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 Linear-equations/246357: What is the slope of any line parallel to the line 9x + 4y = 7 ? since 4y=-9x+7 i think its -9/4 but iam not even sure how i got that im so lost please explain it to me thanks1 solutions Answer 179954 by jim_thompson5910(28595)   on 2009-12-06 14:39:29 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. So the equation is now in slope intercept form where the slope is and the y-intercept is note: the y-intercept is the point
 Trigonometry-basics/246385: Find all solutions of the equation in the interval [0,2π) algebraically. Sec^2 x - sec x =2 what are the steps to do this problem? how do i start? 1 solutions Answer 179953 by jim_thompson5910(28595)   on 2009-12-06 14:36:26 (Show Source): You can put this solution on YOUR website!Hint: Let . So which means that the equation becomes . Use the quadratic formula to solve for 'z'. Once you have the solutions in terms of z, use them to find the solutions in terms of x.
Divisibility_and_Prime_Numbers/246393: Hi! i'm having some trouble with Prime Numbers. Here is my question
Write 270 as a product of prime numbers
1 solutions

Answer 179952 by jim_thompson5910(28595)   on 2009-12-06 14:34:08 (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factor any number
270 is NOT a prime number: 270 = 2 * 3 * 3 * 3 * 5

### Work Shown

270 is divisible by 2: 270 = 135 * 2.
135 is divisible by 3: 135 = 45 * 3.
45 is divisible by 3: 45 = 15 * 3.
15 is divisible by 3: 15 = 5 * 3.
5 is not divisible by anything.


This calculation used this Prime Factorization Algorithm.

 Complex_Numbers/246256: Find the complex number z = a + bi such that z^3= 2 + 2i where a is less than or equal to 0 and b is greater than or equal to 0. I really don't know how to approach this question but I'm guessing you have to use the definition (a + bi)(c + di) = (ac-bd)+(ad+bc)i? 1 solutions Answer 179881 by jim_thompson5910(28595)   on 2009-12-06 02:02:09 (Show Source): You can put this solution on YOUR website!Hint: Convert the complex number into polar form where 'r' is the magnitude and 'x' is the angle. From there, use a variation of De Moivre's Theorem. Let me know if this helps or not.
 Probability-and-statistics/246255: Compute each of the following. Look for simplifications first. a. 20P15 (the 20 and the 15 are small)It's looking for the permutation?? b. (n+1)! ------ (n-1)! Thank you so much in advance. This is so difficult. ~Marney 1 solutions Answer 179880 by jim_thompson5910(28595)   on 2009-12-06 01:58:40 (Show Source): You can put this solution on YOUR website!a) Start with the given formula Plug in and Subtract to get 5 Expand 20! Expand 5! Cancel Simplify Now multiply 20*19*18*17*16*15*14*13*12*11*10*9*8*7*6 to get 20,274,183,401,472,000 ================================================================ b) ... Start with the given expression. ... Expand the numerator. Remember that n! = n(n-1)(n-2)(n-3)...(3)(2)(1). So (n+1)! = (n+1)(n+1-1)(n+1-2)(n+1-3)(n+1-4)...(3)(2)(1) ... Combine like terms. ... Take note that (n-1)! = (n-1)(n-2)(n-3)...(3)(2)(1) which is what the numerator (minus the first two terms) looks like. So rewrite (n-1)(n-2)(n-3)...(3)(2)(1) as (n-1)! Note: if you're asking 'Why did we just do that?' The goal is to cancel out the factorials. Since the denominator has a (n-1)! term, we just need that term in the numerator for it to cancel out. ... Cancel out the common terms. ... Rearrange the terms. ... Distribute So where 'n' is an integer and
 Graphs/246061: Solve each system by addition x+y = 7 x-y =91 solutions Answer 179768 by jim_thompson5910(28595)   on 2009-12-05 14:15:16 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: 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. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Subtract from both sides. Combine like terms on the right side. So the solutions are 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)
 Functions/246034: consider the functions f(x)=-x^2+3x+10 and g(x)=2x^2+2x+11/4. what is the exact distance between the vertices of the graphs of these two functions? cannot use graphing to answer. hopefully this will be my last question of the year.1 solutions Answer 179698 by jim_thompson5910(28595)   on 2009-12-05 02:01:55 (Show Source): You can put this solution on YOUR website!Part 1) Find the vertices of and part a) Let's find the vertex of In order to find the vertex, we first need to find the x-coordinate of the vertex. To find the x-coordinate of the vertex, use this formula: . Start with the given formula. From , we can see that , , and . Plug in and . Multiply 2 and to get . Reduce. So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also . Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex. Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the y-coordinate of the vertex is . So the vertex is . ------------------------ b) Now let's find the vertex of In order to find the vertex, we first need to find the x-coordinate of the vertex. To find the x-coordinate of the vertex, use this formula: . Start with the given formula. From , we can see that , , and . Plug in and . Multiply 2 and to get . Reduce. So the x-coordinate of the vertex is . Note: this means that the axis of symmetry is also . Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex. Start with the given equation. Plug in . Square to get . Multiply and to get . Multiply and to get . Combine like terms. So the y-coordinate of the vertex is . So the vertex is . -------------------------------------------------- So to recap, the vertices of and are and respectively. =============================================================== Part 2) Now use the distance formula to find the distance between the two vertices (which are essentially points) Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . Simplify the square root. So our answer is So the exact distance between the two vertices is units.
Polynomials-and-rational-expressions/245969: I was wondering if you could show me how to factor this equation: 7a2+53a+28
This is the work I got to but then I could go no father.
I used the x-box to find the answer.
After the x-box I got
(a+7)(7a+7)
7a2+56a+28 which does not equal the original question.
(when it says 7a2 it means 7 times a squared)
1 solutions

