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rapaljer answered: 4664 problems
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The quadratic function that models the fireworks’ height s(x) in feet x seconds after they are launched is given by the equation s(x) = -16x^2+200x + 4. When should the fireworks explode so that they go off at the greatest height? What is that height? [Hint: Find the vertex of the quadratic function s(x).]
1 solutions
Answer 63649 by rapaljer(4667)   on 2007-07-09 20:23:32 (Show Source):
You can put this solution on YOUR website!The vertex of the parabola  occurs at  .
Therefore, for your function  , the vertex occurs at  seconds.
The maximum height is at  feet. By the way, I used a graphing calculator, with window: x= [-2,14], y = [-100, 700]. It looks like this:
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Radicals/87661: This question is from textbook algebra structure and method
I'm supposed to put this in simplest radical form.
6square of 7*3square root of 5
could you explain how would I do this.
Thanks
1 solutions
Answer 63625 by rapaljer(4667) on 2007-07-09 13:37:48 (Show Source):
You can put this solution on YOUR website!
Multiply the numbers outside the square root and keep them outside the square root. Multiply the numbers that are inside the square root and keep them inside the square root.
Also, see my lesson plans on square roots in the algebra.com lesson plans. See also my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for MATH IN LIVING COLOR, "Basic Algebra", then "Chapter 5" topics.
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Polynomials-and-rational-expressions/87716: Hello. My question is based on common monomial factors. The directions state: "Find the greatest common factor and factor it out of the expression."
The question is:
15x^5-10x^4+5x^2
Thanks.
1 solutions
Answer 63614 by rapaljer(4667) on 2007-07-09 12:51:31 (Show Source):
You can put this solution on YOUR website!
The greatest common factor is the largest factor that divides evenly into all three terms. In this case it would be  .
What is left is this:
You should probably see my detailed explanation on my own website. Click on my tutor name "rapaljer" anywhere in algebra.com. Look for the topic called "Basic Algebra", then "Samples from Basic Algebra: One Step at a Time", go to Chapter 2, and look for "Section 2.03 Factoring the Common Factor".
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test/87701: Question 87686: Which does not represent a possible intersection of a line and a rectangle?: Which does not represent a possible intersection of a line and a rectangle?
0 points
1 point
2 points
3 points
1 solutions
Answer 63608 by rapaljer(4667) on 2007-07-09 12:38:06 (Show Source):
You can put this solution on YOUR website!A line can intersect a rectangle in no points by not crossing it at all, in one point by just touching the corner of the rectangle, or in two points by crossing the rectangle. It cannot cross in three points.
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test/87706: Which of the following applies to the graph of 3x - y = 9?
The choices are:
m = -3, passes through (9, 0)
m = 3, y-intercept = -9
m = -3, x-intercept = -9
m = 1/3, passes through (0,-9)
1 solutions
Answer 63605 by rapaljer(4667) on 2007-07-09 12:30:18 (Show Source):
You can put this solution on YOUR website!You must solve for y to determine the slope and y-intercept:
3x - y = 9
Add -3x to each side:
3x-3x -y=-3x + 9
-y = -3x +9
Divide both sides by -1
Y intercept is -9, and the slope is 3.
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test/87702: Identify the equation of the line having a slope of -3 and a y-intercept of 7.
1 solutions
Answer 63602 by rapaljer(4667) on 2007-07-09 12:25:15 (Show Source):
You can put this solution on YOUR website!Given slope of -3 and a y-intercept of 7.
The equation of a line is y = mx+b, where m = slope of the line, and b = y-intercept.
The equation of the line is  .
You should see my Lesson Plan in algebra.com called "Graphing and Slope of a Line" in Graphs topic.
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Exponents/87669: Factor: 16x^4 – 2xy^3
It has been a while since I had Algebra, Trig, etc.
1. How do you express (say) this sequence above?
2. What is the answer?
3. Finally, please direct me to the appropriate page on your web site where I might be able to learn a little more about this, and perhaps "brush up" on what I have forgot?
Many, many thanks for your assistance,
Sam Genovese
1 solutions
Answer 63599 by rapaljer(4667) on 2007-07-09 12:20:00 (Show Source):
You can put this solution on YOUR website!
The first step is to factor out the common factor:
Now, this is the difference of two cubes. There is a formula that goes like this:
Notice that this factors into a binomial times a trinomial. The binomial is pretty simple, but the trinomial is a bit harder. If you have never seen this before, you should see my website, which I will mention later.
