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Inequalities/221115: can someone tell me if this statement is true or false when solving for x ,4x+8<12 I came up with x < 1 1 solutions Answer 165896 by jim_thompson5910(28476)   on 2009-10-03 17:36:46 (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 solution is which means that you're correct.

Points-lines-and-rays/221112: Please help me solve this problem. Write an equation of the line containing the given point and perpendicular to the given line. (8,-2) 8x+5y=6 I thought that you would plug 8 in place of x and plug -2 in place of y and then solve. But I am not so sure. So confused.Please help! 1 solutions Answer 165895 by jim_thompson5910(28476)   on 2009-10-03 17:35:12 (Show Source): You can put this solution on YOUR website! Method #1 Start with the given equation. ANY equation perpendicular to the equation above will be in the form (note: just swap the coefficients and negate the second coefficient). So just plug in (8,2) to find 'c': . So which means that the perpendicular equation is which in slope-intercept form is So you were thinking of something similar to this (actually I think you were trying to use a rule for parallel equations). If the method above made no sense, then check out this alternative... ========================================================= Method #2 Start with the given equation. Subtract from both sides. Rearrange the terms. Divide both sides by to isolate y. Break up the fraction. Reduce. We can see that the equation has a slope and a y-intercept . Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is . Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Rewrite as Distribute Multiply Subtract 2 from both sides. Combine like terms. So the equation of the line perpendicular to that goes through the point is . This equation is in standard form. So the answer is either or . Here's a graph to visually verify our answer: Graph of the original equation (red) and the perpendicular line (green) through the point .

Angles/221104: find the masurement of each angle in the triangle. (6n+31) (5n-19) (n+12) now i tired 5n-19=180 -19+19=0 180+19=199 5n=199 5n*5=0 199*5=39.8 saying that my answer is 39.8 but i know this is wrong because it's multiple choice and it didnt fit so i didnt do the other ones yet 1 solutions Answer 165890 by jim_thompson5910(28476)   on 2009-10-03 17:23:21 (Show Source): You can put this solution on YOUR website! Remember, all angles in a triangle add to 180 degrees. This means Start with the given equation. Remove the parenthesis. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Now just plug this value into the given angles to get: So the three angles are 109, 46, and 25 degrees.

Probability-and-statistics/221110: The sum of the digits of a number is 9. What is the probability that the number is prime? 1 solutions Answer 165886 by jim_thompson5910(28476)   on 2009-10-03 17:18:58 (Show Source): You can put this solution on YOUR website! Since "The sum of the digits of a number is 9", this means that the number is divisible by 9. So the chances that the number is prime is 0% (since 9 is a factor of this number).

Numbers_Word_Problems/221043: the difference between two whole numbers is 8 and the difference between their reciprocals is 1/6. find the two numbers 1 solutions Answer 165841 by jim_thompson5910(28476)   on 2009-10-03 14:59:24 (Show Source): You can put this solution on YOUR website! Let's assume that these numbers are positive. "the difference between two whole numbers is 8 " means that . Note: I'm implying that . Solve this equation for 'y' to get Also, " the difference between their reciprocals is 1/6" means that (note: since , this means ) Start with the second equation. Plug in Multiply EVERY term by the LCD to clear out the fractions. Simplify Multiply Distribute Get everything to one side. Combine like terms. 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 . 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 solutions are or But let's ignore the negative solution. So this means that the two numbers are 12 and 4.

logarithm/221046: how do u do 4^(log(base 8) of 27 without a calculator Problem: 4^(log(27)/log(8)) 1 solutions Answer 165840 by jim_thompson5910(28476)   on 2009-10-03 14:49:32 (Show Source): You can put this solution on YOUR website! In order to evaluate , we need to simplify the exponent ... Start with the given expression. ... Use the change of base formula. ... Rewrite 27 as and rewrite 8 as ... Pull down the exponents using the identity ... Cancel out the common terms. ... Use the change of base formula. So ---------------------------------------------------------------------- ... Start with the partially simplified expression. ... Rewrite as ... Multiply the exponents. ... Place the coefficient as the exponent using the identity ... Use the identity to simplify. ... Square 3 to get 9. So =================================== Answer: This means that

Money_Word_Problems/221018: how many years will it take for $2000 to double itself if is invested at 5% simple interest? 1 solutions Answer 165838 by jim_thompson5910(28476)   on 2009-10-03 14:37:43 (Show Source): You can put this solution on YOUR website! Start with the simple interest formula. Plug in (double of the initial investment of $2000), , and (the decimal equivalent of 5%). Multiply and to get . Subtract from both sides. Combine like terms. Divide both sides by to isolate 't'. Divide. Rearrange the equation. So it will take 20 years for an investment of $2000 to grow to $4000 with interest rate of 5% (using simple interest).

