading term 7x and other with leading term x.
The -42 contant term in the trinomial means you need to find which factorizations of -42 will make the two binomials work.

42=2*21
42=6*7
42=3*14
maybe also 42=1*42

You may need 6 to 8 combinations to try. You could also try synthetic division if you know it, but not likely if you're just in Algebra 1.

Trying: (7x_____2)(x____21_)
2x and 63x ?
No, not work.

Try: (7x_____21)(x_____2)
21x and 14x
No.

Try: (7x____3)(x____14)
3x and 98x
NO.

Try: (7x_____14)(x_____3)
7x and 14x
Not useful.

Try: (7x____6)(x_____7)
6 and 49
Looks like might work.
NOW Which sign goes where? You want 6 and 49 somehow to give you -43.

Question 757133: When the sum of 6 and twice a positive number is subtracted from a square of the number, 0 results. Find the number.
Answer by josgarithmetic(1774)   (Show Source):
You can put this solution on YOUR website!

not factorable.

Use solution to quadratic equation:

or

Question 757123: 4x-8+5x+5
Answer by Alan3354(31529)   (Show Source):
You can put this solution on YOUR website!
4x-8+5x+5
----------
Do you have a question?

Question 757121: I have to find x and y.
X squared +2x-8 and y= 2x+1
This is from aug 2012 regents. I am practicing for my regents test. Thank you, K

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
I have to find x and y.
X squared +2x-8 and y= 2x+1
-------
y = x^2 + 2x - 8
y = 2x+1
------
x^2 + 2x -8 = 2x + 1
------
x^2 - 9 = 0
(x-3)(x+3) = 0
x = 3 or x = -3
----
If x = 3, y = 2x+1 = 7
If x = -3, y = 2x+1 = -5
===========================
Cheers,
Stan H.
===========================

Answer by MathLover1(6812)   (Show Source):
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.......1 and
..........2
______________here you have system to solve.....subtract 2 from 1

or

or
now find
..........2..plug in

and

so, intersection points are: (,) and (,)
see it on a graph:

Question 757001: Dear tutor,
Please help me to resolve the below-mentioned question. Thank you very much.
C1 and C2 are quadratic curves which intersect at points (0,3) and (8,s). C1 has a maximum point (m, 11) while C2 has a minimum point (m,n) where m is a positive integer.
(i) Explain why s =3
(ii) Find the value of m.
(iii) Show that the equation of C1 is y = -0.5x^2 + 4x +3
It is also known that the equation of C2 is 2y = x^2 -8x + 6.
(iv) By expressing the equation of C2 in the form y = a(x-k)^2 + h, where a, k and h are non-zero constant, find the value of n.
(v) An enclosed area A is bounded by the curves C1 and C2 for 0 < x < 8. A rectangle R, which has lengths and breadths are parallel to the x-axis and y-axis, is drawn inside the area A. By completing the square, find the largest possible perimeter of rectangle R.

Answer by solver91311(17077)   (Show Source):
You can put this solution on YOUR website!

ii). has to be half-way between 0 and 8 by symmetry. Hence,

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

Question 756794: A rectangular parking lot has a length that is 6 yards greater than the width. The area of the parking lot is 720 square yards. Find the length and width.
Answer by Cromlix(741)   (Show Source):
You can put this solution on YOUR website!
Width = x
Length = x + 6
Area = Length * Width
720 yds^2 = x(x + 6)
x^2 + 6x = 720
x^2 + 6x - 720 = 0
(x + 30)(x - 24) = 0
x = -30 (No answer)
x = 24
Width = 24yds
Length = 30yds
Area = 30 * 24 = 720 yds^2
Hope this helps.
:-)

Question 756753: Hello,
Thanks for your help ...
is the ordered pair a solution?
(8,7); 3x-y=31
9x-6y=30
Answer by Alan3354(31529)   (Show Source):
You can put this solution on YOUR website!
is the ordered pair a solution?
(8,7);
3x-y=31
9x-6y=30
===========
Sub 8 for x & 7 for y, see if it's equal.