Use this formula to factor as follows:
See my website by clicking on my tutor name "rapaljer" anywhere in algebra.com, then look for MATH IN LIVING COLOR, go to Intermediate Algebra, and look for Section 2.01 Factoring the Sum and Difference of Cubes.
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test/87687: Which of the following is the equation in slope-intercept form of the line that passes through (0, 2) and has a slope of -3.
1 solutions
Answer 63587 by rapaljer(4667) on 2007-07-09 11:36:41 (Show Source):
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test/87694: Which does not represent a possible intersection of a line and a triangle?:
0 points
1 point
2 points
3 points
1 solutions
Answer 63585 by rapaljer(4667) on 2007-07-09 11:34:22 (Show Source):
You can put this solution on YOUR website!In two dimensions, a line can intersect a triangle in NO points if the line is above or below the triangle and it does not intersect it at all. It can intersect the triangle in ONE point if it just touches a vertex of the triangle. The line can intersect the triangle in TWO points if it crosses the triangle. However, a line CANNOT intersect the triangle in THREE points.
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test/87692: Determine the coordinates of the midpoint of the line segment whose endpoints are A(0, 2, 4) and B(-8, 2, -6).
1 solutions
Answer 63583 by rapaljer(4667) on 2007-07-09 11:28:41 (Show Source):
You can put this solution on YOUR website!To find the midpoint of any point, no matter how many dimensions, just add the corresponding coordinates together and divide by 2.
A(0, 2, 4) and B(-8, 2, -6)
Midpoint x =  , y=  , z= 
(-4,2,-1)
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test/87691: Find the coordinate of the image of point (1, 2) translated left 2 units and reflected over the x-axis.
1 solutions
Answer 63579 by rapaljer(4667) on 2007-07-09 11:16:59 (Show Source):
You can put this solution on YOUR website!(1, 2) translated left 2 units and reflected over the x-axis.
2units left, means subtract 2 from the x coordiate.
Reflected over the x-axis means to take the negative of the y coordinate.
This would be (-1,-2).
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expressions/87660: [m] = 3m if m is odd
[m] = 1/2m if m is even
[9]x[6] is equivalent to
a. 81
b. 54
c. 27
d. 18
e. 6 (can't remember)
answer is 27 but I don't have explanation from practice test
1 solutions
Answer 63572 by rapaljer(4667) on 2007-07-09 09:23:11 (Show Source):
You can put this solution on YOUR website!I'm sorry, but I get the answer of 81.
[m] = 3m if m is odd
[m] = 1/2m if m is even
Since 9 is odd, [9]=3*9=27
Since 6 is even, [6]= 1/2*6 = 3
[9]x[6] is equivalent to 27x3 = 81.
Maybe the answer is wrong. You may want to re-post this question and see if anyone else has a different idea about it.
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Numbers_Word_Problems/87658: Help a mother teaching her son Algebra
The story problem is Jose was taking a trip from point a to point b, on the way there, he drove 45mph. On the way back, he drove the same distance at 50mph and got back 20 minutes faster. What was the distance for point a to point b. (The equations that I came up with was 45x=50x-20 to get the time but I know that it is not totally correct. I came up with 180 miles but the answer in the teachers guide is 150. Don't know how they got it.)
1 solutions
Answer 63571 by rapaljer(4667) on 2007-07-09 09:17:05 (Show Source):
You can put this solution on YOUR website!The equation is that Distance going = Distance returning.
Let t = time (in hours) of the return trip
t+1/3 = time going
50 MPH = rate of the return
45 MPH = rate going
Distance going = Distance returning
RT = RT
45(t+1/3) = 50(t)
45t + 15= 50t
15= 50t-45t
15=5t
t= 3 hours
Distance = 3*50= 150 miles
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Problems-with-consecutive-odd-even-integers/87656: Find two consecutive integers whose product is 15 less than the square of the smaller number.
1 solutions
Answer 63570 by rapaljer(4667) on 2007-07-09 09:06:26 (Show Source):
You can put this solution on YOUR website!Let x = smaller of the consecutive integers
x+1 = larger of the consecutive integers
Please see my Lesson Plans on Word Problems in algebra.com. Also, see my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Look for the page called "MATH IN LIVING COLOR", then go to "Basic Algebra", and look in Chapter 1 for "Word Problems".