Answer 179649 by jim_thompson5910(28595)   on 2009-12-04 18:40:11 (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 :
1,2,4,7,14,28,49,98,196
-1,-2,-4,-7,-14,-28,-49,-98,-196

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

These factors pair up and multiply to .
1*196 = 196
2*98 = 196
4*49 = 196
7*28 = 196
14*14 = 196
(-1)*(-196) = 196
(-2)*(-98) = 196
(-4)*(-49) = 196
(-7)*(-28) = 196
(-14)*(-14) = 196

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

First NumberSecond NumberSum
11961+196=197
2982+98=100
4494+49=53
7287+28=35
141414+14=28
-1-196-1+(-196)=-197
-2-98-2+(-98)=-100
-4-49-4+(-49)=-53
-7-28-7+(-28)=-35
-14-14-14+(-14)=-28

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 .

In other words, .

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

 Trigonometry-basics/245808: Use Descartes' Rule of Sign to determine how many positive and negative zeros each polynomial function may have. 1 solutions Answer 179612 by jim_thompson5910(28595)   on 2009-12-04 16:08:26 (Show Source): You can put this solution on YOUR website! First count the sign changes of From to , there is a sign change from negative to positive From to , there is no change in sign From to , there is no change in sign From to , there is no change in sign So there is 1 sign change for the expression . So there is 1 positive zero. ------------------------------------------------ Now let's replace each with Simplify Now let's count the sign changes of From to , there is no change in sign From to , there is a sign change from positive to negative From to , there is no change in sign From to , there is a sign change from negative to positive So there are 2 sign changes for the expression . So there are 2 or 0 negative zeros
 Systems-of-equations/245919: Is each equation a direct variation? If it is, find the constant of variation. y=5x1 solutions Answer 179610 by jim_thompson5910(28595)   on 2009-12-04 16:01:54 (Show Source): You can put this solution on YOUR website!Yes it is an equation of direct variation since it is of the form where 'k' is the constant of variation. Looking at the equation, we see that the constant of variation is
 Square-cubic-other-roots/245743: how do u factor x^3+64 and what are the roots of the polynomials?1 solutions Answer 179466 by jim_thompson5910(28595)   on 2009-12-04 00:28:26 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as . Rewrite as . Now factor by using the sum of cubes formula. Remember the sum of cubes formula is Multiply ----------------------------------- Answer: So factors to . In other words, So to find the roots of , just find the roots of . In other words, solve the equation:
 Quadratic_Equations/245751: I need to find the zeros of f(x)=x^2+2ix-3. I tried using the quadratic equation, but the i is confusing me. Help?1 solutions Answer 179460 by jim_thompson5910(28595)   on 2009-12-04 00:03:34 (Show Source): You can put this solution on YOUR website!Just treat this quadratic as you normally would, but make sure to follow the rules of complex arithmetic. Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Square to get Note: Since , Multiply -4, 1 and -3 to get Multiply 2 and 1 to get 2. Combine like terms. Simplify the square root. Reduce. or Break up the 'plus/minus' So the solutions are or
 Equations/245698: solve: 9/5=3x+9/151 solutions Answer 179414 by jim_thompson5910(28595)   on 2009-12-03 21:05:35 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Linear-equations/245694: I need help with this problem 2y=7, I need to change the equation to slope-intercept form. I tried dividing both sides by 2 but, I'm missing m and b. The slope-intercept form form is y=mx+b. Thanks for your help! Ivelisse1 solutions Answer 179413 by jim_thompson5910(28595)   on 2009-12-03 21:04:34 (Show Source): You can put this solution on YOUR website!It is possible for 'm' to be equal to zero. You're on the right track. If you divide both sides by 2, you get which is in form where and . If you can't see it, then write as (which is perfectly valid).
 expressions/244936: Please simplify 6(r+1)-2+2(r-5)= Also (x^2+3x-2)-(x^2-2x-5)= Thanks!1 solutions Answer 179111 by jim_thompson5910(28595)   on 2009-12-02 13:13:43 (Show Source): You can put this solution on YOUR website!I'll do the first one to get you started. # 1 So
 Exponential-and-logarithmic-functions/245000: find the inverse of log(base 2) (x^5) when i worked it out i got 2^x^5....but i didnt know if that could be simplified any further? 1 solutions Answer 179110 by jim_thompson5910(28595)   on 2009-12-02 13:08:23 (Show Source): You can put this solution on YOUR website!Let . Now swap x and y to get . The goal here is to solve for y. Start with the given equation. Convert to exponential form. Take the 5th root of both sides to isolate 'y' So the inverse is
