Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 122661: Using the form of x^2=k for an equation. Is the solution always going to be real numbers?
Click here to see answer by jim_thompson5910(35256)

Question 122663: If the value of b^2-4ac is negative, the equation ax^2+bx+c=0. Is there always a real number solution?
Click here to see answer by jim_thompson5910(35256)

Question 122670: A rectangular field is 200m by 300m. A roadway of width xm is to be built just inside the field. What is the widest the roadway can be and still leave 50,000m^2 in the region?
60,000 - 400x - 600x +x = 50,000
Am I on the right track for solving the problem with this formula? I feel like I'm missing something.
Click here to see answer by jim_thompson5910(35256)

Question 122675: A small manufacturers weekly profit in dollars is given by p=-3x^2+270x. Find the number of items that must be produced to realize a profit of $5775.
5775 = -3x^2+270x
-3x^2+270x-5775 =0
3(x^2-90x+1925)=0
3(x-35)(x-55)=0
(x-35)(x-55)=0
I came up with the answer of x=35,55 but the question is asking for the number of items so I need some help. Thanks in advance.
Click here to see answer by jim_thompson5910(35256)

Question 122671: My economic class is quite challenging. Here is a question regarding the CPI.
I(t) = - 0.2t2 + 3t = 200 , t = 0 and corresponds to the year of 1995 where as 0 ≤ t & ≤ 5
What would the CPI by at in 1996?
What�s the rate of change from 1995 � 96?
How�s the index changing in 1998?
Any help in answering these questions on the CPI would be greatly appreciated. Thank you so much in advance!

Click here to see answer by stanbon(75887)

Question 122621: find an equation with coefficients whose roots are 2 plus and minus the square root of 3 divided by 3
Click here to see answer by ankor@dixie-net.com(22740)

Question 122758: Solve.

(x+7)squared = 13
x squared - 4x = 12
Click here to see answer by checkley71(8403)

Question 122777: -14x = -2x^2 + 36 also, in the radical symbol, since the set-up shows b^2 - 4ac would that make the 4 negative there? thank you so much!
Click here to see answer by checkley71(8403)

Question 122779: The sum of the lengths of one side of a right triangle and the hypotenuse is 20cm. The other leg is 5cm shorter than the hypotenuse. Find the length of each side.
x^2+(x-5)^2=20^2
x^2+x^2-25x+25=400
2x^2-25x-375=0
x^2-5x-178.50=0
I just want to double check my steps to make sure I did this right. Thanks is advance.
Click here to see answer by GSems22(3)

Question 122820: If the square of 3 more than a number is 9, find the numbers?
Click here to see answer by bucky(2189)

Question 122822: Hello, I have an algebra 2 question relating to application of the Quadratic formula.
The problem is: 2y+3/4y-1=3y-2/3y+2
I have no idea how to do that using the quadratic formula.
I appreciate your assistance and thank you in advance.
Click here to see answer by jim_thompson5910(35256)

Question 122834: please can you show me a method of how to work out this equation x^2+9x+14=0
Click here to see answer by jim_thompson5910(35256)

Question 122834: please can you show me a method of how to work out this equation x^2+9x+14=0
Click here to see answer by Earlsdon(6294)

Question 122858: Hello, I have a question relating to the application of the quadratic formula on the following problem:
(d-12)=(d) - 2
The (d-12) and (d) are under a radical, but the -2 is not.
I tried this a few ways, but cannot get the answer 16 from the back of the book.
I really appreciate your assistance on this and thank you in advance.
Click here to see answer by Earlsdon(6294)

Question 122875: Solve.
The equation h = -16t squared + 112t gives the height of an arrow, shot upward from the ground with an initial velocity of 112 ft/s, where t is the time after the arrow leaves the ground. Find the time it takes for the arrow to reach a height of 180 ft.
Click here to see answer by jim_thompson5910(35256)

Question 122787: A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
I do not have the ISBN number - the book is Beginning Algebra (6th ed.) chapter 10.
Click here to see answer by ankor@dixie-net.com(22740)

Question 123245: how to factor y=x^2-2x-3
Click here to see answer by stanbon(75887)

Question 123243: how to calculate the vertex of y=x^2-2x-3
Click here to see answer by solver91311(24713)

Question 123263: A rectangular parking lot has dimensions 16 metres by 40 metres. The total area of the parking lot is increased by 512 square metres by paving an extra strip of uniform width around the entire lot. How wide is the strip?
Click here to see answer by solver91311(24713)

Question 123264: A rectangular lawn has dimensions 30 metres by 40 metres. A strip of uniform width is to be mowed around the perimeter.How wide should the strip be so that exactly half of the lawn gets mowed ?
Click here to see answer by checkley71(8403)