Linear-equations/221024: find the equation of the following lines, write the answer in slop-intercept form. through (7,10) and (-1,-1) 1 solutions Answer 165837 by jim_thompson5910(28476)   on 2009-10-03 14:25:28 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and 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 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 Distribute Multiply Add 10 to both sides. Combine like terms. So the equation that goes through the points and is

Quadratic_Equations/221042: What is the value of x when it's 4x squared + 8x + 4 = O? Can you show me how to solve it without using the quadratic formula? 1 solutions Answer 165836 by jim_thompson5910(28476)   on 2009-10-03 14:23:35 (Show Source): You can put this solution on YOUR website! We can solve this by factoring. Start with the given expression. Factor out the GCF . Now let's try to factor the inner expression --------------------------------------------------------------- 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 -1 Note: list the negative of each factor. This will allow us to find all possible combinations. These factors pair up and multiply to . 1*1 = 1 (-1)*(-1) = 1 Now let's add up each pair of factors to see if one pair adds to the middle coefficient : First Number Second Number Sum 1 1 1+1=2 -1 -1 -1+(-1)=-2 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 Condense the terms. -------------------------------------------------- So then factors further to So completely factors to . In other words, . So is equivalent to ----------------------------------------------------------- Now let's solve Start with the given equation. Divide both sides by . Reduce. 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 . Since -0 is really 0, this means we have one equation: Subtract from both sides. Combine like terms. -------------------------------------- Answer: So the only solution is .

Linear-equations/221025: find the equation of the following lines, write the answer in slop-intercept form. Parallel to y=3/7x-2 through (4,0) 1 solutions Answer 165835 by jim_thompson5910(28476)   on 2009-10-03 14:18:37 (Show Source): You can put this solution on YOUR website! We can see that the equation has a slope and a y-intercept . Since parallel lines have equal slopes, this means that we know that the slope of the unknown parallel line is . Now let's use the point slope formula to find the equation of the parallel line by plugging in the slope and the coordinates of the given point . Start with the point slope formula Plug in , , and Simplify Distribute Multiply So the equation of the line parallel to that goes through the point is . Here's a graph to visually verify our answer: Graph of the original equation (red) and the parallel line (green) through the point .

Inequalities/221037: Can someone please show me how to work these two examples? 0.9x + 6 ≤ 1.3x -3 The solution set should be {x|x __ __} The second is -3 ≤ 3x-2 ≤ -1, the solution set {x| __ ≤ x ≤ __} I have been trying for hours to figure these and just can not seem to do so. Thank you. 1 solutions Answer 165832 by jim_thompson5910(28476)   on 2009-10-03 14:07:09 (Show Source): You can put this solution on YOUR website! # 1 Start with the given inequality. 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 solution is Which in decimal form is So the answer in interval notation is [) Also, the answer in set-builder notation is ================================================================ # 2 Start with the given compound inequality. Add to all sides. Combine like terms on the left side. Combine like terms on the right side. Divide all sides by 3. So the solution is So the answer in interval notation is [] Also, the answer in set-builder notation is

Matrices-and-determiminant/220975: evaluate the determinant 3 -1 2 -2 1 -3 4 -1 3 1 solutions Answer 165823 by jim_thompson5910(28476)   on 2009-10-03 13:44:58 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Finding the Determinant of a 3x3 Matrix If you have the general 3x3 matrix: the determinant is: Which further breaks down to: Note: , and are determinants themselves. If you need help finding the determinant of 2x2 matrices (which is required to find the determinant of 3x3 matrices), check out this solver -------------------------------------------------------------- From the matrix , we can see that , , , , , , , , and Start with the general 3x3 determinant. Plug in the given values (see above) Multiply Subtract Multiply Combine like terms. ====================================================================== Answer: So , which means that the determinant of the matrix is

Travel_Word_Problems/221029: A car is traveling at 60 kilometers per hour. Determine the time required for the car to travel 12 kilometers 1 solutions Answer 165820 by jim_thompson5910(28476)   on 2009-10-03 13:39:49 (Show Source): You can put this solution on YOUR website! Start with the distance-rate-time formula. Plug in and . Divide both sides by 60 to isolate 't'. Divide to get . Rearrange the equation. So it will take hours (which is minutes) to go km traveling at kilometers per hour.

test/220874: hello, i am in 10th grade, advanced algebra, and i need helpz with dis... a+b, for a = 1, and be = 2 so if im correct its 1+2???? but wth is the answer? 1 solutions Answer 165691 by jim_thompson5910(28476)   on 2009-10-02 20:07:12 (Show Source): You can put this solution on YOUR website! Simply plug a=1 and b=2 and add:

