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test/140011: Factor completely and match your result to the correct answer below. r2 + 2r – 80 A)(r + 10)(r + 8) B)(r – 10)(r + 8) C)(r – 10)(r – 8) D)(r + 10)(r – 8) 1 solutions Answer 102038 by jim_thompson5910(28595)   on 2008-05-04 19:30:54 (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 -80 respectively. Now multiply the first coefficient 1 and the last coefficient -80 to get -80. Now what two numbers multiply to -80 and add to the middle coefficient 2? Let's list all of the factors of -80: Factors of -80: 1,2,4,5,8,10,16,20,40,80 -1,-2,-4,-5,-8,-10,-16,-20,-40,-80 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -80 (1)*(-80) (2)*(-40) (4)*(-20) (5)*(-16) (8)*(-10) (-1)*(80) (-2)*(40) (-4)*(20) (-5)*(16) (-8)*(10) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2 First Number Second Number Sum 1 -80 1+(-80)=-79 2 -40 2+(-40)=-38 4 -20 4+(-20)=-16 5 -16 5+(-16)=-11 8 -10 8+(-10)=-2 -1 80 -1+80=79 -2 40 -2+40=38 -4 20 -4+20=16 -5 16 -5+16=11 -8 10 -8+10=2 From this list we can see that -8 and 10 add up to 2 and multiply to -80 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 ) ------------------------------------------------------------ Answer: So factors to

test/140010: Factor: st + 5b – bs – 5t A) (s – 5)(t + b) B) (s – 5)(t – b) C) (s + 5)(t – b) D) The expression is prime. 1 solutions Answer 102037 by jim_thompson5910(28595)   on 2008-05-04 19:29:15 (Show Source): You can put this solution on YOUR website! Start with the given expression Rearrange the terms Group like terms Factor out the GCF "s" from the first group. Factor out the GCF -5 from the second group Rearrange in the second group to get Combine like terms ----------------------------- Answer: So factors to

test/140008: Factor completely: 12p2 + 20p A)2(6p2 + 10) B)4p(3p + 20) C)4p(3p + 5) D)6p(2p + 5) 1 solutions Answer 102036 by jim_thompson5910(28595)   on 2008-05-04 19:23:36 (Show Source): You can put this solution on YOUR website! Start with the given expression Factor out the GCF ----------------------------------------------------------- Answer: So factors to

test/140007: Factor: z2 – 14z + 49 A) (z – 7)2 B) (z – 7)(z + 7) C) (z – 14)(z + 1) D) The expression is prime. 1 solutions Answer 102035 by jim_thompson5910(28595)   on 2008-05-04 19:21:53 (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 49 respectively. Now multiply the first coefficient 1 and the last coefficient 49 to get 49. Now what two numbers multiply to 49 and add to the middle coefficient -14? Let's list all of the factors of 49: Factors of 49: 1,7 -1,-7 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 49 1*49 7*7 (-1)*(-49) (-7)*(-7) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14 First Number Second Number Sum 1 49 1+49=50 7 7 7+7=14 -1 -49 -1+(-49)=-50 -7 -7 -7+(-7)=-14 From this list we can see that -7 and -7 add up to -14 and multiply to 49 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 ) note: is equivalent to since the term occurs twice. So also factors to ------------------------------- Answer: So factors to

test/140006: Factor: y2 – 64 A) (y – 8)(y + 8) B) (y – 8)2 C) (8 – y)(8 + y) D) The expression is prime. 1 solutions Answer 102034 by jim_thompson5910(28595)   on 2008-05-04 19:21:05 (Show Source): You can put this solution on YOUR website! Start with the given expression Rewrite as Rewrite as Now use the difference of squares. Remember, the difference of squares formula is where in this case and Plug in and So the expression factors to Notice that if you foil the factored expression, you get the original expression. This verifies our answer.

