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 Polynomials-and-rational-expressions/173300: (11x+3y)(x+4y)1 solutions Answer 128137 by jim_thompson5910(28546)   on 2008-12-14 18:11:49 (Show Source): You can put this solution on YOUR website! Start with the given expression. Now let's FOIL the expression. Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms:. Multiply the Outer terms:. Multiply the Inner terms:. Multiply the Last terms:. --------------------------------------------------- Now collect every term to make a single expression. Now combine like terms. So FOILs to . In other words, .
 Equations/173299: how do you solve this problem? x+x _ _ 5 71 solutions Answer 128131 by jim_thompson5910(28546)   on 2008-12-14 17:32:46 (Show Source): You can put this solution on YOUR website! Start with the given expression Take note that the LCD is 35. Multiply the first fraction by Multiply the second fraction by Combine the fractions (this is now possible since the denominators are equal) Add So
 Radicals/173294: how do you solve this problem 2 sq. root 2 + 8 s. root 2- sq. root 21 solutions Answer 128122 by jim_thompson5910(28546)   on 2008-12-14 17:04:54 (Show Source): You can put this solution on YOUR website!Let So the expression becomes Now combine like terms to get . Now replace "z" with to get So
 Equations/173293: how do you solve this problem x+4=x-3 _ _ 2 31 solutions Answer 128121 by jim_thompson5910(28546)   on 2008-12-14 17:02:30 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD 6 to clear the fractions. Simplify. Distribute. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the answer is
Polynomials-and-rational-expressions/173291: Can you please explain the following in full depth:
3x^2+26xy+16y^2

1 solutions

Answer 128119 by jim_thompson5910(28546)   on 2008-12-14 16:54:55 (Show Source):
You can put this solution on YOUR website!

Looking at we can see that the first term is and the last term is where the coefficients are 3 and 16 respectively.

Now multiply the first coefficient 3 and the last coefficient 16 to get 48. Now what two numbers multiply to 48 and add to the middle coefficient 26? Let's list all of the factors of 48:

Factors of 48:
1,2,3,4,6,8,12,16,24,48

-1,-2,-3,-4,-6,-8,-12,-16,-24,-48 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 48
1*48
2*24
3*16
4*12
6*8
(-1)*(-48)
(-2)*(-24)
(-3)*(-16)
(-4)*(-12)
(-6)*(-8)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to 26? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 26

First NumberSecond NumberSum
1481+48=49
2242+24=26
3163+16=19
4124+12=16
686+8=14
-1-48-1+(-48)=-49
-2-24-2+(-24)=-26
-3-16-3+(-16)=-19
-4-12-4+(-12)=-16
-6-8-6+(-8)=-14

From this list we can see that 2 and 24 add up to 26 and multiply to 48

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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

