Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 141322: Solve for x:
sqrt x-6 + sqrt x+6 = 6
a. 3
b. 16
c. 10
d. Cannot be solved
This is what I have but it is not an answer.
sqrt x-6 = sqrt x+6 +6
(sqrt x-6)^2 = (sqrt x+6+6)^2
(sqrt x+6)^2 + 2 * sqrt x+6*6+6^2
x+6 + 2 sqrt x+6 + 6 + 36
(sqrt x-6)^2 = (sqrt x+6+6)^2
x-6 = x + 6 + 2sqrt x+6+36
x-6 + x + 42 + 2sqrt x+6
2x - 6 = 2sqrt x+6
4x^2 + 36x - 36 + 4 (x+6)
4x^2 + 36x - 36 = 4x + 24
4x^2 - 32x = 0
4x(x - 8x) = 0
4x = 0 and x - 8 = 0
x = 0 x = 8
Click here to see answer by stanbon(75887) |
Question 141308: Which method is best used to find the solutions to:
k(w) = -w^2 + 4
a. Using the square root property
b. Completing the square
c. Using the quadratic formula
d. This cannot be solved since the variable is not 'x'
I selected D; because a,b,c all require a 'x' variable
Click here to see answer by scott8148(6628)  |
Question 141572: A framer at a photo gallery wants to frame a print with a matte of uniform width all around the print. To make it pleasing to the eye, the area of the matte should equal the area of the print. If the print measures 40 cm by 60 cm, how wide should the matte be?
Click here to see answer by edjones(8007)  |
Question 141577: Raj and his sister cut the lawn. The lawn is a square and Raj says he will cut a path around the outside 3m wide. His sister will cut the remaining lawn. If the part he cuts is the same area as the part she cuts, what are the dimensions of the lawn?
Click here to see answer by scott8148(6628)  |
Question 141577: Raj and his sister cut the lawn. The lawn is a square and Raj says he will cut a path around the outside 3m wide. His sister will cut the remaining lawn. If the part he cuts is the same area as the part she cuts, what are the dimensions of the lawn?
Click here to see answer by edjones(8007)  |
Question 141673: A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H=15 + 23t - 5t^2,where H is the height in metres and t is the time in seconds.
a)how long does it take for the rocket to pass a window 10 m above the ground.
b) when does the rocket hit the ground?
c) what is the maximum height the rocket reaches above the roof of the school?
Click here to see answer by stanbon(75887) |
Question 141699: Trains A and B are travelling at the same direction on paralell tracks. Train A is travelling at 40 miles per hour and Train B is travelling at 60 miles per hour. Train A passes a station at 3:25 AM. If train B passes the same station at 3:37AM. At what time will train B catch up with train A??
How do I figure this one out??
Click here to see answer by stanbon(75887) |
Question 141576: A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H = 15 + 23t -5t squared, where H is the height in metres and t is the time in seconds.
a) How long does it take for the rocket to pass a window 10 m above the ground?
b) When does the rocket hit the ground?
c)What is the max height the rocket reaches above the roof of the school?
Click here to see answer by ankor@dixie-net.com(22740)  |
Question 141840: Hi I need help in understanding one of the steps in "completing the square" for a quadratic equation.Here is my problem
x^2+9x+8=0
IN the 2ND step my homework tells me that I have to multiply the equation by A, whatever value it has.Now everytime they show a model there is a different value for "A" everytime.How do I find the value of "A" for my own homework equations.Here is one of my models from my school...
Solve x^2 + 7x + 12 = 0 by completing the square.
1. Write the quadratic equation in general for and identify A and B.
A is 1 and B is 7.
2. Multiply the terms of the equation by 4A.
4A is 4: 4[x^2 + 7x + 12]= 4[0]
4x^2 + 28x + 48 = 0
3.Isolate the constant term on the right side of the equation.
4x^2 + 28x = -48
4.Add B^2 to each side of the equation.
B^2 is 49: [4x^2 + 28x] +49 = [-48]+49
4x^2 + 28x + 49 = 1
5.Factor the left side of the equation to the square of a binomial.
(2x + 7)(2x + 7) = 1
(2x + 7)^2 = 1
Now solve:
1^2 is 1, so (-1)^2 is 1, so
2x + 7 = 1 2x + 7 = -1
2x = -6 2x = -8
x = -3 x = -4
The solution set is {-4, -3}.
What I dont understand is step 2 how did they decide to multiply the equation by 4? Why dont they use any other number like 2 or 6?
I hope I gave you enough information.Thanks for your help...
Click here to see answer by nabla(475) |
Question 141840: Hi I need help in understanding one of the steps in "completing the square" for a quadratic equation.Here is my problem
x^2+9x+8=0
IN the 2ND step my homework tells me that I have to multiply the equation by A, whatever value it has.Now everytime they show a model there is a different value for "A" everytime.How do I find the value of "A" for my own homework equations.Here is one of my models from my school...
Solve x^2 + 7x + 12 = 0 by completing the square.
1. Write the quadratic equation in general for and identify A and B.
A is 1 and B is 7.
2. Multiply the terms of the equation by 4A.
4A is 4: 4[x^2 + 7x + 12]= 4[0]
4x^2 + 28x + 48 = 0
3.Isolate the constant term on the right side of the equation.
4x^2 + 28x = -48
4.Add B^2 to each side of the equation.
B^2 is 49: [4x^2 + 28x] +49 = [-48]+49
4x^2 + 28x + 49 = 1
5.Factor the left side of the equation to the square of a binomial.
(2x + 7)(2x + 7) = 1
(2x + 7)^2 = 1
Now solve:
1^2 is 1, so (-1)^2 is 1, so
2x + 7 = 1 2x + 7 = -1
2x = -6 2x = -8
x = -3 x = -4
The solution set is {-4, -3}.
What I dont understand is step 2 how did they decide to multiply the equation by 4? Why dont they use any other number like 2 or 6?
I hope I gave you enough information.Thanks for your help...
Click here to see answer by solver91311(24713)  |
Question 141870: Solve. Then Graph.
7x >_ 63 (The _ is supposed to be under the >)
Would the solution be {xlx<9} ?? AND
the graph be a hollow circle on the 9 and and arrow towards the numbers higher than 9? Am I even close?
Click here to see answer by rapaljer(4671)  |
Question 142116: Soybean meal is 16% protein; cornmeal is 8% protein. How many pounds of each should be mixed together in order to get 320-lb. mixture with 15% protein?
How many pounds of the cornmeal should be in the cornmeal mixture?
How many pounds of the soybean meal should be in the mixture?
HELP I hate word problems!!!! PLEASE!
Click here to see answer by scott8148(6628)  |
Question 142348: In the equation : x^a - x^b = z , where 'x' & 'z' is a positive integer, where a>b and 'a' & 'b' are positive integers. Can we find the value of 'a' & 'b' ? when the value of 'z' and 'x' is given. Is there any method. For example given eqn 2^a - 2^b = 32512. Here can we find that a=15 and b=8.
For example given eqn 3^a - 3^b = 6318. Here can we find that a=8 and b=5.
I need method to find a and b. This is the question of finding two variables in an equation. Please help me to know this. If possible please find URL where solution is present.(FROM SHIVA)
Click here to see answer by scott8148(6628)  |
Question 142372: A high school class wants to raise money by recycling newspapers. The class decided to rent a truck at a cost of $150 for the week. The market price for recycled newspapers is $15 per ton. Write an equation representing the amount of money the class will make based on the number of tons of newspapers collected...
15*x-150= T
Click here to see answer by jojo14344(1513) |
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