Geometric_formulas/139954: 1 solutions Answer 102009 by jim_thompson5910(28595)   on 2008-05-04 13:25:13 (Show Source): You can put this solution on YOUR website! Let x=supplement to angle A Remember, supplement angles add to 180. So if we want to find the supplement to angle A, then Subtract 72 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So our answer is So the supplement to angle A is 108 degrees

Geometric_formulas/139952: 7. Find the measure of angle x and measure of angle y. 1 solutions Answer 102008 by jim_thompson5910(28595)   on 2008-05-04 13:20:11 (Show Source): You can put this solution on YOUR website! Notice how angle x and 135 degrees form a 180 degree angle. So this means that Subtract 135 from both sides Combine like terms on the right side Also, notice how angle x and angle y also form a 180 degree angle. So But we know what x is, so plug in the value of x Plug in Subtract 45 from both sides Combine like terms on the right side -------------------------------------------------------------- Answer: So the values are and

Geometric_formulas/139951: 6. Find the missing angle. 1 solutions Answer 102006 by jim_thompson5910(28595)   on 2008-05-04 13:14:15 (Show Source): You can put this solution on YOUR website! To find the missing angle, first add up the two given angles So the sum of the two angles is 148 degrees. Now subtract this answer from 180 (remember the sum of the three angles of a triangle is 180 degrees) So the missing angle is 32 degrees

Geometric_formulas/139950: 5. Which two triangles are similar? 1 solutions Answer 102005 by jim_thompson5910(28595)   on 2008-05-04 13:08:48 (Show Source): You can put this solution on YOUR website! First, we need to find the missing angles of each triangle. For the first triangle, first add up the two given angles 69 and 48 to get Now subtract 117 from 180 to get So the first triangle has these angles --------------------------------------------------------- For the second triangle, first add up the two given angles 63 and 48 to get Now subtract 111 from 180 to get So the second triangle has these angles ------------------------------------------------------------ For the third triangle, first add up the two given angles 63 and 48 to get Now subtract 111 from 180 to get So the third triangle has these angles ---------------------------------------------------------- Summary: So the three triangles have these angles ---------------------------------------------------------- Answer: Remember, similar triangles have equal angles. From the figure, we can see that triangles a) and b) have equal angles. So triangles a) and b) are similar triangles.

Geometric_formulas/139948: 4. The two triangles are similar. Find the indicated side. Find y. 1 solutions Answer 102003 by jim_thompson5910(28595)   on 2008-05-04 12:54:18 (Show Source): You can put this solution on YOUR website! Since the triangles are similar, this means that the length of the sides are dependent on one another. In fact, these sides form the ratio: Multiply both sides by y Multiply both sides by 8 Multiply Divide both sides by 10 Simplify So our answer is

Geometric_formulas/139946: 3. Identify the hypotenuse of the triangle by giving its letter 1 solutions Answer 102002 by jim_thompson5910(28595)   on 2008-05-04 12:48:23 (Show Source): You can put this solution on YOUR website! The hypotenuse is the longest side. So in this case, the hypotenuse is z.

Geometric_formulas/139945: Find the missing length of the right triangle 1 solutions Answer 102001 by jim_thompson5910(28595)   on 2008-05-04 12:45:30 (Show Source): You can put this solution on YOUR website! Let's use Pythagoreans theorem to solve this problem Pythagoreans theorem: where a and b are the legs of the triangle and c is the hypotenuse Plug in a=7, b=24. Now lets solve for c. Square each individual term Combine like terms Take the square root of both sides Simplify the square root So our answer is So the length of the unknown side is 25 units.

Geometric_formulas/139941: 1. Approximate by giving the two whole numbers that it lies between 1 solutions Answer 102000 by jim_thompson5910(28595)   on 2008-05-04 12:10:17 (Show Source): You can put this solution on YOUR website! First, note that the numbers 25 and 36 are perfect squares. In other words, and . So since 31 is in between 25 and 36, this means that the square root of 31 is in between 5 and 6. In other words, since , this means . Notice how 31 is 6 units away from 25 and 5 units away from 36. So 31 is about the halfway point from 25 to 36. So a good approximation for is 5.5 since 5.5 is halfway between 5 and 6. So If we take the square root of 31 with a calculator, we get . So this shows us that our approximation is very close.

