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 Equations/146082: Multipy. Write result in a+bi form. 3i(3+8i) Answers: A) 24+9i B) -15i C) -24+9i D) 17i1 solutions Answer 106619 by jim_thompson5910(28705)   on 2008-06-22 17:49:36 (Show Source): You can put this solution on YOUR website! Start with the given expression Distribute 3i to Multiply Replace with -1 Multiply Rearrange the terms
 Linear-systems/146072: Solve by elimination x+y=38 175000x+200000y=72000001 solutions Answer 106616 by jim_thompson5910(28705)   on 2008-06-22 16:33:57 (Show Source): You can put this solution on YOUR website! Start with the given system of equations: Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for y. In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for , we would have to eliminate (or vice versa). So lets eliminate . In order to do that, we need to have both coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated. So to make the coefficients equal in magnitude but opposite in sign, we need to multiply both coefficients by some number to get them to an common number. So if we wanted to get and to some equal number, we could try to get them to the LCM. Since the LCM of and is , we need to multiply both sides of the top equation by and multiply both sides of the bottom equation by like this: Multiply the top equation (both sides) by Multiply the bottom equation (both sides) by Distribute and multiply Now add the equations together. In order to add 2 equations, group like terms and combine them Combine like terms and simplify Notice how the x terms cancel out Simplify Divide both sides by to isolate y Reduce Now plug this answer into the top equation to solve for x Start with the first equation Plug in Multiply Subtract 22 from both sides Combine like terms on the right side So our answers are and
 Inequalities/146070: 19) Solve  4x-7 <-5 or 4x-7 > 2 8 8 1 solutions Answer 106615 by jim_thompson5910(28705)   on 2008-06-22 16:19:15 (Show Source): You can put this solution on YOUR website!Let's solve Start with the first inequality. Multiply both sides by 8. Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So our first answer is Which approximates to ======================================================================== Now let's solve Start with the given inequality. Multiply both sides by 8. Distribute and multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So our second answer is Which approximates to ----------------------------- Summary ----------------------------- So the final answer is OR which is approximately OR
 Inequalities/146068: 15) Solve -5< x+3 <51 solutions Answer 106614 by jim_thompson5910(28705)   on 2008-06-22 16:12:11 (Show Source): You can put this solution on YOUR website!# 15 Start with the given inequality Subtract 3 from all sides So the solution is Which in interval notation is: (-8,2) Now let's graph the solution set Note: at there is a open circle (which means this point is excluded) and at there is a open circle (which means this point is excluded)
 Inequalities/146067: 1) Determine whether the given numbers are solutions of the inequality. 5,-13,-18,-1 1 solutions Answer 106613 by jim_thompson5910(28705)   on 2008-06-22 16:09:05 (Show Source): You can put this solution on YOUR website!# 1 a) Let's see if is a solution for the inequality . Start with the given inequality. Plug in . Evaluate and simplify the left side. Evaluate and simplify the right side. Since the inequality is not true, this means that is not a solution. ----------------------------------- b) Let's see if is a solution for the inequality . Start with the given inequality. Plug in . Evaluate and simplify the left side. Evaluate and simplify the right side. Since the inequality is true, this means that is a solution. ----------------------------------- c) Let's see if is a solution for the inequality . Start with the given inequality. Plug in . Evaluate and simplify the left side. Evaluate and simplify the right side. Since the inequality is true, this means that is a solution. ----------------------------------- d) Let's see if is a solution for the inequality . Start with the given inequality. Plug in . Evaluate and simplify the left side. Evaluate and simplify the right side. Since the inequality is not true, this means that is not a solution. --------------------- Summary ---------------------- So and are the only solutions of the group.
 expressions/146064: (-6-b)-5(2b+a)1 solutions Answer 106610 by jim_thompson5910(28705)   on 2008-06-22 14:45:57 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute. Group like terms Combine like terms So
 expressions/146062: (3x-2y)-2(5x-4y)1 solutions Answer 106609 by jim_thompson5910(28705)   on 2008-06-22 14:42:44 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute. Group like terms Combine like terms So
 Equations/146061: 1 - y^2 ____ x^2 __________ 1 - y __ x 1 solutions Answer 106608 by jim_thompson5910(28705)   on 2008-06-22 14:35:44 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply both numerator and denominator by the LCD Distribute. Notice how the inner denominators cancel. Factor the numerator. Factor the denominator. Cancel like terms. Simplify. So simplifies to
