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Functions/330410: i was studying for the ACT compass test and i am having problems with functions. the question was: if f(4)=0 and f(6)=6 then which of the following could represent f(x)? The answer is 3x-12, but i do not understand how to get to that answer, what does the 4 and 6 have to do with it? thank you ahead of time 1 solutions Answer 236814 by jim_thompson5910(28476)   on 2010-08-09 21:45:46 (Show Source): You can put this solution on YOUR website! Hint: If f(4)=0, then we have the point (4,0). Recall that f(x) is really 'y'. So if f(4)=0, then x=4 and y=0. Similarly, if f(6)=6, then we have the second point (6,6)

Problems-with-consecutive-odd-even-integers/330409: 3-(-8) 1 solutions Answer 236813 by jim_thompson5910(28476)   on 2010-08-09 21:44:37 (Show Source): You can put this solution on YOUR website! 3-(-8) = 3+8 = 11

Complex_Numbers/330414: I am trying to see if prime numbers occur and does the formula yeild a composite number. X^2 - X + 41 I need to use 0 and 2 even numbers and 2 odd numbers. can you help? 1 solutions Answer 236812 by jim_thompson5910(28476)   on 2010-08-09 21:43:33 (Show Source): You can put this solution on YOUR website! When x=0, which is prime. When x=1, which is prime. When x=2, which is prime. When x=3, which is prime. When x=4, which is prime. You can try more numbers, but it turns out that is prime for integer values of x where When x=41, then which is NOT prime. So it's composite. and when x=42, then which is NOT prime. So it's composite.

Rectangles/330413: The question was Use point-slope form to write the equation of the line passing through the two given points. Write each equation in slope-intercept form: P(4,0), Q(6,-8) 1 solutions Answer 236807 by jim_thompson5910(28476)   on 2010-08-09 21:36:35 (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 Simplify 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

Coordinate-system/330378: how do I graph y=6 equation 1 solutions Answer 236806 by jim_thompson5910(28476)   on 2010-08-09 21:34:53 (Show Source): You can put this solution on YOUR website! simply graph a horizontal line that passes through y=6

Polynomials-and-rational-expressions/330341: Collect like terms and then arrange them in descending order. -3x+3x^4-4x+8x^4+4 I have no idea where to start... 1 solutions Answer 236804 by jim_thompson5910(28476)   on 2010-08-09 21:33:48 (Show Source): You can put this solution on YOUR website! So

Equations/330384: 5s-6=2s 1 solutions Answer 236803 by jim_thompson5910(28476)   on 2010-08-09 21:32:42 (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

Rectangles/330407: the question was find the slope of the line passing through each pair of points, if possble. I got both questions wrong on my test. It was P(3,7);Q(6,16) and the other was P(5,17);Q(17,17) the sample they gave for these did not prepare me for that test. 1 solutions Answer 236802 by jim_thompson5910(28476)   on 2010-08-09 21:31:34 (Show Source): You can put this solution on YOUR website! I'll do the first one to get you started Let's find the slope of the line passing 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

Square-cubic-other-roots/330328: what is the root (5;3) 1 solutions Answer 236762 by jim_thompson5910(28476)   on 2010-08-09 18:19:36 (Show Source): You can put this solution on YOUR website! Using a calculator, we find that

Equations/330319: (-4x^3) (-2x^-5) (1/16x) It just says to simplify and I am so lost please help 1 solutions Answer 236756 by jim_thompson5910(28476)   on 2010-08-09 17:56:52 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as Multiply -2 and to get Combine the fractions. Multiply , -2 and 1 to get Multiply and to get Reduce to get Break up to get Break up to get Highlight the common terms Cancel out the common terms Simplify Multiply out to get So simplifies to In other words,

