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 Inequalities/185901: This question is from textbook 5(12-3w)>15w+601 solutions Answer 139405 by jim_thompson5910(28478)   on 2009-03-09 18:32:35 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. 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
 Graphs/185898: y is greater than or equal to x squared. how would you graph this? 1 solutions Answer 139404 by jim_thompson5910(28478)   on 2009-03-09 18:29:05 (Show Source): You can put this solution on YOUR website!First, graph the equation (this curve will serve as the boundary) Note: since there is an '=' sign in the inequality, this means that the boundary is a solid line Graph of Now pick a point that is NOT on the curve of . Let's pick the point (0,1). This means that we have the values and . Now plug them into the inequality: Go back to the inequality Plug in and Square 0 to get 0 Since this inequality is true, this means that we shade the ENTIRE region that this point lies in. So just shade the region above the graph to get the following: Graph of where the red line is the boundary equation (solid line) with the shaded region in green.
 Conjunction/185877: Write the following compound statement in symbolic form Let p: Today is Monday q: Tomorrow is the day Sara leaves If tomorrow is not the day Sara leaves, then today is Monday 1 solutions Answer 139403 by jim_thompson5910(28478)   on 2009-03-09 18:20:19 (Show Source): You can put this solution on YOUR website!Note: the symbol is used for "not" and is used for "if...then..." So "If tomorrow is not the day Sara leaves, then today is Monday " translates to "If NOT Q, then P" where NOT Q translates to . Afterwards, the entire expression translates to So "If tomorrow is not the day Sara leaves, then today is Monday " completely translates to
 Rectangles/185858: If i have the shortest side of a rectangle to be 8 how do i get the other three sides?1 solutions Answer 139384 by jim_thompson5910(28478)   on 2009-03-09 16:12:08 (Show Source): You can put this solution on YOUR website!Well one of the three sides will be of the same length as the shortest side. So you'll have two sides that are 8 units in length. To find the other 2 sides (which are both equal to each other), you're going to need either the area of the rectangle or the perimeter of the rectangle.
 logarithm/185778: Fill in the blank to make a true statement. To solve 8^x=26, we can take the logarithm of each side of the equation to get log (8^x)=log(26). The power rule for logarithms would then provide a way of moving the variable x from its position as an___________________________ to the position of a coefficient. a) none of these b) negative value c) function d) log e) base f) exponent1 solutions Answer 139383 by jim_thompson5910(28478)   on 2009-03-09 16:02:42 (Show Source): You can put this solution on YOUR website!The power rule for logarithms would then provide a way of moving the variable x from its position as an exponent to the position of a coefficient. Note: the exponent is simply the term that is being "raised" over other terms. So for instance the "2" is the exponent of
 expressions/185857: -7 - 8 + 5 + (-2) - 6 = ? I tried to do this problem but I'm not confident that I'm doing it correctly. Please show your work so I can better understand how to solve it. Thank you1 solutions Answer 139382 by jim_thompson5910(28478)   on 2009-03-09 15:58:32 (Show Source): You can put this solution on YOUR website! Start with the given expression Subtract -8 from -7 to get -15 (ie ) Rewrite as Subtract 2 from 5 to get 3 (ie ) Add 3 to -15 to get -12 (ie ) Subtract -6 from -12 to get -15 (ie ) So
 logarithm/185731: a=p(1+r/n)^nt 5000=250(1+r/4)^40 ? I don't know where to go from here.1 solutions Answer 139379 by jim_thompson5910(28478)   on 2009-03-09 15:54:41 (Show Source): You can put this solution on YOUR website!I'm assuming that you want to solve for "r" right? If so, then I'll start where you left off. Start with the given equation Divide both sides by 250 Reduce Take the 40th root of both sides (this is probably where you got stuck) Evaluate the 40th root of 20 to get roughly 1.0778 Subtract 1 from both sides. Subtract Multiply both sides by 4 to isolate "r" Multiply So the answer is which means that the interest rate is 31.12% (just multiply by 100 to get a percentage)
 logarithm/185729: This question is from textbook Alegbra 2 Explain why the expression and are not defined.1 solutions Answer 139377 by jim_thompson5910(28478)   on 2009-03-09 15:47:20 (Show Source): You can put this solution on YOUR website! Start with the given expression Set "y" equal to the expression Use the property to rewrite the equation. Now the question is: what value of "y" will make equal to -1? Since there is NO value of "y" that will make negative (because is ALWAYS positive), this means that there are no solutions to This in turn means that you CANNOT take the log of a negative number (or zero). So that's why is undefined In fact, is undefined where and -------------------------------------- Start with the given expression Use the change of base formula to rewrite the expression. Evaluate the log of 1 to get 0. Now remember, division by zero is undefined. So we cannot go further. So this shows us that is undefined.
 Rational-functions/185802: rewrite without rational exponents 16 5/71 solutions Answer 139374 by jim_thompson5910(28478)   on 2009-03-09 15:39:23 (Show Source): You can put this solution on YOUR website!Remember, the identity can be used to convert to and from radical and exponential notation. So...
 Radicals/185800: √33/√77 Rationalize the denominator and simplify: 1 solutions Answer 139373 by jim_thompson5910(28478)   on 2009-03-09 15:35:18 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply both the numerator and denominator by Multiply by to get Factor 33 into 3*11 and factor 77 into 11*7 Combine the roots. Multiply Break up the square root Take the square root of to get 11 Recombine the square roots. Multiply Factor 77 into 7*11 Cancel out the common terms. Simplify So
 Polynomials-and-rational-expressions/185809: This question is from textbook Beginning and Intermediate Algebra I'm having trouble with this fraction. 1-8r^3 ________ 8r^2+4r+21 solutions Answer 139370 by jim_thompson5910(28478)   on 2009-03-09 15:28:03 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor the numerator using the difference of cubes formula Factor the GCF 2 from the denominator. Rearrange the terms in the numerator in descending order. Highlight the common terms. Cancel out the common terms. Simplify So simplifies to In other words,
 Exponents/185816: Simplify. Assume all variables represent positive numbers. √ (x^4 y^3)1 solutions Answer 139367 by jim_thompson5910(28478)   on 2009-03-09 15:19:06 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor to get (note: we want to factor the expression into a product of squares) Factor to get Break up the square root. Take the square root of to get Take the square root of to get Multiply So where every variable is non-negative.
Conjunction/185765: This question is from textbook A Survey of Mathematics with Application
I am actually getting myself confused here: Please Help!
a.) If today is Monday, then tomorrow is not Wednesday.
b.) If it is false that today is Monday and tomorrow is not Wednesday
c.) Today is not Monday or tomorrow is Wednesday.
I personally would say that A & B are equivalent, but the more I read over it and convince myself that A & B are equivalent, the more I confuse myself. Can you please help me determine which statements are equivalent. Thanks A million everyone

