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rapaljer answered: 4664 problems
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1 solutions
Answer 219935 by rapaljer(4667)   on 2010-05-22 19:07:15 (Show Source):
You can put this solution on YOUR website!
Break it down instead of multiplying it out.
Multiply the numbers that are 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, as follows:
For additional explanation on square roots, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 5 for an entire chapter on Square Roots. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
In addition, there is a FREE video of me teaching this topic a few years ago. To see the video, from my Homepage, look for "Rapalje Videos in Living Color." Choose Basic Algebra, and look for the video called "Radicals."
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Equations/307409: y=0.15+0.79 represents the cost of gasoline each year, the line 0.11x-y=-0.85 estimates the cost of gasoline in Janurary of each year. Would the lines be parallel or perpendicular and explain.
1 solutions
Answer 219921 by rapaljer(4667) on 2010-05-22 17:52:13 (Show Source):
You can put this solution on YOUR website!Do you mean y=0.15x+.79?
If so, then the lines are NOT perpendicular or parallel.
The other line is 0.11x-y=-0.85. If you solve for y in this other equation, you get y=0.11x+ 0.85. The slopes of the lines are 0.15 and 0.11. The slopes are NOT the same, so they are NOT parallel. The slopes are NOT the negative reciprocal of one another, so they are NOT parallel.
Dr. Robert J. Rapalje, Retired
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Graphs/307408: given this linear equation y=0.15x+0.79 what is the slope or rate of exchange and what would the y-intercept be and what does it represent.?
1 solutions
Answer 219918 by rapaljer(4667) on 2010-05-22 17:43:22 (Show Source):
You can put this solution on YOUR website!The slope is always the coefficient of x, which in this case is 0.15. The y-intercept is always the value whenever x=0. In this case it is 0.79. The y-intercept is the initial value, or the value when x=0.
Dr. Robert J. Rapalje, Retired
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Travel_Word_Problems/307403: A car is traveling 15 mph faster than a train. In the time it takes the train to travel 135 miles the car travels 180 miles. What is the speed of the car?
I have tried this:
135/x = 180/ x + 5
135x + 675 = 180x
675/45 = 45x/45
15 = x
15 + 15 = 30
30 was not correct.
HELP
1 solutions
Answer 219913 by rapaljer(4667) on 2010-05-22 17:37:13 (Show Source):
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Distributive-associative-commutative-properties/307399: the question is 3x-1=x-7
subtract x from the right side making the equation 2x-1=-7
then add -7 and -1 making the equation 2x=-6
divide 2x and -6 by 2 making the equation x=-3
then plug -3 into the equation as x to check
3(-3)-1=-3-7
-9-1=-10
-10=-10
This shows that -3 is the correct answer for x.
1 solutions
Answer 219911 by rapaljer(4667) on 2010-05-22 17:32:28 (Show Source):
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Triangles/307397: the measure of the shorter parallel side of B is 6 inches and that of the longer side is 8 inches. the height of that figure is 10 inches. what is the area?
1 solutions
Answer 219909 by rapaljer(4667) on 2010-05-22 17:30:08 (Show Source):
You can put this solution on YOUR website!Is this a right triangle, whose hypotenuse is 10 with legs 6 and 8? If so, then the area is  .
 square inches.
Dr. Robert J. Rapalje
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Distributive-associative-commutative-properties/307396: 3x-1=x-7 what is x?
1 solutions
Answer 219904 by rapaljer(4667) on 2010-05-22 17:15:42 (Show Source):
You can put this solution on YOUR website!3x-1=x-7
Get all the x terms on one side by subtracting x from each side of the equation.
3x-x-1=x-x-7
2x-1=-7
Get all the number terms on the right side by adding +1 to each side:
2x-1+1=-7+1
2x=-6
Divide both sides by 2:
For additional explanation on fractional equations, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 1 for Section 1.08 Equation Solving. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Mixture_Word_Problems/307395: How many bags with 0.08 cement should mix with 2 bags of 0.63 cement to produce a mix containing 0.19 cement?
