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jim_thompson5910 answered: 28586 problems
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Equations/316270: Find the distance between (-2,-3) and (-5,1) 1 solutions Answer 226212 by jim_thompson5910(28598)   on 2010-06-21 15:19:50 (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 . Take the square root of to get . So our answer is So the distance between the two points is 5 units.

Polynomials-and-rational-expressions/316293: (6z^2+36z+54)/(z^2-3z-18) 1 solutions Answer 226210 by jim_thompson5910(28598)   on 2010-06-21 15:17:07 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor the numerator. Factor the denominator. Highlight the common terms. Cancel out the common terms. Simplify. Distribute. So simplifies to In other words,

Graphs/316122: Please help me solve this: Graph: 2x + y = 4 (using the intercept method) 1 solutions Answer 226128 by jim_thompson5910(28598)   on 2010-06-21 01:16:06 (Show Source): You can put this solution on YOUR website! x-intercept To find the x-intercept, plug in and solve for x Start with the given equation. Plug in . Simplify. Divide both sides by to isolate . Reduce. So the x-intercept is . ------------------------------------------ y-intercept To find the y-intercept, plug in and solve for y Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. So the y-intercept is . Now let's plot the points and which are the x and y intercepts respectively. Now draw a straight line through the plotted points to graph . Graph of

Functions/316118: Find the domain of the following function f(x)=x+5/x^2-4 Can you please explain how to work this out!! 1 solutions Answer 226127 by jim_thompson5910(28598)   on 2010-06-21 01:12:07 (Show Source): You can put this solution on YOUR website! The domain is the set of all values that we can plug in for 'x' which will give us some number output for f(x) Since you CANNOT divide by zero, this means that we must look for values that make the denominator equal to zero. So just set it equal to zero and solve. Set the denominator equal to zero. Add 4 to both sides. Take the square root of both sides. Don't forget about the plus/minus. or Break up the plus/minus. or Take the square root of 4 to get 2. So when or , the denominator is equal to zero. To avoid dividing by zero, we then make the restriction that or So the domain of is the set of all real numbers but or In interval notation, we would write that as: Basically, we're taking the number line and picking out the numbers -2 and 2.

Functions/316119: Find f(r+1) f(x)=3/x-6 Teacher wasn't clear and I'm lost as to where to start. Please help!!!! 1 solutions Answer 226126 by jim_thompson5910(28598)   on 2010-06-21 01:02:02 (Show Source): You can put this solution on YOUR website! If the function is , then.... Start with the given function. Plug in . In other words, simply replace each 'x' with 'r+1' Combine like terms. -------------------------------------------------------- OR... If the function is , then.... Start with the given function. Plug in . In other words, simply replace each 'x' with 'r+1' Multiply 6 by Combine the fractions. Distribute. Combine like terms.

Human-and-algebraic-language/316113: 1 solutions Answer 226122 by jim_thompson5910(28598)   on 2010-06-21 00:50:54 (Show Source): You can put this solution on YOUR website! You need to post a problem.

Exponents/316115: Please help me with this problem 3x^2x/6xy= 1 solutions Answer 226120 by jim_thompson5910(28598)   on 2010-06-21 00:47:51 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor 6 to get Highlight the common terms. Cancel out the common terms. Simplify. So

Equations/316092: give an ordered pair (x,y) of numbers that satify this equation 6x - y = 8 1 solutions Answer 226116 by jim_thompson5910(28598)   on 2010-06-21 00:18:58 (Show Source): You can put this solution on YOUR website! Hint: Plug in 0 into either variable and you'll see that the equation will simplify greatly.

Coordinate-system/316094: f(x)=-8-2 find the slope and y intercept. I always start these problems wrong, I just need a shove in the right direction. PLease help 1 solutions Answer 226115 by jim_thompson5910(28598)   on 2010-06-21 00:17:59 (Show Source): You can put this solution on YOUR website! I'm assuming that you meant to write . This can be written as since 'y' and 'f(x)' are really one in the same in this case. Notice how is in slope-intercept form where m is the slope and b is the y-intercept. So this shows us that the slope is and the y-intercept is . The y-intercept is the point (-2,0). That's all there is to it.

logarithm/316105: evaluate log[2]8+log[2]16 1 solutions Answer 226114 by jim_thompson5910(28598)   on 2010-06-21 00:15:51 (Show Source): You can put this solution on YOUR website! So Or alternatively... giving the same answer.