1 solutions

Answer 139314 by jim_thompson5910(28478)   on 2009-03-08 22:27:26 (Show Source):
You can put this solution on YOUR website!
Let P = today is Monday and Q = today is Wednesday

Now translate:

a) "If today is Monday, then tomorrow is not Wednesday" translates to "If P then Q" which symbolically looks like

Now fill out a truth table:

 P Q T T F F T F T T F T F T F F T T

Note: let me know if you need help constructing a truth table

The truth values in red are the values we're going to compare later.

b) "If it is false that today is Monday and tomorrow is not Wednesday" translates to "It is NOT the case that P and not Q are true".
In symbolic form, the expression looks like:

Now fill out a truth table:

 P Q T T F F T T F T T F F T F F T F F T F T

c)
"Today is not Monday or tomorrow is Wednesday" translates to "Not P or Q" which looks like

Now make a truth table
 P Q T T F T T F F F F T T T F F T T

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

Now comparing the truth values that are marked in red from parts a) to c), we see that the red truth values in tables b) and c) are identical. So this means that statements b) and c) are equivalent.

 Equations/185697: 1/4z = 1/3z - 21 solutions Answer 139284 by jim_thompson5910(28478)   on 2009-03-08 18:02:56 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply EVERY term by the LCD to clear any fractions. Multiply and simplify. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Trigonometry-basics/185666: This question is from textbook saxon algebra 2 A=1/2acsinB A=1/2(20)(15)sin132 Question: to finish this out, how do I evaluate for sin132?1 solutions Answer 139265 by jim_thompson5910(28478)   on 2009-03-08 16:16:05 (Show Source): You can put this solution on YOUR website!Either use a calculator (the preferred method) or a table (probably located in the back of your book) to get (note: this value is approximate) So then becomes Multiply everything out and simplify to get (which is approximate)
 Linear-equations/185657: Find the slope if it exists 3x-2y=41 solutions Answer 139250 by jim_thompson5910(28478)   on 2009-03-08 15:29:15 (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
 Graphs/185654: I have another graph question. Grpah the line 2x+3y=12 Thanks so much.1 solutions Answer 139248 by jim_thompson5910(28478)   on 2009-03-08 15:23:32 (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. Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is -2 and the run is 3. This means that to go from point to point, we can go down 2 and over 3 So starting at , go down 2 units and to the right 3 units to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Conjunction/185647: This question is from textbook A Survey of Mathematics with Application Construct a truth table for (~q^p) -> ~q Can you please assist me wit this, i don't even know where to start. 1 solutions Answer 139245 by jim_thompson5910(28478)   on 2009-03-08 15:16:05 (Show Source): You can put this solution on YOUR website!Note: the symbol '^' means "and", the '~' means "not" and '->' means "implies" Remember, a ^ b is ONLY true if BOTH a and b are true (otherwise it is false) For ~a, simply negate any true statements to get a false (and vice versa) Finally, keep in mind that a -> b (a implies b) is only false if "a" is true but "b" is false. Here's the basic outline of the table, let me know if you need me to go in depth for any column  p | q | ~q | ~q ^ p | (~q ^ p) -> ~q ---------------------------------------------------- T | T | F | F | T T | F | T | T | T F | T | F | F | T F | F | T | F | T 
 Distributive-associative-commutative-properties/185651: Assume that all variables are positive and multiply: y^3/7(y^-3/7+7y^4/7) a) 1+7y b)y+7 c) y^-1+7y1 solutions Answer 139242 by jim_thompson5910(28478)   on 2009-03-08 15:05:20 (Show Source): You can put this solution on YOUR website! ... Start with the given expression. ... Distribute ... Multiply by adding the exponents. ... Combine the fractions. ... Combine like terms. ... Reduce ... Simplify So where