Rectangles/330314: how do you calculate the diagnol when you know the length of 2 of the sides 1 solutions Answer 236748 by jim_thompson5910(28476)   on 2010-08-09 16:55:53 (Show Source): You can put this solution on YOUR website! If you know the length of 2 sides, say 'a' and 'b', then you can calculate the diagonal 'c' by using the pythagorean theorem

Equations/330313: 9x=2x+14 1 solutions Answer 236746 by jim_thompson5910(28476)   on 2010-08-09 16:52:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Graphs/330312: write an inequality statement comparing -5/2 and -3 1 solutions Answer 236742 by jim_thompson5910(28476)   on 2010-08-09 16:49:37 (Show Source): You can put this solution on YOUR website! Hint: . So what's the relation between -2.5 and -3?

Miscellaneous_Word_Problems/330311: The length of the line segment whose endpoints are (3,-2)and ( -4,5) is b square root 2 . What is the value of b 1 solutions Answer 236739 by jim_thompson5910(28476)   on 2010-08-09 16:48:56 (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 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 Since and , this means that So

Equations/330201: 4x – (x + 6) = 5(3x - 1) + 8 1 solutions Answer 236736 by jim_thompson5910(28476)   on 2010-08-09 16:47:20 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Radicals/330177: Simplify by Factoring ∜486 Please show each step thank you 1 solutions Answer 236735 by jim_thompson5910(28476)   on 2010-08-09 16:45:49 (Show Source): You can put this solution on YOUR website! So Note: Since , this means that

Linear-systems/330295: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent? x + y=4 and x-y=5? Thank you Shelley 1 solutions Answer 236733 by jim_thompson5910(28476)   on 2010-08-09 16:43:56 (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 . ------------------------------------------------------------------ Now go back to the first equation. Plug in . Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . So the solutions are and . Which form the ordered pair . This means that the system is consistent and independent.

Probability-and-statistics/330304: Hello Can someone advise if this right. I hope I used the correct formula In how many ways you can randomly select 5 students from a 12-student class? ANS: 12C5 = (12*11*10*9*8)/(1*2*3*4*5) = 792 Also Can some please advise on the bwlow item I ansewered question B but I am not the greatest with Sample Space. Consider the probability experiment of drawing one card from a deck of cards. a) Determine the sample space of the probability experiment. ANS: b) Determine the probability of randomly selecting a face (Q, J or K) card. ANS: 12/52=.23 1 solutions Answer 236731 by jim_thompson5910(28476)   on 2010-08-09 16:41:12 (Show Source): You can put this solution on YOUR website! If order doesn't matter, then you are correct in saying that 12 C 5 = 792 a) The sample space is just the set of all possible items that you can select. In this case, the sample space is the set of 52 cards that you can select from. b) Correct. There are 4 suits and 3 face cards (Q, J, K). So there are 12 face cards total out of 52 cards which means that the probability is about 12/52=0.230769 or about a 23.0769% chance

Quadratic_Equations/330307: how do i solve: x^2-7x+3=0 1 solutions Answer 236727 by jim_thompson5910(28476)   on 2010-08-09 16:36:03 (Show Source): You can put this solution on YOUR website! 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 Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . or Break up the expression. So the solutions are or

Expressions-with-variables/329986: A rectangle has a width of 12 feet. If its perimeter is 100 feet, what is its length? Shelley E. 1 solutions Answer 236447 by jim_thompson5910(28476)   on 2010-08-08 17:50:05 (Show Source): You can put this solution on YOUR website! Hint: The formula for the perimeter is . So if "A rectangle has a width of 12 feet" and "its perimeter is 100 feet", then and . So . I'll let you solve for L.