Probability-and-statistics/316102: Please help me understand how to answer this question. Thanks! "As a basketball coach, how many possible ways can you position your players if you have a roster of ten and five different positions?" 1 solutions Answer 226113 by jim_thompson5910(28598)   on 2010-06-21 00:13:01 (Show Source): You can put this solution on YOUR website! You have ten selections and five slots to place them. Let's assume that order matters. So for the first position, you have ten choices. For the second, you have 9 choices (since that first player can't play two positions). The third will have 8 choices, the 4th will have 7 choices, and the fifth position will have 6 choices. Now just multiply all these choices out to get: 10*9*8*7*6 = 30240 So there are 30240 different lineups. Another formal way is to use the permutation formula, but we basically follow the same logic. If we were to use the permutation formula , we'll plug in n=10 and r=5. After a bit of work, you'll end up with 10*9*8*7*6 = 30240 which is the same answer.

expressions/316081: -7x-1-6x-5 1 solutions Answer 226112 by jim_thompson5910(28598)   on 2010-06-21 00:07:52 (Show Source): You can put this solution on YOUR website! so

Equations/316079: I can't remember how to figure out this problem. 0.12 - 0.02 (x+3) = -0.05 (3-x) 1 solutions Answer 226105 by jim_thompson5910(28598)   on 2010-06-20 21:59:49 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Multiply. Multiply EVERY term by 100 to clear out the decimals (this basically moves the decimal 2 spots to the right) Combine like terms on the left side. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Geometry_proofs/316074: Determine whether the statement is a tautology, a self-contradiction, or neither.( p ? q ) ? ( p ? ~ q) 1 solutions Answer 226099 by jim_thompson5910(28598)   on 2010-06-20 21:48:30 (Show Source): You can put this solution on YOUR website! What symbols take place of the question marks?

Functions/316072: State whether the functions f and g are equal f(x)= 2x^2 + x/x;g(x)=2x+1 1 solutions Answer 226095 by jim_thompson5910(28598)   on 2010-06-20 21:42:46 (Show Source): You can put this solution on YOUR website! Since , this means that . So the two functions are equal.

Linear-equations/316062: find the slope of the line 5x+2y=-3 1 solutions Answer 226086 by jim_thompson5910(28598)   on 2010-06-20 20:49:57 (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

Functions/316056: let g(x) = 1/x^2 and h(x)= 1/((sqrt x )- 1) please determine the the following function h(g(x)) 1 solutions Answer 226084 by jim_thompson5910(28598)   on 2010-06-20 20:40:56 (Show Source): You can put this solution on YOUR website! Start with the second function. Plug in Break up the square root. Take the square root of 1 to get 1. Take the square root of to get 'x' (this is assuming that 'x' is non-negative) Rewrite the second '1' as Combine the lower fractions. Take the reciprocal of the lower fraction. So the composite function is

Distributive-associative-commutative-properties/316059: (4b+4)(b+7) 1 solutions Answer 226083 by jim_thompson5910(28598)   on 2010-06-20 20:36:13 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: FOIL (ie Expand) Two Binomials Start with the given expression Now let's FOIL the expression Remember, when you FOIL an expression, you follow this procedure: Multiply the First terms: Multiply the Outer terms: Multiply the Inner terms: Multiply the Last terms: Now collect every term to make a single expression Now combine like terms --------------------- Answer: So FOILs and simplifies to In other words,

Matrices-and-determiminant/316054: Row echelon form of a system of linear equation is: 1 2 4 0 = 1 0 1 -1 2 = 2 0 0 1 3 = 0 0 0 0 1 = -2 a) write the system of equations corresponding to this matrix. us x1 x2 x3 x4 as variables. My answer: x1+2x2+4x3 = 1; x2-x3+2x4 = 2; x3+3x4 = 0; and x4= -2 b) determine whether the system is consistent or inconsistent. if consistent, give the solution. My answer: from the equations above: we know x4 = -2 so plug into x3+3(-2)=0 solve for x3 x3-6=0 +6=0+6 x3=6 we know x4=-2 and x3=6 plug into x2-(6)+2(-2)=2 x2-10=2+10 x2-10+10=12 x2=12 we know x4=-2; x3=6; x2=12 plug into x1+2(12)+4(6)=1 x1+24+24=1 x1=-48+1 x1=47 Can you let me know if this is correct? If not please help me where I have it wrong. Thank you! 1 solutions Answer 226082 by jim_thompson5910(28598)   on 2010-06-20 20:30:49 (Show Source): You can put this solution on YOUR website! You look like you know what you're doing, but you made one slight typo on the last step. The last step should read . Aside from that, everything else looks perfect. Because you are able to find a unique solution to the system, this means that the system is consistent and independent.

Linear-equations/316045: Find the x-intercept and the y-intercept. 10x - 18y = 3 1 solutions Answer 226080 by jim_thompson5910(28598)   on 2010-06-20 20:20:16 (Show Source): You can put this solution on YOUR website! x-intercept To find the x-intercept, plug in and solve for x Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . So the x-intercept is . ------------------------------------------ y-intercept To find the y-intercept, plug in and solve for y Start with the given equation. Plug in . Multiply and 0 to get 0. Simplify. Divide both sides by to isolate . Reduce. So the y-intercept is .