 Graphs/185641: Hey there... How do you graph y=60 do you answer it like horizontal vertical or ughh im confused help!! thanksaton 1 solutions Answer 139237 by jim_thompson5910(28478)   on 2009-03-08 14:36:58 (Show Source): You can put this solution on YOUR website!Simply draw a horizontal line through the tick '60' on the y-axis (make sure you scale the graph correctly). Why is this a horizontal line? Since "x" is nowhere to be found, this means that no matter what "x" is y will ALWAYS be equal to 60. So you'll have points like (0,60), (-2,60), (-10,60), (44,60), etc...
 Quadratic_Equations/185634: Give exact and approximate solutions to three decimal places (x+9)^2=161 solutions Answer 139233 by jim_thompson5910(28478)   on 2009-03-08 14:13:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Take the square root of both sides. or Break up the "plus/minus" to form two equations. or Take the square root of to get . or Subtract from both sides. or Combine like terms. -------------------------------------- Answer: So the solutions are or .
 Graphs/185637: how do you graph y=x? i have been trying to figure it out for an hour and cannot. Thankyou for helping me. 1 solutions Answer 139232 by jim_thompson5910(28478)   on 2009-03-08 14:11:40 (Show Source): You can put this solution on YOUR website! Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is note: really looks like Since this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis So we have one point Now since the slope is comprised of the "rise" over the "run" this means Also, because the slope is , this means: which shows us that the rise is 1 and the run is 1. This means that to go from point to point, we can go up 1 and over 1 So starting at , go up 1 unit and to the right 1 unit to get to the next point Now draw a line through these points to graph So this is the graph of through the points and
 Polynomials-and-rational-expressions/185632: I need to solve y-7/y-9 - 2/y-9 this is just pratice problems to try to improve my skills. 1 solutions Answer 139231 by jim_thompson5910(28478)   on 2009-03-08 14:08:26 (Show Source): You can put this solution on YOUR website! Start with the given expression. Since the fractions have equal denominators, we can combine the fractions. Subtract the fractions. Combine like terms. Cancel out the common terms. Simplify So simplifies to In other words, where
 Expressions-with-variables/185630: Simplify the following expression and place in descending order. Thanks!1 solutions Answer 139230 by jim_thompson5910(28478)   on 2009-03-08 13:52:33 (Show Source): You can put this solution on YOUR website! Start with the given expression. Raise "A" to the 0th power to get 1. Raise "A" to the 1st power to get "A" Multiply Rearrange and group like terms Combine like terms. So
 Quadratic_Equations/185628: x^2+20=4x1 solutions Answer 139229 by jim_thompson5910(28478)   on 2009-03-08 13:39:43 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 4x from both sides. Rearrange the terms. Notice we have a quadratic equation in the form of where , , and Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Break up the fraction for each case. or Reduce. or Simplify. So the answers are or
 Polynomials-and-rational-expressions/185603: 5^-1 + 6^-1 Answer should be a simplified fraction1 solutions Answer 139228 by jim_thompson5910(28478)   on 2009-03-08 13:38:33 (Show Source): You can put this solution on YOUR website! So
 Inequalities/185561: Please show me how to solve the following problem: Thank you!1 solutions Answer 139202 by jim_thompson5910(28478)   on 2009-03-08 00:47:52 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Equations/185551: 135=-9+8p1 solutions Answer 139201 by jim_thompson5910(28478)   on 2009-03-07 23:25:26 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add 9 to both sides. Combine like terms. Divide both sides by 8 to isolate "p". Reduce ==================================================== Answer: So the solution is
Polynomials-and-rational-expressions/185548: Which binomial is factor of 2x^2 – 7x + 3?
1 solutions