1 solutions
Answer 219902 by rapaljer(4667) on 2010-05-22 17:10:55 (Show Source):
You can put this solution on YOUR website!Let x = amount of .08 cement.
2= amount of .63 cement
x+2 = amount of .19 cement
The equation to solve is
.08x + .63*2= .19(x+2)
.08x + 1.26 =.19x+.38
Subtract .08x from each side:
.08x-.08x + 1.26= .19x-.08x + .38
1.26=.11x + .38
Subtract .38 from each side:
1.26-.38 = .11x+.38-.38
.88=.11x
x=.88/.11= 8 bags
For additional explanation on Word Problems, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 1 for Section 1.11 Word Problems. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Circles/307394:
Point C is the center of the circle. What is the measure of angle ACB if the measure of arc ADB is equal to 201 degrees
1 solutions
Answer 219898 by rapaljer(4667) on 2010-05-22 17:03:14 (Show Source):
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Unit_Conversion_Word_Problems/307378: A jogger runs at an average speed of 5.9mi/hr. If she starts a run at 11:15 am, what time is it after she covers 4.75 x 10^4 ft?
1 solutions
Answer 219893 by rapaljer(4667) on 2010-05-22 16:41:35 (Show Source):
You can put this solution on YOUR website!First I would change the rate of 5.9 mi/hr to feet per minute. To do this multiply by 5280 feet per mile, and divide by 60 to change the hours to minutes.
Rate = 5.9 * 5280/60= 519.2 feet per minute.
Now, the distance to be run is 4.75x10^4 =47500 feet.
Use the formula  to solve for t,  .
 minutes, or 1 hour and 31.48 minutes.
Add this to the starting time of 11:15 a.m., and you get
11:15+ 1:31 = 12:46 p.m. approximately.
Dr. Robert J. Rapalje, Retired
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Polynomials-and-rational-expressions/307390: 10 cm cubed of a normal specimen of human blood contains 12 g of hemoglobin. How many grams does 19 cm cubed of the same blood contain?
I have concluded that 19 cm cubed is 2 times more - 1 less than 1o cm cubed. I have not been able to make a rational expression out of this yet, please help.
1 solutions
Answer 219889 by rapaljer(4667) on 2010-05-22 16:19:27 (Show Source):
You can put this solution on YOUR website!Set up a ratio.
Since  means  ,
the above equation can be written 
 g
For additional explanation on ratio and proportion, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 3 for Section 3.08 Ratio and Proportion. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Polynomials-and-rational-expressions/307386: please 2/x+3+5/x+3=-2/x^2-9
}} I have already gotten the common denominator of x+3 which breaks the equation down to 2+5=-2/x+3 Which I am unsure how to continue to get the solution.
1 solutions
Answer 219888 by rapaljer(4667) on 2010-05-22 16:09:21 (Show Source):
You can put this solution on YOUR website!
Factor the third denominator, and the LCD will be (x+3)(x-3).
Multiply both sides by (x-3)(x+3).
Divide out the factors to clear the denominators:
For additional explanation on fractional equations, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Intermediate Algebra in Chapter 2 for Section 2.07 Fractional Equations. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
In addition, there is a FREE video of me teaching this topic a few years ago. To see the video, from my Homepage, look for "Rapalje Videos in Living Color." Choose Intermediate Algebra, and look for the video called "Fractional and Literal Equations."
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Functions/307366: translate into an algebraic expression. The product of 22% and some number. (Type the percentage as a decimal. Use y to represent some number.)
1 solutions
Answer 219887 by rapaljer(4667) on 2010-05-22 15:37:28 (Show Source):
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Radicals/307350: Problem: sqrt (x+3) = -5
Attempted Solution:
x+3 = 25
x=22
when checking: 5 does not equal -5
1 solutions
Answer 219885 by rapaljer(4667) on 2010-05-22 15:30:12 (Show Source):
You can put this solution on YOUR website!Whenever you solve an equation by SQUARING both sides of an equation, you MUST CHECK the solution to make sure that it works. The solutions obtained by squaring both sides are NOT guaranteed. Actually, the way this problem is originally stated, you have a square root equal to a NEGATIVE. In the real numbers, this CANNOT be, so there is automatically NO SOLUTION!!