Coordinate-system/220792: Write the equation in slope-intercept form: (2,4) (5,16) Y= use x as a varible Thank you! 1 solutions Answer 165677 by jim_thompson5910(28476)   on 2009-10-02 16:26:19 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and 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 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 Distribute Multiply Add 4 to both sides. Combine like terms. So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and

Probability-and-statistics/220381: The bus you take every morning is equally likely to be anywhere from 2 minutes early to 15 minutes late. What is the probability that the bus is more than five minutes late? I put 10/15 and got it wrong. The teacher's response was that the denominator was wrong. How so? Please explain. 1 solutions Answer 165637 by jim_thompson5910(28476)   on 2009-10-02 14:08:12 (Show Source): You can put this solution on YOUR website! Think of it like this: There are 15-5=10 minutes in the interval from 5 minutes to 15 minutes. Also, from 2 minutes to 15 minutes, there are 13 minutes. So the chances of the bus being more than 5 minutes late is (since there are 10 instances out of 13 that it could be 5 minutes or more late). It looks like you have the right idea for the numerator, but you just forgot to do the same for the denominator.

Equations/220726: This is a word problem my son just had on a quiz and I couldn't solve either. I thought we didn't have enough info. Marshfield Middle school cluster C has 100 students in honors pre-algebra Cluster C has 30 students enrolled in after school math enrichment. If 105 cluster C students are in only one or the other of these, how many students are in both? Tried a venn diagram to get my mind around it, didn't work. (I keep thinking I need to know the total enrollment of honors pre-alg plus after school)my son said he got 12.5 as an answer, but the teacher said it would come out as a whole number. Thanks, Trish 1 solutions Answer 165625 by jim_thompson5910(28476)   on 2009-10-02 13:13:48 (Show Source): You can put this solution on YOUR website! Let x = Number of students in both classes To find the number of students in only one or the other (not both) class, we subtract out the number that are in both (which is 'x') from the total. In other words, Number that are in one or other (not both) = (Number in pre-algebra + Number in math enrichment) - (Number in both) 105 = (100+30) - x 105 = 130 - x 105-130 = - x - 25 = - x 25 = x x = 25 So there are 25 students in both classes.

Miscellaneous_Word_Problems/220710: Given that the number 5913d8 is divisible by 12, what is the sum of all the digits that could replace d? 1 solutions Answer 165622 by jim_thompson5910(28476)   on 2009-10-02 13:01:18 (Show Source): You can put this solution on YOUR website! 5913d8 is only divisible by 12 only if 5913d8 is divisible by both 3 and 4. 5913d8 is divisible by 4 only if the last two digits are divisible by 4. In other words, 5913d8 is divisible by 4 only if d8 is divisible by 4. This restricts the choices of d to: 0, 2, 4, 6, and 8 5913d8 is divisible by 3 only if the sum of the digits are divisible by 3. So add them up to get: 5+9+1+3+d+8=26+d. Now just plug in the possible values of d to determine if 26+d is divisible by 3. d=0: 26+0=26 which is NOT divisible by 3. So d=0 is eliminated. d=2: 26+2=28 which is NOT divisible by 3. So d=2 is eliminated. d=4: 26+4=30 which is divisible by 3. So d=4 is one digit. d=6: 26+6=32 which is NOT divisible by 3. So d=6 is eliminated. d=8: 26+8=34 which is NOT divisible by 3. So d=8 is eliminated. So the only number that is divisible by 12 is 591348. So the sum of all the digits that could replace 'd' is 4.

Exponents/220721: -(4) to the fourth power = 1 solutions Answer 165621 by jim_thompson5910(28476)   on 2009-10-02 12:53:20 (Show Source): You can put this solution on YOUR website!

Surface-area/220695: which has the smaller area-a circle with a diameter of 4 feet or a rectangle with a length of 5 feet and a width of 3 feet? pleeeeaaaaaaaassssssssssse help!!!!!!!!!!!!! 1 solutions Answer 165620 by jim_thompson5910(28476)   on 2009-10-02 12:36:33 (Show Source): You can put this solution on YOUR website! Let's find the two areas: Area of the Circle: Take note that the radius is units (ie divide the diameter in half to get the radius) Solved by pluggable solver: Find the Area of a Circle Start with the area of a circle formula. Plug in . Replace with (since is approximately 3.14159...). Square to get . Multiply and to get . So the area of the circle with a radius of units is roughly square units. Area of the Rectangle: Solved by pluggable solver: Find the Area of a Rectangle Recall that the area of any rectangle with length L and width W is simply . In other words, to find the area, just multiply the length by the width. Start with the given area formula. Plug in and Multiply and to get (click here if you need a calculator). So the area of a rectangle with the length of 5 units and the width of 3 units is 15 square units. From above, we see that the area of the circle is about 12.566 square units while the area of the rectangle is 15 square units. So the circle has the smaller area.

percentage/220707: is there a simpler way to explain this to me cause im still confused????????? 1 solutions Answer 165618 by jim_thompson5910(28476)   on 2009-10-02 12:16:55 (Show Source): You can put this solution on YOUR website! Please post the entire problem (with full instructions) so we can help you out.