So factors to

 Square-cubic-other-roots/173280: I really messed up posting this the last time so I will try again please bare with me 4/(root(3,5x^2)1 solutions Answer 128114 by jim_thompson5910(28546)   on 2008-12-14 16:49:45 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply the fraction by twice (to get a total of 3 copies of in the denominator) Now notice how So let's replace the denominator with Now multiply out to get So replace the the numerator with Reduce to get ================================================================== Answer: So simplifies to In other words, where
 Square-cubic-other-roots/173283: I need to simplify this problem can you help? sqrt-100/sqrt-25 I got the answer of 2 should it be negitive?1 solutions Answer 128109 by jim_thompson5910(28546)   on 2008-12-14 16:40:04 (Show Source):
 Polynomials-and-rational-expressions/173284: I need to simplify this problem(5-2i)^2 I do not know if I did it right but the answer I got was 25-16i was I close?1 solutions Answer 128105 by jim_thompson5910(28546)   on 2008-12-14 16:34:46 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand FOIL. Multiply. Replace with . Note: . Multiply. Combine like terms. So . So the expression is now in standard form where and
 Equations/173285: 2=(10+Z)/-3 Can you give me step by step instructions on how to solve this. I know the answer is Z=-16, but not sure of how to arrive at it. Thanks. 1 solutions Answer 128103 by jim_thompson5910(28546)   on 2008-12-14 16:32:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by -3. Multiply. Subtract 10 from both sides. Subtract. ============================================= Answer: So the solution is
 Radicals/173273: heres another radical problem I'm not sure of, can you help check my answer?2+sqrt(5)/4+3sqrt(5) the answer I got was 7+2sqrt(5)/291 solutions Answer 128095 by jim_thompson5910(28546)   on 2008-12-14 15:48:31 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by (which is the conjugate of the denominator) Combine the fractions. FOIL the numerator. FOIL the denominator. Multiply. Square to get 5. Multiply. Combine like terms. Reduce So . So you are correct.
 Trigonometry-basics/173275: This question is from textbook Algebra and trigonometry (27^4)^-1/121 solutions Answer 128092 by jim_thompson5910(28546)   on 2008-12-14 15:34:56 (Show Source): You can put this solution on YOUR website! So
 Geometry_proofs/173265: Given: Segment CS and segment AT are altitudes; Segment CS is congruent to segment AT Prove: Segment AS is congruent to segment CT Use this diagram to help you: http://i164.photobucket.com/albums/u27/foxymccloud/geometry.jpg1 solutions Answer 128091 by jim_thompson5910(28546)   on 2008-12-14 15:29:09 (Show Source): You can put this solution on YOUR website! Statement Reason ----------------------------------------------------------------------- 1. Angle ASC is right angle Definition of Altitude (given) 2. Angle ATC is right angle Definition of Altitude (given) 3. Angle ATC = Angle ASC Right Angle Theorem 4. CS = AT Given 5. AC = AC Reflexive Property of Congruence 6. triangle ASC = triangle ATC SAS Postulate 7. AS = CT CPCTC  Notes: # 1 Remember, an altitude is a segment that runs from one vertex to the opposite side (and forms a 90 degree angle with the opposite side). # 2 The Right Angle Theorem states that all right angles are congruent. # 3 CPCTC = Corresponding parts of congruent triangles are congruent.
 Coordinate-system/173255: This question is from textbook how can you write an equation of the line that connects points (-3,7) and (4,2)?1 solutions Answer 128083 by jim_thompson5910(28546)   on 2008-12-14 14:54:45 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Add 7 to both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is
 Equations/173252: -x = -36 what is x1 solutions Answer 128077 by jim_thompson5910(28546)   on 2008-12-14 14:25:36 (Show Source): You can put this solution on YOUR website! Start with the given equation. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Proofs/173249: I can't seem to get to solve this proof. 1. W->S 2. U->F 3. (S and F) -> O 4. ~O THEREFORE (~W v ~U)1 solutions Answer 128073 by jim_thompson5910(28546)   on 2008-12-14 14:14:10 (Show Source): You can put this solution on YOUR website!1. W->S 2. U->F 3. (S and F) -> O 4. ~O THEREFORE (~W v ~U) ------------------------------ 5. ~(S and F) .......................... Modus Tollens (using lines 3, 4) 6. ~S v ~F .......................... DeMorgan's Theorem (using line 5) 7. S -> ~F .......................... Material Implication (using line 6) 8. W -> ~F .......................... Hypothetical Syllogism (using lines 1,7) 9. ~F -> ~U .......................... Transposition (using line 2) 10. W -> ~U .......................... Hypothetical Syllogism (using lines 8,10) 11. ~W v ~U .......................... Material Implication (using line 10)
 Polynomials-and-rational-expressions/173199: This question is from textbook Introductory Algebra Divide and, if possible, simplify. x^2 + 7x + 10/x + 5 divided by x^2 - 4/5x - 101 solutions Answer 128071 by jim_thompson5910(28546)   on 2008-12-14 13:57:58 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the first fraction by the reciprocal of the second fraction . Factor to get . Factor to get . Factor to get . Combine the fractions. Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where , or
 Triangles/173177: Can you please help me with this question: The altitudes of a triangle are concurrent at a point called the _________? (1)centroid (2)circumcenter (3)incenter (4)orthocenter 1 solutions Answer 128067 by jim_thompson5910(28546)   on 2008-12-14 13:49:34 (Show Source): You can put this solution on YOUR website!The altitudes of a triangle are concurrent at a point called the orthocenter.
 Linear-systems/173188: This question is from textbook algebra2 -4x+y=-5 2x+y=71 solutions Answer 128066 by jim_thompson5910(28546)   on 2008-12-14 13:47:40 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the second equation by 2. Distribute and multiply. So we have the new system of equations: Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this: Group like terms. Combine like terms. Notice how the x terms cancel out. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So our answer is and . Which form the ordered pair . This means that the system is consistent and independent. Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer. Graph of (red) and (green)
 Polynomials-and-rational-expressions/173191: This question is from textbook Introductory Algebra Factor by grouping x^3 - 8x^2 + 5x - 401 solutions Answer 128065 by jim_thompson5910(28546)   on 2008-12-14 13:45:57 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms So factors to
Polynomials-and-rational-expressions/173192: This question is from textbook Introductory Algebra
Factor completely
4x^3 + 4x^2 - 80x
1 solutions