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Exponents/307374: (3x+1)^1/2=4 how do you work a fraction as an exponent?
1 solutions
Answer 219884 by rapaljer(4667) on 2010-05-22 15:23:44 (Show Source):
You can put this solution on YOUR website!Raising to the 1/2 power means the same as "square root." In this equation, in order to "undo" the square root, you must SQUARE both sides of the equation.
Check:
It checks!
For additional explanation on fractional exponents, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Intermediate Algebra in Chapter 3 for Section 3.05 Fractional Exponents. There you will find a detailed explanation, and solutions!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Signed-numbers/307324: When solving this problem and using PEMDAS, have I done this correctly?:
36/(-2)^2+4[5-3(8-9)^5]
36/(-2)^2+4[5-3(-1)^5]
36/(-2)^2+4[5-3-1^5]
36/(-2)^2+4[2-1^5]
36/(-2)^2+4[1]
36/-4+4*1
-19*4*1
-76*1=-76
1 solutions
Answer 219883 by rapaljer(4667) on 2010-05-22 15:07:39 (Show Source):
You can put this solution on YOUR website!36/(-2)^2+4[5-3(8-9)^5]
36/(-2)^2+4[5-3(-1)^5]
36/4+4[5-3*(-1)]
9+4[5+3]
9+4*8
9+32
41
For additional explanation on signed numbers and order of operations, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 1 for the appropriate sections. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something. I'm not selling anything. If you get a good explanation, math is usually not as hard as you think it is.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Polynomials-and-rational-expressions/307298: I need explanations and examples on
(1)"H.C.F AND L.C.M OF POLYNOMIALS IN ALGEBRA"
(2)"FACTORISATION IN ALGEBRA"
1 solutions
Answer 219862 by rapaljer(4667) on 2010-05-22 10:15:34 (Show Source):
You can put this solution on YOUR website!I think I have just what you need!! For additional explanation on the many different types of factoring, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic or Intermediate Algebra in Chapter 2 for sections on Factoring. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
To see my FREE video explanation, look for the link on either my Basic OR Intermediate Algebra, and look for the topic of "Factoring."
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something. I'm not selling anything. If you get a good explanation, math is usually not as hard as you think it is.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Functions/307299: find the vertical asymptotes, if any, of the graph of the rational function
h(x)=x+3/x(x+1)
type the equation of the vertical asymptotes
1 solutions
Answer 219860 by rapaljer(4667) on 2010-05-22 10:10:01 (Show Source):
You can put this solution on YOUR website!Vertical asymptotes occur whenever the denominator equals to zero. In this case, the denominator is x(x+1), which equals to zero when x=0 and x=-1. These are the vertical asymptotes.
Dr. Robert J. Rapalje
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Functions/307300: find the vertical asymptotes, if any, of the graph of the rational function
f(x)=x/x^2+8
the equation of the vertical asymptote is
x=
1 solutions
Answer 219859 by rapaljer(4667) on 2010-05-22 10:06:43 (Show Source):
You can put this solution on YOUR website!Vertical asymptotes occur whenever the denominator equals zero. In this case, the denominator is x^2 +8, which NEVER equals zero (in the real numbers), so there are NO vertical asymptotes.
Dr. Robert J. Rapalje
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Functions/307302: find the horizontal asymptote, if any, of the graph of the rational function
g(x)=14x^2/7x^2+2
type the equation of the horizontal asymptote
1 solutions
Answer 219857 by rapaljer(4667) on 2010-05-22 10:03:10 (Show Source):
You can put this solution on YOUR website!Any time the degree of the numerator is EQUAL to the degree of the denominator, which it is in this problem, then the horizontal asymptote is y= a number, where the number is the ratio of the leading coeffients. In this case, it would be y=14/7, or y=2.