Equations/139872: Find the slope of a line whose equation is y= -6x+3 1 solutions Answer 101938 by jim_thompson5910(28595)   on 2008-05-03 15:09:29 (Show Source): You can put this solution on YOUR website! 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

Quadratic_Equations/139853: Please help me solve this equation: 5x+4y=12 I have tried the equation by doing this: 5x+4y=12 5x-5x+4y=12-5x 4y=12-5x 4y/4=12-5x/4 My answer came totaled to: y=3-5x 1 solutions Answer 101934 by jim_thompson5910(28595)   on 2008-05-03 14:14:02 (Show Source): You can put this solution on YOUR website! Do you want to solve for y? Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by Break up the fraction Reduce

Polynomials-and-rational-expressions/139800: Solve for z: z^2-2z+1=-4 1 solutions Answer 101926 by jim_thompson5910(28595)   on 2008-05-03 11:25:36 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 4 to both sides. Combine like terms Let's use the quadratic formula to solve for z: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=-2, and c=5 Negate -2 to get 2 Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .) 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 1 to get 2 After simplifying, the quadratic has roots of or

Complex_Numbers/139806: please help solve Divide and express the result in standard form 6 -5i / 8 + 4i 1 solutions Answer 101925 by jim_thompson5910(28595)   on 2008-05-03 11:22:33 (Show Source): You can put this solution on YOUR website! Start with the given expression Multiply the fraction by Foil and Multiply Break up the fraction. Reduce. So the expression is now in form where and

Circles/139830: What is the radius of the circle 2x^2+2y^2-8x+16y-32=0? I think it is 6??????? 1 solutions Answer 101924 by jim_thompson5910(28595)   on 2008-05-03 11:17:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Rearrange the terms Add to both sides Complete the square for the x terms Complete the square for the y terms Combine like terms Add to both sides Combine like terms Factor out the common term 2 Divide both sides by 2 ----------- Notice how the equation is now in the form . This means that this conic section is a circle where (h,k) is the center and is the radius. So the circle has these properties: Center: (2,-4) Radius: --------------------------- Answer: So the radius of the circle is 6 units

Quadratic_Equations/139775: x2+4x-21=0 trying to find the two solutions??? I was fine till c was a value... when c = o I had no problems solving now that c = a value.. im stuck help i can get this far: a=1 b=4 c= -21 -4+_ 4sqd + 4(1)(-21) divided by 2(1) then, -4+- 4sqd + -84 divided by 2 then i get confused.... help 1 solutions Answer 101881 by jim_thompson5910(28595)   on 2008-05-02 17:14:14 (Show Source): You can put this solution on YOUR website! 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 ( notice , , and ) Plug in a=1, b=4, and c=-21 Square 4 to get 16 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 1 to get 2 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or Notice when we graph , we get: and we can see that the roots are and . This verifies our answer

Polynomials-and-rational-expressions/139640: Hi, I am having trouble with a problem I hope some one can help me please. Factor Completety: 3x - 3x^2 + 6x - 18 I would like to thank you for your help. 1 solutions Answer 101798 by jim_thompson5910(28595)   on 2008-05-01 20:48:46 (Show Source): You can put this solution on YOUR website! Are you sure it's not supposed to read: ??? Start with the given expression Combine like terms Factor out the GCF Now let's focus on the inner expression ------------------------------------------------------------ Looking at we can see that the first term is and the last term is where the coefficients are 1 and -6 respectively. Now multiply the first coefficient 1 and the last coefficient -6 to get -6. Now what two numbers multiply to -6 and add to the middle coefficient 1? Let's list all of the factors of -6: Factors of -6: 1,2,3,6 -1,-2,-3,-6 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -6 (1)*(-6) (2)*(-3) (-1)*(6) (-2)*(3) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to 1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 1 First Number Second Number Sum 1 -6 1+(-6)=-5 2 -3 2+(-3)=-1 -1 6 -1+6=5 -2 3 -2+3=1 From this list we can see that -2 and 3 add up to 1 and multiply to -6 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 ) ------------------------------------------------------------ So our expression goes from and factors further to ------------------ Answer: So factors to

test/139597: This question is from textbook factoring using the Distributive property. x3+3x2-4x-12 1 solutions Answer 101786 by jim_thompson5910(28595)   on 2008-05-01 18:40:13 (Show Source): You can put this solution on YOUR website! Start with the given expression Group like terms Factor out the GCF out of the first group. Factor out the GCF out of the second group Since we have the common term , we can combine like terms Factor by using the difference of squares to get So factors to