Miscellaneous_Word_Problems/329980: graph each line using slope and y-intercept y = x + 7 y = -x + 2 1 solutions Answer 236443 by jim_thompson5910(28476)   on 2010-08-08 17:19:49 (Show Source): You can put this solution on YOUR website! I'll graph the first one to show you how to do these problems. 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 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

Exponential-and-logarithmic-functions/329935: Please help me factor this completely: x^2+6x+9-a^2 thanks alot 1 solutions Answer 236442 by jim_thompson5910(28476)   on 2010-08-08 17:13:25 (Show Source): You can put this solution on YOUR website! First factor to get (see this page for steps how to factor ). So Now factor by using the difference of squares to get So completely factors to In other words,

Graphs/329651: linear substitution. y = 5x - 2 3x + 7y = 5 i did this question and i got x = 1/2 and y = 1/2 is this correct? 1 solutions Answer 236305 by jim_thompson5910(28476)   on 2010-08-07 13:25:46 (Show Source): You can put this solution on YOUR website! You are correct. Good job.

Equations/329606: five-sixths of a number is -60 what is the number 1 solutions Answer 236301 by jim_thompson5910(28476)   on 2010-08-07 12:10:48 (Show Source): You can put this solution on YOUR website! Hint: "five-sixths of a number is -60" means that where 'x' is the unknown number.

Exponents/329626: Solve showing steps: (3^-1+2^-1)^2 thanks 1 solutions Answer 236300 by jim_thompson5910(28476)   on 2010-08-07 12:09:34 (Show Source): You can put this solution on YOUR website! In short,

Linear-equations/329634: what is the graph of the equation x+5y=25 1 solutions Answer 236299 by jim_thompson5910(28476)   on 2010-08-07 12:07:32 (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 -1 and the run is 5. This means that to go from point to point, we can go down 1 and over 5 So starting at , go down 1 unit and to the right 5 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

Radicals/329636: I need Finding b^2-4ac and the number real solutions for this equation. -3x^2 + 7x = 0 1 solutions Answer 236298 by jim_thompson5910(28476)   on 2010-08-07 12:04:26 (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 Subtract from to get So the discriminant is Since the discriminant is greater than zero, this means that there are two real solutions. Note: because the discriminant is a perfect square, this means that the two solutions are rational solutions.

Proportions/329639: The ratio of men to women at a certain company is 5 to 7. How many male employees does the company have if there are 204 employees? 1 solutions Answer 236297 by jim_thompson5910(28476)   on 2010-08-07 12:02:07 (Show Source): You can put this solution on YOUR website! Let x = number of male employees and y = number of female employees So because "there are 204 employees", this means that . Solve for y to get Also, since "The ratio of men to women at a certain company is 5 to 7", this means that (basically the ratio of 'x' men to 'y' women is 5 to 7) Start with the given equation. Plug in Cross multiply Distribute. 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 So this means that the company has 85 male employees.

Finance/328537: A total of $10, 126 was invested into two saving accounts. One account yields 8.5% simple interest and the other 9% simple interest. The person would like to find the amount placed in each account if a total of $901.66 in interest is received after one year. Write a system of linear equations to express this problem. I tried 901.66 = 10126 - (8.5x+9y) But that looks really wrong to me. 1 solutions Answer 235331 by jim_thompson5910(28476)   on 2010-08-03 16:11:40 (Show Source): You can put this solution on YOUR website! "A total of $10, 126 was invested into two saving accounts" means that where 'x' is the amount invested at 8.5% and 'y' is the amount invested at 9%. So because the total interest from both accounts yields $901.66, this means that Note: 0.085x is the amount of interest from the 8.5% account alone and 0.09y is the amount of interest from the 9% account alone. Add these two up to get the total 901.66 So the system is

Equations/327812: (x + 2)^2 =1 I need solving this 3 decimal 1 solutions Answer 234760 by jim_thompson5910(28476)   on 2010-08-01 18:16:02 (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 .

Linear-equations/327798: I need help bad!! 2x-y =5 Graph using the slope and the y-intercept. 1 solutions Answer 234756 by jim_thompson5910(28476)   on 2010-08-01 18:08:37 (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 1. This means that to go from point to point, we can go up 2 and over 1 So starting at , go up 2 units 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