Question 756600: Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no real solution, enter NO REAL SOLUTION
x^3 − 7x^2 + 6x − 47 = x^2 + 1
Answer by ankor@dixie-net.com(15746)   (Show Source):
You can put this solution on YOUR website!
x^3 − 7x^2 + 6x − 47 = x^2 + 1
:
x^3 - 7x^2 - x^2 + 6x - 47 - 1 = 0
:
x^3 - 8x^2 + 6x - 48 = 0
Group factor
x^2(x - 8) + 6(x - 8) = 0
Factor out (x-8)
(x - 8)(x^2 + 6) = 0
Solutions
x = 8, the only real solution
and
x^2 = -6; non-real solutions
x = +/-
x = +
x = -
:
:
Check in original problem with x=8
x^3 - 7x^2 + 6x - 47 = x^2 + 1
8^3 - 7(8^2) + 6(8) - 47 = 8^2 + 1
512 - 448 + 48 - 47 = 64 + 1
65 = 65; confirms our solution

Question 756665: The length of a rectangle is three times its width, and its area is 9 cm2. Find the
dimensions of the rectangle.
Answer by Alan3354(31529)   (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is three times its width, and its area is 9 cm2. Find the
dimensions of the rectangle.
------------------
Area = L*W = 9
L = 3W
3W*W = 9

Question 756611: Find all real solutions of the equation. (Enter your answers as a comma-separated list.
x3 − 7x2 + 6x − 47 = x2 + 1
Answer by lwsshak3(6761)   (Show Source):
You can put this solution on YOUR website!
Find all real solutions of the equation.
x3 − 7x2 + 6x − 47 = x2 + 1
x^3-8x^2+6x-48=0
using Rational Roots Theorem:
...0...|.....1......-8........6........-48..........
...1...|.....1......-7......-1........-49..
...2...|.....1......-6......-6........-60...
...7...|.....1......-1......-1........-55.
...8...|.....1........0.......6...........0 (8 is a root)
f(x)=(x-8)(x^2+6)
roots are 8 and 2 imaginary roots
note: I skipped trying some positive numbers because I knew the answer is 8 from my graphic calculator. Anyway, I showed you the method you can use.

Question 756612: Write a quadratic equation in standard form with the solution set {2-sqrt5, 2+sqrt 5}.
The quadratic equation in standard form is ___.
(Simplify your answer. Type an equation using x as the variable.)
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
Write a quadratic equation in standard form with the solution set
{2-sqrt5, 2+sqrt 5}.
----
f(x) = [x-(2-sqrt(t)][x-(2+sqrt(5)]
------
Rearrange:
f(x) = [(x-2)+sqrt(5)][(x-2)-sqrt(5)]
---------
Multiply:
------
f(x) = (x-2)^2 - 5
----
f(x) = x^2 -4x +4 -5
----
f(x) = x^2 -4x -1
========================
Cheers,
Stan H.
=====================

Question 756320: Algebraically determine the EXACT roots in simplest for for x(x-2)=-3
Answer by josgarithmetic(1774)   (Show Source):
You can put this solution on YOUR website!

Question 756516: x^2 + 12x +28 / x+8
Answer by nihar*2013(7)   (Show Source):
You can put this solution on YOUR website!

x+8 x^2 + 12x +28
x+8=0
x=-8
-8 1 12 28
0 -8 -32
1 +4 -4 ( Remainder)
Answer is x+4
OR
x+4

x+8 x^2 + 12x +28
x^2 + 8x
- -
0 + 4x + 28
+ 4x +32
- -
0 + -4
Quotient is x+ 4
Remainder is -4
I think 1st method is easy if u still don't understand i will help u online to explain thanks

Question 756464: A person standing close to the edge on the top of a 170 foot building throws a baseball vertically upward. The quadratic function given below models the ball's height above the ground, s(t), in feet, t in seconds after it was thrown.
S(t)=-16t+64t+170
The ball reaches its maximum height of ___ feet after ____seconds.
Answer by KMST(1936)   (Show Source):
You can put this solution on YOUR website!
The equation must be

A quadratic equation of the form with is the equation of a parabola in standard form. It has a minimum at the vertex if , and it has a maximum at the vertex if .
The equation can be written in vertex form as based on the coordinates of the vertex: and

is the equation of a parabola, and the function has a maximum at the vertex of that parabola.
You may remember formulas to find the coordinates of that vertex.
Otherwise, you can always transform the equation into the vertex form.

REMEMBERING FORMULAS:
The axis of symmetry of is the line and contains the vertex. In other words, thw x-coordinate of the vertex is .
The axis of symmetry of is the line --> --> seconds.
That is the time-coordinate of the vertex of , the time when is maximum.
At that time, the height of the baseball is maximum, and that height is
--> --> --> feet.

TRANSFORMING THE EQUATION INTO VERTEX FORM:
--> --> -->
Now we can "complete the square."
--> --> --> --> --> -->
is the vertex form of the equation
The equation tells you that the maximum happens
for seconds, when , is less than that.