Exponential-and-logarithmic-functions/139562: This question is from textbook College Algrbra Find (f o g)(16) if f(x)=3^x and f(x)=log4(x) I got this far g(16)=log4(16)=4 Please help.Thanks 1 solutions Answer 101784 by jim_thompson5910(28595)   on 2008-05-01 18:29:09 (Show Source): You can put this solution on YOUR website! Remember (f o g)(x) is the same as f(g(x)) So (f o g)(16)=f(g(16)) So (note: asks: "4 raised to what power gives me 16?". Since , this means ) So g(16)=2 Now this means that f(g(16))=f(2) So f(g(16))=9

Quadratic_Equations/139592: This question is from textbook Factor each expression. x2-3x-40 1 solutions Answer 101783 by jim_thompson5910(28595)   on 2008-05-01 18:23:39 (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 -40 respectively. Now multiply the first coefficient 1 and the last coefficient -40 to get -40. Now what two numbers multiply to -40 and add to the middle coefficient -3? Let's list all of the factors of -40: Factors of -40: 1,2,4,5,8,10,20,40 -1,-2,-4,-5,-8,-10,-20,-40 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -40 (1)*(-40) (2)*(-20) (4)*(-10) (5)*(-8) (-1)*(40) (-2)*(20) (-4)*(10) (-5)*(8) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -3? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -3 First Number Second Number Sum 1 -40 1+(-40)=-39 2 -20 2+(-20)=-18 4 -10 4+(-10)=-6 5 -8 5+(-8)=-3 -1 40 -1+40=39 -2 20 -2+20=18 -4 10 -4+10=6 -5 8 -5+8=3 From this list we can see that 5 and -8 add up to -3 and multiply to -40 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 ) ------------------------------- Answer: So factors to

expressions/139593: This question is from textbook Factor each expression. 5x2+16x+3 1 solutions Answer 101782 by jim_thompson5910(28595)   on 2008-05-01 18:21:36 (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 5 and 3 respectively. Now multiply the first coefficient 5 and the last coefficient 3 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 16? Let's list all of the factors of 15: Factors of 15: 1,3,5,15 -1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to 15 1*15 3*5 (-1)*(-15) (-3)*(-5) note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16 First Number Second Number Sum 1 15 1+15=16 3 5 3+5=8 -1 -15 -1+(-15)=-16 -3 -5 -3+(-5)=-8 From this list we can see that 1 and 15 add up to 16 and multiply to 15 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 ) ------------------------------- Answer: So factors to

Miscellaneous_Word_Problems/139591: This question is from textbook Algebra Structure and Method I have been struggling with this problem and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank you! Factoring Patterns for ax^2+bx+c Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime. 2(x-y)^2-9(x-y)z-5z^2 1 solutions Answer 101781 by jim_thompson5910(28595)   on 2008-05-01 18:19:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Let Plug in Sort the terms in descending order Factor out a negative one Now let's factor the inner polynomial Looking at we can see that the first term is and the last term is where the coefficients are 5 and -2 respectively. Now multiply the first coefficient 5 and the last coefficient -2 to get -10. Now what two numbers multiply to -10 and add to the middle coefficient 9? Let's list all of the factors of -10: Factors of -10: 1,2,5,10 -1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -10 (1)*(-10) (2)*(-5) (-1)*(10) (-2)*(5) note: remember, the product of a negative and a positive number is a negative 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 Number Second Number Sum 1 -10 1+(-10)=-9 2 -5 2+(-5)=-3 -1 10 -1+10=9 -2 5 -2+5=3 From this list we can see that -1 and 10 add up to 9 and multiply to -10 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 factors to This means that factors to (remember, we pulled out a negative one previously) Now replace "w" with Distribute ------------------------------- Answer: So factors to

Radicals/139576: If √96 is simplified to a√b such that a and b are integers, what is the value of a? √ = Radical sign Thank you, in advance. 1 solutions Answer 101780 by jim_thompson5910(28595)   on 2008-05-01 18:12:17 (Show Source): You can put this solution on YOUR website! Start with the given expression The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number. So let's list the factors of 96 Factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Notice how 16 is the largest perfect square, so lets factor 96 into 16*6 Factor 96 into 16*6 Break up the square roots using the identity Take the square root of the perfect square 16 to get 4 So the expression simplifies to ----------------------------------------------------- Answer: So in this case, the value of ---------------------------- Check: Notice if we evaluate the square root of 96 with a calculator we get and if we evaluate we get This shows that . So this verifies our answer