 Equations/146057: write each expression in lowest terms -2x-8/z^2+2x-8 my answer is -2x-8 not sure if this is correct1 solutions Answer 106603 by jim_thompson5910(28705)   on 2008-06-22 14:10:41 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor to get . Factor to get . Highlight the common terms. Cancel out the common terms. Simplify. So simplifies to . In other words, where or
 Inequalities/146060: Solve 1 solutions Answer 106602 by jim_thompson5910(28705)   on 2008-06-22 14:06:12 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Multiply both sides by 8. Multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the answer is Which approximates to
 Inequalities/146059: Solve 1 solutions Answer 106601 by jim_thompson5910(28705)   on 2008-06-22 13:58:52 (Show Source): You can put this solution on YOUR website! Start with the given inquality. Multiply both sides by the LCD to clear any fractions. note: If you need help with finding the LCD, check out this solver. Distribute and multiply. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is Which approximates to
 Inequalities/146058: Solve 1 solutions Answer 106600 by jim_thompson5910(28705)   on 2008-06-22 13:56:38 (Show Source): You can put this solution on YOUR website! Start with the given inquality. Multiply both sides by 10 to clear out the decimals. Distribute and multiply. 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the answer is Which approximates to
 Polynomials-and-rational-expressions/145979: i need help please what find the product (2x-3)3x2+5x-7) find the product (-8ab5) (5a4b) factor completely 5x2-45x factor completely , if possible x2-13x+36 factor completely , if possible x2+x-30 send it to my email please i need this today monday i have to gave my homewok to school so please 1 solutions Answer 106550 by jim_thompson5910(28705)   on 2008-06-21 16:18:03 (Show Source): You can put this solution on YOUR website!I'll do the first two to get you started # 1 Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, . # 2 Start with the given expression. Multiply the coefficients and to get When you multiply monomials, simply add the exponents. Add. So .
 Inequalities/145962: In order to achieve maximum results from aerobic exercise, one should maintain one's heart rat at a certain level. A 45 year old woman with a resting heart rate of 80 beats per minute, should keep her heart rate between 137 and 156 beats per minute while exercising. She checks her pulse for 10 sec while exercising. What should the number of beats be? 1 solutions Answer 106521 by jim_thompson5910(28705)   on 2008-06-20 23:23:21 (Show Source): You can put this solution on YOUR website!Let x= number of beats per minute Since the number of beats per minute (bpm) should be within 137 and 156 , this means that we have the given inequality But since we only want to know the bpm in 10 seconds, we need to divide everything by 6 (since ) Simplify So in 10 seconds, she should be between 23 and 26 bpm
 Inequalities/145961: Determine whether the ordered pair is a solution of the inequality (-4,8); 7x+y<-91 solutions Answer 106520 by jim_thompson5910(28705)   on 2008-06-20 23:10:50 (Show Source): You can put this solution on YOUR website! Start with the given inequality Plug in and Multiply Add Since the inequality is true, the ordered pair (-4,8) is a solution.
 Inequalities/145960: Graph the inequality on a plane y>6x1 solutions Answer 106519 by jim_thompson5910(28705)   on 2008-06-20 23:06:58 (Show Source): You can put this solution on YOUR website! Start with the 1st inequality Replace the inequality sign with an equals sign So in order to plot , we need to plot the equation first Graph of Now lets pick a test point, say (0,1). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality with the test point Substitute (0,1) into the inequality Plug in and Simplify (note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of Firefox to see these images.) Since this inequality is true, we simply shade the entire region that contains (0,1) Graph of with the boundary (which is the line in red) and the shaded region (in green) (note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
 Inequalities/145959: Graph the inequality on a plane 1 solutions Answer 106517 by jim_thompson5910(28705)   on 2008-06-20 23:02:33 (Show Source): You can put this solution on YOUR website! Start with the 1st inequality Replace the inequality sign with an equals sign Solve for y So in order to plot , we need to plot the equation first Graph of Now plug in a test point (0,0) into the inequality Plug in and Evaluate and simplify Since the inequality is true, this means that we shade the entire region that contains the point (0,0) Graph of with the shaded region in green
 Inequalities/145954: Solve and graph x+8<-6 or x+8>31 solutions Answer 106512 by jim_thompson5910(28705)   on 2008-06-20 22:09:41 (Show Source): You can put this solution on YOUR website!Let's solve Start with the first inequality Subtract 8 from both sides Combine like terms on the right side So the first part of our answer is Here's the graph of the solution set ------------- Now let's solve Start with the given inequality Subtract 8 from both sides Combine like terms on the right side So the second part of our answer is Here's the graph of the solution set -----------------------Solution So the answer is or which looks like