Answer 128064 by jim_thompson5910(28546)   on 2008-12-14 13:44:32 (Show Source):
You can put this solution on YOUR website!

Factor out the GCF

Now let's focus on the inner expression

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

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -20 respectively.

Now multiply the first coefficient 1 and the last coefficient -20 to get -20. Now what two numbers multiply to -20 and add to the middle coefficient 1? Let's list all of the factors of -20:

Factors of -20:
1,2,4,5,10,20

-1,-2,-4,-5,-10,-20 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -20
(1)*(-20)
(2)*(-10)
(4)*(-5)
(-1)*(20)
(-2)*(10)
(-4)*(5)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1

First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=1

From this list we can see that -4 and 5 add up to 1 and multiply to -20

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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

So our expression goes from and factors further to

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

So factors to

 Linear-equations/173208: What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)? What is the equation in standard form that passes through the point (-2,6) and has a slope of 4?1 solutions Answer 128060 by jim_thompson5910(28546)   on 2008-12-14 13:34:20 (Show Source): You can put this solution on YOUR website!# 1 Problem: What is the equation in slope intercept form of the line that passes through (5,-7) and (2,1)? Solution: First let's find the slope of the line through the points and Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is Now let's use the point slope formula: Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Subtract 7 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. Simplify So the equation that goes through the points and is # 2 Problem: What is the equation in standard form that passes through the point (-2,6) and has a slope of 4 Solution: If you want to find the equation of line with a given a slope of which goes through the point (-2,6), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get Subtract from both sides. Add 6 to both sides. Combine like terms. Multiply EVERY term by -1 to make the "x" coefficient positive. ----------------------------------- Answer: So the equation in standard form that has a slope of 4 and passes through the point (-2,6) is
Distributive-associative-commutative-properties/173210: Factorize 10x^2-x-3
1 solutions

Answer 128058 by jim_thompson5910(28546)   on 2008-12-14 13:27:02 (Show Source):
You can put this solution on YOUR website!

Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .

Now multiply the first coefficient by the last term to get .

Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?

To find these two numbers, we need to list all of the factors of (the previous product).

Factors of :
1,2,3,5,6,10,15,30
-1,-2,-3,-5,-6,-10,-15,-30

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*(-30)
2*(-15)
3*(-10)
5*(-6)
(-1)*(30)
(-2)*(15)
(-3)*(10)
(-5)*(6)

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First NumberSecond NumberSum
1-301+(-30)=-29
2-152+(-15)=-13
3-103+(-10)=-7
5-65+(-6)=-1
-130-1+30=29
-215-2+15=13
-310-3+10=7
-56-5+6=1

From the table, we can see that the two numbers and add to (the middle coefficient).