 logarithm/244987: x=12^(log base 12 of 5) I think that's the same as: x=12^(5 log base 12), but I'm just trying to follow previous patterns and I'm lost1 solutions Answer 179109 by jim_thompson5910(28595)   on 2009-12-02 13:05:57 (Show Source): You can put this solution on YOUR website!It turns out that . In this problem, it's useful to know . In this case, a=12 and b=5. So which means that the answer is
 Exponential-and-logarithmic-functions/244839: I don't know where to start on this one. I know it should be a log, but don't know how to set it up.1 solutions Answer 179004 by jim_thompson5910(28595)   on 2009-12-01 22:52:21 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the log of both sides. Evaluate the log base 10 of 100 to get 2. Break up the log using the identity Pull down the exponents using the identity Factor out the GCF 'x' Divide both sides by Place the coefficient as the exponent using the identity Raise 2 to the 4th power to get 16 Combine the logs using the identity Multiply So the solution is which approximates to
 Graphs/244833: My problem is 3/2,-3 0,2/5 this involves the y2-y1 x2-x2 I'm having some problems with the fractions.1 solutions Answer 179002 by jim_thompson5910(28595)   on 2009-12-01 22:44:20 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Multiply the first fraction by the reciprocal of the second fraction. Multiply. So the slope of the line that goes through the points and is
 Trigonometry-basics/244836: Solving trigonomic equations algebraically, in terms of pi cot^2(x)=1 so far i got cot(x)=√1 then what?1 solutions Answer 179001 by jim_thompson5910(28595)   on 2009-12-01 22:41:12 (Show Source): You can put this solution on YOUR website!Well remember that . So take the square root of both sides to get . So taking the square root of 1 is just 1. This gets you: . Now use the identity Multiply both sides by tan(x) So . Can you solve it from here? You'll need to use the unit circle if you're not familiar with all of the trig values.
 Equations/244834: A person has quarters, dimes, nickels,and pennies with a total value of $3.86. The number of nickels is twice the number of quarters. The number of quarters is two less than the number of dimes. There are 40 coins in all. Write and solve an equation to find the number of each coin. I have figured out that there are eight quarters, sixteen nickels, ten dimes, and six pennies. I can not figure out how to write an equation for this problem. Can you help me?1 solutions Answer 178999 by jim_thompson5910(28595) on 2009-12-01 22:38:22 (Show Source): You can put this solution on YOUR website!Let p = # of pennies, n = # of nickels d = # of dimes q = # of quarters Since "There are 40 coins in all", this means that (ie add up the individual coin counts to get the total). This is your first equation. Because "The number of nickels is twice the number of quarters", we know that Since "The number of quarters is two less than the number of dimes", we also know that Finally, because "A person has quarters, dimes, nickels,and pennies with a total value of$3.86", we get the equation Remember that a penny is $0.01, a nickel is$0.05, a dime is $0.10, and a quarter is$0.25. If you multiply those individual values by their counts (the defined variables) and add them all up, you'll get the total coin value \$3.86 So the fourth and final equation is At the end of the translations, you get the four equations From here, all you need to do is solve the system. There are plenty of options available, but I recommend using a calculator to set up a matrix to solve this problem.
 Quadratic_Equations/244806: For the following equation, state the value of the discriminant and then describe the nature of the solutions. 2x^2-10x-12=0 What is the value of the discriminant? Which one of the statements below is correct? a. The equation has two imaginary solutions. b. The equation has two real solutions. c. The equation has one real solution? Thanks for your help!1 solutions Answer 178995 by jim_thompson5910(28595)   on 2009-12-01 22:26:13 (Show Source): You can put this solution on YOUR website! From we can see that , , and Start with the discriminant formula. Plug in , , and Square to get Multiply to get Rewrite as Add to to get Since the discriminant is greater than zero, this means that there are two real solutions.
 expressions/244776: can you help me simplify x^2-6x+8/x-31 solutions Answer 178994 by jim_thompson5910(28595)   on 2009-12-01 22:25:06 (Show Source): You can put this solution on YOUR website!Check out this page for the solution.
 Equations/244754: how do I solve the problem 4k-3k+7=-13?1 solutions Answer 178993 by jim_thompson5910(28595)   on 2009-12-01 22:21:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. ---------------------------------------------------------------------- Answer: So the solution is
Expressions-with-variables/244746: How i solve this problem 10x^2-19x+6
1 solutions