Evaluation_Word_Problems/316047: the circumference of a circle is ab out 3 1/7 times the diameter of the circle. what is the circumeference of a circle who diameter is 42 cm? 1 solutions Answer 226079 by jim_thompson5910(28598)   on 2010-06-20 20:15:46 (Show Source): You can put this solution on YOUR website! First note that . Now just multiply by 42 to get . So the circumference is about 132 cm.

Linear-equations/316042: is the ordered pair a solution of the given equation (8, -5) 3x - 7y = 59 1 solutions Answer 226077 by jim_thompson5910(28598)   on 2010-06-20 20:12:12 (Show Source): You can put this solution on YOUR website! The ordered pair (8, -5) tells us that x=8 and y=-5. Plug these values in to get: . Now compute the left side to get 3(8)-7(-5)=24+35=59. Since is indeed correct, this verifies that (8, -5) is a solution to 3x - 7y = 59

Linear-equations/316044: Find three ordered pairs that are solutions of the given linear equation. y = 2/7x - 4 1 solutions Answer 226076 by jim_thompson5910(28598)   on 2010-06-20 20:10:27 (Show Source): You can put this solution on YOUR website! Simply pick values of 'x' to plug in to find values of 'y'. To make things easier, select values of 'x' that are multiples of 7 (so they divide into 7). For instance, if x=7, then giving you the ordered pair (7,-2)

Complex_Numbers/316038: (-7+6i)(-7-5i) 1 solutions Answer 226071 by jim_thompson5910(28598)   on 2010-06-20 19:54:08 (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 .

Quadratic_Equations/316035: Rewrite the following in simplified radical form? Square root 8z^12 1 solutions Answer 226070 by jim_thompson5910(28598)   on 2010-06-20 19:53:02 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor 8 into 4*2 Rewrite as Break up the square root. Take the square root of 4 to get 2. Take the square root of to get . Rearrange the terms. So where

Trigonometry-basics/316032: P(2,-5) is a point on the terminal side of the angle theta. Find the exact values of sin theta. I know that: sin=y/r r= squrert(x^2)+(y^2) r= squrert 4+25 r= squrert 29 so answer is -5/squrert 29 Thanks you so much 1 solutions Answer 226069 by jim_thompson5910(28598)   on 2010-06-20 19:50:11 (Show Source): You can put this solution on YOUR website! You are correct in stating that . Good job.

Exponents-negative-and-fractional/316029: What is 4.1 x 10 to the power of 4 - 1 x 10 to the power of 3? 1 solutions Answer 226068 by jim_thompson5910(28598)   on 2010-06-20 19:36:51 (Show Source): You can put this solution on YOUR website! When you multiply by , you're basically going to move the decimal point 4 spots to the right. So . Similarly, multiplying by moves the decimal point to the right 3 spots. So . Note: -1 = -1.0 Altogether, we get So

Graphs/316028: y = 1/3x graph the equation and identify the y-intercept. 1 solutions Answer 226067 by jim_thompson5910(28598)   on 2010-06-20 19:32:12 (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 3. This means that to go from point to point, we can go up 1 and over 3 So starting at , go up 1 unit 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

Inequalities/316027: Give two values of t≤-4 which satisfy the inequality? 1 solutions Answer 226066 by jim_thompson5910(28598)   on 2010-06-20 19:26:07 (Show Source): You can put this solution on YOUR website! Just pick any two numbers that are less than or equal to -4.

Numeric_Fractions/316026: What is the answer to 3/4 - 2/9? 1 solutions Answer 226065 by jim_thompson5910(28598)   on 2010-06-20 19:20:55 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Fractions Solver Start with the given expression In order to subtract these two fractions, these fractions need to have a common denominator. In order to do that, we simply find that the LCM of 4 and 9 is 36 (note: if you need help with finding the LCM, check out this solver) Now we need to get each denominator to 36 Multiply by Multiply and to get Multiply by Multiply and to get Since both fractions have a common denominator of 36, we can now combine the fractions Combine the fractions Subtract the numerators So

Trigonometry-basics/316023: what is the reference angle for theta= 5pi/3? I know that 300 degrees= 5pi/3. so this means that theta lies in quadrant four and this means that you subtract theta from 360 degrees. so i'm thinking 360-300 = 60degrees or pi/3 radians as the answer. thanks in advance 1 solutions Answer 226064 by jim_thompson5910(28598)   on 2010-06-20 19:17:32 (Show Source): You can put this solution on YOUR website! Or simply remember that 360 degrees = radians. So (which is 60 degrees). Either way, you get the same answer. So good job.