Miscellaneous_Word_Problems/139589: This question is from textbook Algebra Structure and Method I have been struggling with this problem for awhile now and I was wondering if anyone could help me? I would deeply appreciate it! Please and Thank you! Factoring Patterns for ax^2+bx+c Factor. Check by multiplying the factors. If the polynomial is not factorable, write prime. 8+45r-18r^2 1 solutions Answer 101779 by jim_thompson5910(28595)   on 2008-05-01 18:09:59 (Show Source): You can put this solution on YOUR website! Start with the given expression Sort the terms in descending order Factor out a negative one Looking at the inner polynomial , we can see that the first term is and the last term is -8 Now multiply the first coefficient 18 and the last term -8 to get -144. Now what two numbers multiply to -144 and add to the middle coefficient -45? Let's list all of the factors of -144: Factors of -144: 1,2,3,4,6,8,9,12,16,18,24,36,48,72 -1,-2,-3,-4,-6,-8,-9,-12,-16,-18,-24,-36,-48,-72 ...List the negative factors as well. This will allow us to find all possible combinations These factors pair up and multiply to -144 (1)*(-144) (2)*(-72) (3)*(-48) (4)*(-36) (6)*(-24) (8)*(-18) (9)*(-16) (-1)*(144) (-2)*(72) (-3)*(48) (-4)*(36) (-6)*(24) (-8)*(18) (-9)*(16) note: remember, the product of a negative and a positive number is a negative number Now which of these pairs add to -45? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -45 First Number Second Number Sum 1 -144 1+(-144)=-143 2 -72 2+(-72)=-70 3 -48 3+(-48)=-45 4 -36 4+(-36)=-32 6 -24 6+(-24)=-18 8 -18 8+(-18)=-10 9 -16 9+(-16)=-7 -1 144 -1+144=143 -2 72 -2+72=70 -3 48 -3+48=45 -4 36 -4+36=32 -6 24 -6+24=18 -8 18 -8+18=10 -9 16 -9+16=7 From this list we can see that 3 and -48 add up to -45 and multiply to -144 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 ) So factors to ------------------------------- Answer: So factors to

Inequalities/139501: how do you solve for this 2x – 9 > 0 1 solutions Answer 101724 by jim_thompson5910(28595)   on 2008-05-01 11:42:00 (Show Source): You can put this solution on YOUR website! Start with the given inequality Add 9 to both sides Combine like terms on the right side Divide both sides by 2 to isolate x -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Coordinate-system/139504: Find the domain of the function f(x)=1 _____ x-4 1 solutions Answer 101723 by jim_thompson5910(28595)   on 2008-05-01 11:40:42 (Show Source): You can put this solution on YOUR website! Start with the given function Set the denominator equal to zero. Remember, dividing by 0 is undefined. So if we find values of x that make the denominator zero, then we must exclude them from the domain. Add 4 to both sides Combine like terms on the right side Since makes the denominator equal to zero, this means we must exclude from our domain So our domain is: which in plain English reads: x is the set of all real numbers except So our domain looks like this in interval notation note: remember, the parenthesis excludes 4 from the domain If we wanted to graph the domain on a number line, we would get: Graph of the domain in blue and the excluded value represented by open circle Notice we have a continuous line until we get to the hole at (which is represented by the open circle). This graphically represents our domain in which x can be any number except x cannot equal 4

Equations/139536: -5(x-2)+3=5 1 solutions Answer 101722 by jim_thompson5910(28595)   on 2008-05-01 11:39:40 (Show Source): You can put this solution on YOUR website! Start with the given equation Distribute Combine like terms on the left side Subtract 13 from both sides Combine like terms on the right side Divide both sides by -5 to isolate x Reduce -------------------------------------------------------------- Answer: So our answer is (which is approximately in decimal form)

Coordinate-system/139503: Graph 3x-2y=-18 1 solutions Answer 101721 by jim_thompson5910(28595)   on 2008-05-01 11:38:59 (Show Source): You can put this solution on YOUR website! Start with the given equation Subtract from both sides Rearrange the equation Divide both sides by 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 3 and the run is 2. This means that to go from point to point, we can go up 3 and over 2 So starting at , go up 3 units and to the right 2 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