Answer 178991 by jim_thompson5910(28595)   on 2009-12-01 22:21:03 (Show Source):
You can put this solution on YOUR website!
I'm assuming that you want to factor this.

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 :
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60

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

These factors pair up and multiply to .
1*60 = 60
2*30 = 60
3*20 = 60
4*15 = 60
5*12 = 60
6*10 = 60
(-1)*(-60) = 60
(-2)*(-30) = 60
(-3)*(-20) = 60
(-4)*(-15) = 60
(-5)*(-12) = 60
(-6)*(-10) = 60

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

First NumberSecond NumberSum
1601+60=61
2302+30=32
3203+20=23
4154+15=19
5125+12=17
6106+10=16
-1-60-1+(-60)=-61
-2-30-2+(-30)=-32
-3-20-3+(-20)=-23
-4-15-4+(-15)=-19
-5-12-5+(-12)=-17
-6-10-6+(-10)=-16

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 .

In other words, .

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

 Linear-systems/244750: 3x-5y=-3,-9x-15y=9 how do you solve using the elimination method?1 solutions Answer 178990 by jim_thompson5910(28595)   on 2009-12-01 22:20:09 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Multiply the both sides of the first equation by 3. 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. Simplify. Divide both sides by to isolate . Reduce. ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply. Divide both sides by to isolate . Reduce. So the solutions are 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)
 Radicals/244805: How would I simplify ^5√√3?1 solutions Answer 178984 by jim_thompson5910(28595)   on 2009-12-01 22:13:53 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as using the property Convert to using the property Multiply the exponents using the idea that Combine the fractions. Multiply Convert back to radical notation So
 Graphs/244814: find the slope of the line passing through (2,-4) AND (7,3)1 solutions Answer 178983 by jim_thompson5910(28595)   on 2009-12-01 22:10:53 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that 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
 Sequences-and-series/244819: Write an expression for the apparent nth term of the sequence. (Assume n begins with 1.) 5/2, 6/5, 7/8, 8/11, 9/14, ... How do you do this?1 solutions Answer 178981 by jim_thompson5910(28595)   on 2009-12-01 22:09:16 (Show Source): You can put this solution on YOUR website!Hint: Look at the sequences of the numerators and denominators separately Sequence of numerators: 5, 6, 7, 8, 9, ... Sequence of denominators: 2, 5, 8, 11, 14, ... Do you see the patterns? If not, then repost or let me know.
 expressions/244747: what is equal to 5a+8-2(a+4) 1 solutions Answer 178969 by jim_thompson5910(28595)   on 2009-12-01 21:31:30 (Show Source): You can put this solution on YOUR website! So
 Subset/244742: Let Set 1 be the entire alphabet. Let Set 2 = {u, v, w, x, y, z} a. What is the complement of Set 2 in Set 1? b. Set 3 = {v, w, x, y}. Is Set 3 a proper subset of Set 2? Explain your reasoning 1 solutions Answer 178967 by jim_thompson5910(28595)   on 2009-12-01 21:28:52 (Show Source): You can put this solution on YOUR website!a) The complement of Set 2 in Set 1 is simply the set of every letter BUT the letters u, v, w, x, y, z are NOT in the set. So write out Set 1, then cross out those letters to form the complement of Set 2 in Set 1. b) The question you should first ask is: Is set 3 a subset of set 2? All you need to do is see if every element of set 3 is in set 2. Since v, w, x, y (elements of set 3) are all members of set 2, this means that set 3 is indeed a subset of set 2. Because there are fewer elements in set 3 than set 2, this means that set 3 is a proper subset of set 2.