 Inequalities/145953: Solve 1 solutions Answer 106509 by jim_thompson5910(28705)   on 2008-06-20 22:03:45 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 6 to all sides Divide every side by 4 to isolate x. So the solution in interval notation is:
 Inequalities/145952: Solve =2< x+4< 12 1 solutions Answer 106508 by jim_thompson5910(28705)   on 2008-06-20 22:01:04 (Show Source): You can put this solution on YOUR website! Start with the given inequality Subtract 4 from all sides So the solution in interval notation is: (-2,8) Now let's graph the solution set Note: at there is a open circle (which means this point is excluded) and at there is a open circle (which means this point is excluded)
 Inequalities/145950: Bayside Insurance offers two health plans. Under plan A, Giselle would have to pay the first $50 of her medical bills, plus 25% of the rest. Under plan B, Giselle would pay the first$230, but only 20% of the rest. For what amount of medical bills will plan B save Giselle money? Assume she has over $230 in bills. Suppose Giselle has a certain amount in medical bills, such as$5000. How much would she pay under each plan? 1 solutions Answer 106507 by jim_thompson5910(28705)   on 2008-06-20 21:59:29 (Show Source): You can put this solution on YOUR website!"For what amount of medical bills will plan B save Giselle money?" Let x=amount of the bill Under plan A, the expression is Under plan B, the expression is So to figure out when plan B will save her money, simply set the plan B expression less than the plan A expression Distribute Combine like terms Subtract 0.25x from both sides. Subtract 184 from both sides. Combine like terms Divide both sides by 0.45 So if she has any bills over $2,930, then Plan B will cost less than Plan A. ----------------------- "Suppose Giselle has a certain amount in medical bills, such as$5000. How much would she pay under each plan?" Start with the Plan A expression Plug in Subtract from to get . Multiply and to get . Add and to get . So under Plan A, she will pay $1,287.50 ---------------------- Start with the Plan B expression Plug in Subtract from to get . Multiply and to get . Add and to get . So under Plan B, she will pay$1,184.00
 Inequalities/145948: The body mass index, I, can be used to determine an individuals risk for heart disease. An index less than 25 indicates a low risk. The body mass index is given by the formula or model where w=weight, in pounds and h=height, in inches. Francis weighs 168 pounds and stands 68 inches tall. What is his approximate body mass index? Find an inequality describing all weights w that Francis can have and be in the low-risk category.1 solutions Answer 106504 by jim_thompson5910(28705)   on 2008-06-20 21:40:17 (Show Source): You can put this solution on YOUR website!"What is his approximate body mass index?" Start with the given equation. Plug in and Multiply and to get . Square to get . Divide. So his approximate body mass index is about 25.43 ------------------------------- "Find an inequality describing all weights w that Francis can have and be in the low-risk catergory." Start with the given equation. Plug in Set the left side less than 25. Square to get . Multiply both sides by . Divide both sides by to isolate w. So any weights less than 165 pounds will put him in the low-risk category.
 Inequalities/145944: Solve; 1 solutions Answer 106499 by jim_thompson5910(28705)   on 2008-06-20 20:22:20 (Show Source): You can put this solution on YOUR website! Start with the given inequality Multiply both sides by 5. Multiply. Divide both sides by 4. Divide. Add 1 to both sides Combine like terms on the right side Divide both sides by 8 to isolate x Divide -------------------------------------------------------------- Answer: So our answer is So the answer in interval notation is Here's the graph of the solution set note: there is an open circle at which means we're excluding that value from the solution set.
 Inequalities/145922: Could you describe to me what the graph of interval (-4,10) looks like?1 solutions Answer 106495 by jim_thompson5910(28705)   on 2008-06-20 18:41:25 (Show Source): You can put this solution on YOUR website!The graph of the interval (-4,10) is simply the shaded region from -4 to 10 on the number line. Notice how parenthesis are used, so this means that we must use open circles at the endpoints So here's what the graph looks like: note: the open circles at -4 and 10 tell us to exclude -4 and 10 from the solution set.
 Signed-numbers/145912: i am having trouble solving this problem 3 -4(6 -3)= 1 solutions Answer 106491 by jim_thompson5910(28705)   on 2008-06-20 17:10:00 (Show Source): You can put this solution on YOUR website! Start with the given expression. Subtract from to get . Multiply and to get . Subtract from to get . So
 Rational-functions/145907: Simplify by removing factors of 1 48u^6z^9/18u^4z^41 solutions Answer 106486 by jim_thompson5910(28705)   on 2008-06-20 16:28:20 (Show Source): You can put this solution on YOUR website! Start with the given expression. Divide the coefficients and to get When you divide monomials, simply subtract the exponents. Subtract. So .
Polynomials-and-rational-expressions/145894: Factor completely:
7x^2 + 58x + 16