Question 756427: Find an equation of the line that satisfies the given conditions.
Through the points of (1/2,-2/5)
perpendicular to the line 3x − 6y = 1
Answer by sachi(463)   (Show Source):
You can put this solution on YOUR website!
the line 3x − 6y = 1
or the eqn can be rewritten as y=x/2-1/6 of the form y=mx+c
so the slope is m=1/2
the reqd line is perpemndicular to the given line
so the slope=-1/m=-2
the point is (1/2,-2/5)
so the reqd eqn is [y-(-2/5)]/[x-1/2]=-2
or [y+2/5]=-2=-2x+1
or 5y+2=-10x+5
or 5y+10x=3

Question 756408: How do i solve the question and whats the answer for it. I'd like the steps so that i can know in the future how to do similar ones.
x^2 - 2x - 4 = 11
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
How do i solve the question and whats the answer for it. I'd like the steps so that i can know in the future how to do similar ones.
x^2 - 2x - 4 = 11
---
Rearrange:
x^2 - 2x - 15 = 0
---
Factor:
(x-5)(x+3) = 0
----
x = 5 or x = -3
=====================
Note: Your problem was factorable. If your problem is not
factorable use the Quadratic Formula to find the solutions.
==============================
Cheers,
Stan H.
=====================

Question 756174: hi the type of homework i have is called " factoring complex quadratics" the equation is m^2+18m+77. my teacher had us do this square with four boxes that you work with (im sorry i forgot with its called) so i put m^2 into the top left side and the 77 in the bottom right corner. then im supposed to make an X chart and i put 77m^2 on the top and the 18m on the bottom leaving the two sides blank, im supposed to find out two numbers that make 77 and 18 but i cant figure it out and its taking forever, i hope you get what i am talking about. please help.
Answer by josgarithmetic(1774)   (Show Source):
You can put this solution on YOUR website!
The description you give of the process is like an attempt to factorize the given quadratic expression. By just looking at the polynomial , we might not know if it uses complex roots or complex binomial factors; maybe it does.

So you want two numbers, like u and v so that uv=77 and u+v=18. The idea is that . We will still get another quadratic equation in trying to find u and v.

Try first, all the factorizations for 77. What are they?
and . The second one does not promise much help. Let's try seeing what the first one will do for us:

Will the product be 77 and the sum be 18?
as we expect.
which is what we also wanted.
The numbers for u and v then are and .

The factorization for your given quadratic expression is .

---------------------------------------------------------

::: You WERE trying to put entries into a grid arrangment, so let's look at that.

_________m___________(___)________
-
-
m_______m^2__________(___)____
-
-
(__)____(___)_________77______

And maybe you are trying to fill in like this?....

_________m___________(u_)________
-
-
m_______m^2__________(u*m_)____
-
-
(v)____(v*m_)_________77______

That might help you to see how the terms occur in the multiplication process but you would still need to show combining the terms of m so as to say um+vm=18m which is how you knew that you want u+v=18.

Question 756178: How fast would a ball have to be thrown upward to reach a maximum height of 121 ft? [Hint: Use the discriminant of the equation 16t2 − v0t + h = 0.]
Answer by Alan3354(31529)   (Show Source):
You can put this solution on YOUR website!
How fast would a ball have to be thrown upward to reach a maximum height of 121 ft?
---------
It's the speed the ball would reach if dropped from 121 feet
find the time:
121 = 16t^2
t = 11/4 seconds
-----------
v = at
v = 32*(11/4)
v = 88 ft/sec

Question 756138: You are designing a rectangular birthday card for a friend. You want the card's length to be 1 in. more than twice the card's width. The area of the card is 88 in.^2. What are the dimensions of the card? Round to the nearest tenth if necessary.
Any help is appreciated.
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
You are designing a rectangular birthday card for a friend. You want the card's length to be 1 in. more than twice the card's width. The area of the card is 88 in.^2. What are the dimensions of the card? Round to the nearest tenth if necessary.
----
Width = x
length 2x+1
---
Equation:
x(2x+1) = 88
2x^2 + x - 88 = 0
----
x = [-1 +- sqrt(1-4*2*-88)}/4
----
x = [-1 +- sqrt(1+704)]/4
----
x = [-1 +- 26.55]/4
----
Positive solution:
x = 25.55/5
---
x = 5.11 inches
x+1 = 6.11 inches
====================
Cheers,
Stan H.
======================

Question 756137: What is the vertex of the function g(x)=(x+5)2? I need a quick answer please
Answer by stanbon(57967)   (Show Source):
You can put this solution on YOUR website!
What is the vertex of the function g(x)=(x+5)2?
Form:
y-0 = (x+5)^2
----
Vertex: (-5,0)
===================
Cheers,
Stan H.
=====================