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test/87604: Identify a counterexample for the conjuncture If the sum of two integers is even, then both integers are even.
1 solutions
Answer 63569 by rapaljer(4667) on 2007-07-09 09:00:59 (Show Source):
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logarithm/87655: If log (p+q) = log p- log q, show that p(1-q)=q^2
1 solutions
Answer 63568 by rapaljer(4667) on 2007-07-09 08:58:12 (Show Source):
You can put this solution on YOUR website!Remember the law of logarithms:  .
Therefore, if you are given that  ,
then replace the right side as follows: 
Take the antilog of each side and it looks like this: 
Muliply both sides by q: 
Subtract pq from each side:
Factor the right side:
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Radicals/87483: Solve the radical equation (2x-1)^1/2=x-2
1 solutions
Answer 63541 by rapaljer(4667) on 2007-07-09 00:43:50 (Show Source):
You can put this solution on YOUR website!
Square both sides:
It's a quadratic equation, so set equal to zero by subtracting 2x and adding +1 to each side of the equation:
Which FACTORS!! (They all do when solving radical equations!!)
 or 
Answers are NOT guaranteed, so you need to check the answers in the original equation to see if they work!
x=5
 It checks!!
x=1
 Reject. This does NOT check!!
The answer is x=5.
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Miscellaneous_Word_Problems/87617: Please i need help with this problem:
The water level of a swimming pool, 75 feet by 42 feet, is to be raised 4 inches. The number of gallons of water needed for this purpose is....
(1 cubic foot equals 7 1/2 gallons)
1 solutions
Answer 63538 by rapaljer(4667) on 2007-07-09 00:12:41 (Show Source):
You can put this solution on YOUR website!Volume of water needed = 75 feet by 42 feet by 4 inches.
V= 75*42*1/3=1050 cubic feet
Convert to gallons by multiplying by 7.5 gallons per cubic foot
V= 1050*7.5 = 7875 gallons.
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Miscellaneous_Word_Problems/87635: Please i need help on this question:
Under certain conditions, sound travels at about 1100 ft. per second. If 88 ft. per second is approximately equivalent to 60 miles per hour, the speed of sound, under the above conditions, is, of the following, closest to:
A. 730 miles per hour B. 740 miles per hour C. 750 miles per hour
D. 760 miles per hour
1 solutions
Answer 63536 by rapaljer(4667) on 2007-07-09 00:08:15 (Show Source):
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Travel_Word_Problems/87634: The time, t, in seconds, for a free-falling object to fall d feet is modeled by the formula t=(d/16)^1/2
How many feet will a skydiver fall in 10 seconds?
1 solutions
Answer 63532 by rapaljer(4667) on 2007-07-08 23:58:11 (Show Source):
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Radicals/87636: solve the radical equation (2x-1)^1/2=x-2
1 solutions
Answer 63530 by rapaljer(4667) on 2007-07-08 23:54:18 (Show Source):
You can put this solution on YOUR website!
Square both sides:
It's a quadratic equation, so set equal to zero by subtracting 2x and adding +1 to each side of the equation:
Which FACTORS!! (They all do when solving radical equations!!)
or
Answers are NOT guaranteed, so you need to check the answers in the original equation to see if they work!
x=5
It checks!!
x=1
Reject. This does NOT check!!
The answer is x=5.
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Miscellaneous_Word_Problems/87637: Please i need help on this question:
Of the following, the most nearly accurate set of equivalents is:
A. 1ft. equals 30.48 centimeters B. 1 centimeter equals 2.54 inches
C. 1 rod equals 3.28 meters D. 1 meter equals 1.09 feet
1 solutions
Answer 63528 by rapaljer(4667) on 2007-07-08 23:44:41 (Show Source):
You can put this solution on YOUR website!Of your 4 choices:
A. 1ft. equals 30.48 centimeters --TRUE, since 12*2.54 = 30.48 cm.
B. 1 centimeter equals 2.54 inches FALSE--1 inch = 2.54 cm.
C. 1 rod equals 3.28 meters -- I have no idea!! Do a Google search for "Unit of Measure Rod" and see what you get!
D. 1 meter equals 1.09 feet--FALSE, since a meter is slightly more than a yard (which is 3 feet!)
My answer is A.
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