1 solutions

Answer 106485 by jim_thompson5910(28705)   on 2008-06-20 16:25:19 (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 7 and 16 respectively.

Now multiply the first coefficient 7 and the last coefficient 16 to get 112. Now what two numbers multiply to 112 and add to the middle coefficient 58? Let's list all of the factors of 112:

Factors of 112:
1,2,4,7,8,14,16,28,56,112

-1,-2,-4,-7,-8,-14,-16,-28,-56,-112 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 112
1*112
2*56
4*28
7*16
8*14
(-1)*(-112)
(-2)*(-56)
(-4)*(-28)
(-7)*(-16)
(-8)*(-14)

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

Now which of these pairs add to 58? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 58

First NumberSecond NumberSum
11121+112=113
2562+56=58
4284+28=32
7167+16=23
8148+14=22
-1-112-1+(-112)=-113
-2-56-2+(-56)=-58
-4-28-4+(-28)=-32
-7-16-7+(-16)=-23
-8-14-8+(-14)=-22

From this list we can see that 2 and 56 add up to 58 and multiply to 112

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 )

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So factors to

Polynomials-and-rational-expressions/145892: Factor completely:
x^2 + 9x + 8

1 solutions

Answer 106484 by jim_thompson5910(28705)   on 2008-06-20 16:24:31 (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 1 and 8 respectively.

Now multiply the first coefficient 1 and the last coefficient 8 to get 8. Now what two numbers multiply to 8 and add to the middle coefficient 9? Let's list all of the factors of 8:

Factors of 8:
1,2,4,8

-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 8
1*8
2*4
(-1)*(-8)
(-2)*(-4)

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

Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9

First NumberSecond NumberSum
181+8=9
242+4=6
-1-8-1+(-8)=-9
-2-4-2+(-4)=-6

From this list we can see that 1 and 8 add up to 9 and multiply to 8

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 )

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