Question 123275: 1. Please solve the following by factoring:
a) x^2- 6x - 16 = 0
b) 6x^2 + 42x = 0
2. If f(t) = 2t^2 - 4t - 1, find
a) f(2)
b) f(-1)
Please help, I need step by step instructions.
Click here to see answer by stanbon(75887)

Question 123260: A 4 by 6 inch photograph is to be matted such that the area of the mat is double the area of the photo. Assuming that the mat is the same width all around the picture, what is the width of the mat ?
Click here to see answer by checkley71(8403)

Question 123291: A rectangular field had a length of x^3 + 2x^2 � 4 feet and a width
of 4x^2 � 5 feet. Express the area as a polynomial in x.

Click here to see answer by stanbon(75887)

Question 123257: Hank travels home to Smithville every weekend from Ottawa.The distance each way is 800km. Anxious to return home, he decides to increase his speed by 20km/h and realizes that he arrives home two hours earlier than the time it took him to travel from home to Ottawa. How long does the trip to Ottawa usually take?
Click here to see answer by rajagopalan(174)

Question 123304: If f(x) = 3x^2 + 2x � 7 represents the attitude score f(x) for a
person x years old, find and interpret f(30).

Click here to see answer by chitra(359)

Question 123395: I am having a very hard time trying to figure this out. Can you please help me?
Find the axis of symmetry.
y = -x squared + 6x - 2
Click here to see answer by Fombitz(32388)

Question 123394: I am having a very hard time trying to figure this out. Can you please help me?
I am sorry, I forgot to put in there what it is I need to do with the problem.
Find the axis of symmetry.
y = x squared - 5x + 3
Click here to see answer by checkley71(8403)

Question 123608: The data in the table shows the height in metres above the ground of a snowball at various times. Showing all work algebraically, create a function that represents the height of the snowball after t seconds.
TIME(sec)--- 1,2,3,4,5
HEIGHT(m)---25.1,38.4,41.9,35.6,19.5
Can someone please help me?
Click here to see answer by Edwin McCravy(20054)

Question 123616: Local building codes require that a rectangular factory building must be surrounded by a parking lot of uniform width. The total area occupied by the factory and the parking lot must be double the factory area. If the factory is to be 80m wide and 120m long. How wide must the parking lot be? HELP:)
Click here to see answer by checkley71(8403)

Question 123613: Write two equations whose roots have a sum of -2/3 and a product of 1/2.
Click here to see answer by checkley71(8403)

Question 123618: A certain radioactive element decays to 1/2 of its original amount every 20 years. If there was 100mg to start with, how much will be present after 200 years? Set up an equation and solve the problem. Can someone please help me ??
Click here to see answer by stanbon(75887)

Question 123615: Find the value(s) of k if the equation 3k^2+5x+2=0 have no real roots.
Click here to see answer by stanbon(75887)

Question 123486: John used completing the square to find the zeros of the function y=9x^2-12x-33. Can someone please show please show me the steps for solving this ???
Click here to see answer by ankor@dixie-net.com(22740)

Question 123803: The cost per hour of running an assembly line in a manufacturing plant is a function of the number of items produced per hour. The cost function is C(x)=0.3x^2-1.2x+2, where c(x) is the cost per hour in thousands of dollars, and x is the number of items produced per hour, in thousands. Determine the most economical production level.
Click here to see answer by stanbon(75887)

Question 123806: Determine the maximum or minimum value of the quadratic function.
f(x)=x^2-6x+2
Click here to see answer by stanbon(75887)

Question 123806: Determine the maximum or minimum value of the quadratic function.
f(x)=x^2-6x+2
Click here to see answer by rapaljer(4671)

Question 123833: Solve.
x squared - 4x = 12
Click here to see answer by solver91311(24713)

Question 123834: Find the x-intercept of y = x squared - 3x - 10
Click here to see answer by solver91311(24713)

Question 123798: Please help me, i need to know how to solve this for a test tommorow!
What are the zeros of f(x)=-3(x-2)^2 + 5

Click here to see answer by rapaljer(4671)

Question 123842: What formula do you use to put this in vertex form where you can graph it? What are the "zeros" of this equation? and how do you find the "zeros".

f(x)=-3(x-2)^2+5
Click here to see answer by rapaljer(4671)

Question 123857: how do you express f(x)=-3(x-2)^2+5 in standard form? What formula do you use?
Click here to see answer by stanbon(75887)

Question 123857: how do you express f(x)=-3(x-2)^2+5 in standard form? What formula do you use?
Click here to see answer by johnnico6426(16)

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