So the two numbers and both multiply to and add to

Now replace the middle term with . Remember, and add to . So this shows us that .

Replace the second term with .

Group the terms into two pairs.

Factor out the GCF from the first group.

Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.

Combine like terms. Or factor out the common term

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

So factors to .

Note: you can check the answer by FOILing to get or by graphing the original expression and the answer (the two graphs should be identical).

Miscellaneous_Word_Problems/173173: This question is from textbook
Can someone explain this to me and show step by step so I can have a better understand of this problem thank you so much.
True or false: The function "f(x) = 3x" grows three times faster than the function "g(x) = x". Explain.

thank you so much

1 solutions

Answer 128052 by jim_thompson5910(28546)   on 2008-12-14 13:12:58 (Show Source):
You can put this solution on YOUR website!
I'm assuming that the first function is

If , then and .

If , then and .

If , then and .

If , then and .

So we have this table of values

xf(x)g(x)
010
131
292
3273

From the table, we can see that increments by 1 as x increments by 1. On the other hand, we can see that goes from 1 to 3 (a difference of 2), 3 to 9 (a difference of 6), 9 to 27 (a difference of 18), etc. So the differences between each term is: 2, 6, 18, etc....

This means that from x=0 to x=1, the average rate of change for g(x) is 2. From x=1 to x=2, the average rate of change for g(x) is 6. From x=2 to x=3, the average rate of change for f(x) is 18.

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

So dividing the first average rate of change 2 by 1, we get . So from x=0 to x=1, is growing twice as fast as .

Dividing the second average rate of change 6 by 1, we get . So from x=1 to x=2, is growing six times as fast as .

Dividing the third average rate of change 18 by 1, we get . So from x=2 to x=3, is growing eighteen times as fast as .

As you can see, the exponential function is not growing at a constant rate. So cannot be growing 3 times faster than

Note: the function does however grow three times faster than , but that is for another problem.

So that means that the statement is false.

 Inequalities/173180: This question is from textbook Introductory Algebra Solve using the addition and multiplication principles. 4z - 3 > 3z - 131 solutions Answer 128051 by jim_thompson5910(28546)   on 2008-12-14 13:11:27 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the answer is
 Complex_Numbers/173218: What does the product (4+7i)(2-5i) equal? What does the quotient (1+4i)/(5-2i) equal?1 solutions Answer 128050 by jim_thompson5910(28546)   on 2008-12-14 13:07:53 (Show Source): You can put this solution on YOUR website!# 1 Start with the given expression. FOIL. Multiply. Replace with . Note: . Multiply. Combine like terms. So . So the expression is now in standard form where and # 2 Start with the given expression. Multiply the fraction by (which is the complex conjugate of the denominator). Combine the fractions. FOIL the numerator. FOIL the denominator. Multiply. Combine like terms. Break up the fraction. So . So the expression is now in standard form where and
 Equations/173221: I need help on the equation 2(6d+3)= 18 - 3(16 - 3d)1 solutions Answer 128048 by jim_thompson5910(28546)   on 2008-12-14 13:00:02 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Quadratic_Equations/173222: Use completing the square to solve x²+8x-11=01 solutions Answer 128047 by jim_thompson5910(28546)   on 2008-12-14 12:57:46 (Show Source): You can put this solution on YOUR website! Start with the given left side of the given equation. Take half of the coefficient to get . In other words, . Now square to get . In other words, Now add and subtract . Make sure to place this after the "x" term. Notice how . So the expression is not changed. Group the first three terms. Factor to get . Combine like terms. So after completing the square, transforms to . So . So is equivalent to . ------------------------------------------------------------ Start with the given equation. Add to both sides. Combine like terms. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Simplify the square root. or Subtract from both sides. -------------------------------------- Answer: So the solutions are or .