Permutations/220699: 2!+(4!)(3!) 1 solutions Answer 165617 by jim_thompson5910(28476)   on 2009-10-02 12:16:07 (Show Source): You can put this solution on YOUR website! 2!+(4!)(3!) = 2*1+(4*3*2*1)(3*2*1) = 2+(24)*(6) = 2+144 = 146

Quadratic_Equations/220696: I need help with a quadratic Equation 2x^2=90 How do i use the quadratic formula if there is no middle term? Thank you 1 solutions Answer 165616 by jim_thompson5910(28476)   on 2009-10-02 12:13:40 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract 90 from both sides Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve (note: since the polynomial does not have an "x" term, the 2nd coefficient is zero. In other words, b=0. So that means the polynomial really looks like notice , , and ) Plug in a=2, b=0, and c=-90 Square 0 to get 0 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 2 to get 4 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So the solutions are: or

Equations/220594: 5t-26=18t 1 solutions Answer 165549 by jim_thompson5910(28476)   on 2009-10-01 23:54:03 (Show Source): You can put this solution on YOUR website! Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

logarithm/220533: Can someone please help? Solve the equation. e^(x+3) = e^(x) + 9 x=? 1 solutions Answer 165540 by jim_thompson5910(28476)   on 2009-10-01 22:32:09 (Show Source): You can put this solution on YOUR website! Remember that . So this means that . If you let you can rewrite the equation into and easily solve for 'z' (since it's now a linear equation). Once you have the solution in terms of 'z', use the equation to find the solution in terms of 'x'. Note: 'e' is just the constant number 2.71828...

Graphs/220537: Help solve this inequality: 7y-12<8y+15 and i have to graph it 1 solutions Answer 165534 by jim_thompson5910(28476)   on 2009-10-01 22:14:22 (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. 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 solution is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on a number line: Note: there is an open circle at the endpoint.

Points-lines-and-rays/220549: (0.0) on a coordinate plane, 6 letter word, this is a cross word puzzle 1 solutions Answer 165532 by jim_thompson5910(28476)   on 2009-10-01 22:10:19 (Show Source): You can put this solution on YOUR website! The point (0, 0) is also known (and often referred to) as the origin.

Travel_Word_Problems/220543: I need help solving the problem: The Great Seto Bridge in Japan is about 7.6 mi long. How long would it take you to cross the bridge if you were walking at 3mi/hr? This is what I have done: I set up a chart: Rate:4 Time:t Distance:7.6 So would it be 4t=7.6? I have no idea what I am doing. Please help. Your guidance would be greatly appreciated. Thank you. -Michelle (Freshman) 1 solutions Answer 165529 by jim_thompson5910(28476)   on 2009-10-01 22:08:33 (Show Source): You can put this solution on YOUR website! Recall that the distance 'D' is related to the rate/speed 'r' and time 't' by the formula: (ie multiply the speed by the time to get the distance traveled). Plug in (the given distance) and (the given speed) Now the goal is to simply solve for 't': Divide both sides by 3 to isolate 't'. Divide 7.6 into 3 to get 2.533 (this is approximate). Rearrange the equation. So the solution is which means that it takes about 2.5 hours to walk 7.6 miles.

Equations/220546: Solve for x. 4(3-x)+6= x over 2 1 solutions Answer 165526 by jim_thompson5910(28476)   on 2009-10-01 22:03:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

logarithm/220510: Can anyone help me with this problem? The equation e^{2x} - 7e^{x} +10 = 0 has two solutions. One larger solution, and smaller solution. 1 solutions Answer 165518 by jim_thompson5910(28476)   on 2009-10-01 21:19:40 (Show Source): You can put this solution on YOUR website! Hint: Rewrite as and let . Now replace each with 'z' to get . From here, solve for 'z' and use the equation to find the solutions in terms of 'x'.

Complex_Numbers/220507: (-4-8i)(3+i) 1 solutions Answer 165516 by jim_thompson5910(28476)   on 2009-10-01 21:17:56 (Show Source): You can put this solution on YOUR website! 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