Dr. Robert J. Rapalje
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Functions/307301: find the horizontal asymptote, if any, of the graph of the rational function.
f(x)=14x/7x^2+6
type the equation of the horizontal asymptote
1 solutions
Answer 219855 by rapaljer(4667) on 2010-05-22 10:00:26 (Show Source):
You can put this solution on YOUR website!Any time the degree of the numerator is smaller than the degree of the denominator, the horizontal asymptote is the x axis, or y=0.
Dr. Robert J. Rapalje
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Square-cubic-other-roots/307105: Simplify by taking roots of the numerator and the demoninator. Assume that all expressions under radicals represent positive numbers.
The square root of 243x^6/y^20 to the fifth root.
Here is what I have so far: the square root of 243x^6 to the fifth root divided by the square root of 4^20 to the fifth root.
This is the answer that I got but I'm sure it is wrong.
3x^4 x^2 to the fifth root divided by y^4.
1 solutions
Answer 219697 by rapaljer(4667) on 2010-05-21 10:07:20 (Show Source):
You can put this solution on YOUR website!I'm not exactly sure what your problem is. Do you mean the FIFTH root of the given fraction?
That is,  ?
If so, then you are almost correct. Notice that 243 is actually 3^5, and also notice that to be a perfect 5th power, a power must be divisible by 5. I would start by making TWO 5th roots. Place the perfect 5th powers in one 5th root, and leftover factors in the second 5th root.
Sorting it out looks like this:
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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Numbers_Word_Problems/307100: Dachun has five times as many coins as Austin. Dachun also has 16 more than Austin.
1 solutions
Answer 219696 by rapaljer(4667) on 2010-05-21 09:52:24 (Show Source):
You can put this solution on YOUR website!Let D = number of coins of Dachun
A= number of coins of Austin
There are actually two equations:
D= 5A
D= A+ 16
Since both equations are in the form "D=___", they are equal to each other:
5A=A+16
Subtract A from each side:
4A=16
A=4 coins
Solve for D in the first equation:
D=5A
D=5*4=20 coins.
Check in the other equation:
D=A+16
20=4+16 It checks!!
For additional explanation on the many different types of word problems, please see my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Basic Algebra in Chapter 1 for Section 1.10 on Word Problems. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something. I'm not selling anything. If you get a good explanation, math is usually not as hard as you think it is.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
|
Polynomials-and-rational-expressions/307097: Factor the expression: 24q^7-42q^4r+36q^3r^2-63r^3
1 solutions
Answer 219695 by rapaljer(4667) on 2010-05-21 09:45:24 (Show Source):
You can put this solution on YOUR website!This is a classic "Factoring by Grouping" problem. It almost always works out to group the first two terms and the last two terms. In this case, take a common factor of  from the first two terms, and take out a common factor of  from the last two terms.
Did you notice that you now have a COMMON FACTOR of  ? So, take out this common factor, and you have
HOWEVER, there remains a common factor of 3 in the second factor, so now you have to take out this factor:
This is tough grouping problem. If you need to see some additional problems, mostly simpler than this, then you may want to check out my own website. You can find my website by doing a Google search for my name "Dr. Robert J. Rapalje". Look for "Rapalje Homepage", which should be the first item on the search. Once you find my homepage, for a written explanation, click on "Basic, Intermediate, and College Algebra: One Step at a Time." Look in Intermediate Algebra in Chapter 2 for Section 2.01 on Factoring, in particular the part on Factoring by Grouping. There you will find a detailed explanation, and solutions to problems in LIVING COLOR!!
To see my FREE video explanation, look for the link on my homepage called "Rapalje Videos in Living Color." Again, choose Intermediate Algebra (or Basic Algebra also!), and look for the topic of "Factoring."
I have many other topics explained in this way from Basic, Intermediate, and College Algebra. Please check out my website to see what I have. It's all FREE, and if you send me an Email, I'll be glad to help you find something. I'm not selling anything. If you get a good explanation, math is usually not as hard as you think it is.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
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