Answer 139200 by jim_thompson5910(28478)   on 2009-03-07 23:23:19 (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 :
1,2,3,6
-1,-2,-3,-6

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

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

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

First NumberSecond NumberSum
161+6=7
232+3=5
-1-6-1+(-6)=-7
-2-3-2+(-3)=-5

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

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

Answer:

So factors to .

So and are factors of

Polynomials-and-rational-expressions/185549: Which binomial is a factor of 6x^2 + x – 2?

1 solutions

Answer 139199 by jim_thompson5910(28478)   on 2009-03-07 23:21:41 (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 :
1,2,3,4,6,12
-1,-2,-3,-4,-6,-12

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

These factors pair up and multiply to .
1*(-12)
2*(-6)
3*(-4)
(-1)*(12)
(-2)*(6)
(-3)*(4)

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

First NumberSecond NumberSum
1-121+(-12)=-11
2-62+(-6)=-4
3-43+(-4)=-1
-112-1+12=11
-26-2+6=4
-34-3+4=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

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

Answer:

So factors to .

This means that and are factors of

 Polynomials-and-rational-expressions/185547: The sum of a positive number and its square is 12. What is the number? 1 solutions Answer 139198 by jim_thompson5910(28478)   on 2009-03-07 23:16:25 (Show Source): You can put this solution on YOUR website!"The sum of a positive number and its square is 12" translates to Start with the given equation. Subtract 12 from both sides. Rearrange the terms. Notice we have a quadratic equation 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 . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, the problem states that the number is positive. So we must ignore So the only answer is which means that the number is 3