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# Recent problems solved by 'jim_thompson5910'

jim_thompson5910 answered: 28465 problems
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 Square-cubic-other-roots/682000: 3------ 64(x-10)3 I need to simplify assuming all variables are real numbers its cube root of the bottom if that make sense1 solutions Answer 422946 by jim_thompson5910(28476)   on 2012-11-17 18:06:57 (Show Source): You can put this solution on YOUR website! So simplifies to
 logarithm/681997: Help me please solve this equation: Determine the domain of the function: g(x)=^9 Thank you!1 solutions Answer 422943 by jim_thompson5910(28476)   on 2012-11-17 17:55:02 (Show Source): You can put this solution on YOUR website!I'm assuming the function is This is an odd nth root radical function. So you can plug in any real number in for x and get some real number out for y. Therefore, Domain: set of all real numbers.
test/681999: X^2-7x+12
1 solutions

Answer 422941 by jim_thompson5910(28476)   on 2012-11-17 17:53:24 (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 = 12
2*6 = 12
3*4 = 12
(-1)*(-12) = 12
(-2)*(-6) = 12
(-3)*(-4) = 12

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

First NumberSecond NumberSum
1121+12=13
262+6=8
343+4=7
-1-12-1+(-12)=-13
-2-6-2+(-6)=-8
-3-4-3+(-4)=-7

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 .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 logarithm/681996: Please help me solve this equation: ^3 = -5 This is what I have gotten but not sure if it is correct: 3x-2=-5^3 3x-2=-75 3x=-73 x=-73/3 Thanks 1 solutions Answer 422937 by jim_thompson5910(28476)   on 2012-11-17 17:45:49 (Show Source): You can put this solution on YOUR website!-5^3 is NOT -75 it is -5^3 = -(5^3) = -(5*5*5) = -125, so it should be 3x-2=-5^3 3x-2=-125 3x=-123 x=-123/3 x = -41
 Linear-equations/681927: What would the equation of the line be for the points (2,12) and (1,6)1 solutions Answer 422920 by jim_thompson5910(28476)   on 2012-11-17 16:49:11 (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 12 to both sides. Combine like terms. Remove the trailing zero So the equation that goes through the points and is
 Exponents/681925: 7.86*10^-41 solutions Answer 422917 by jim_thompson5910(28476)   on 2012-11-17 16:45:41 (Show Source): You can put this solution on YOUR website!Move the decimal over to the left 4 spots to get this: 7.86*10^-4 = 0.000786
 Trigonometry-basics/681871: how to construck standard position in sine theta is equal to 4 over 5 ?1 solutions Answer 422916 by jim_thompson5910(28476)   on 2012-11-17 16:44:36 (Show Source): You can put this solution on YOUR website!Draw a right triangle in which the hypotenuse is 5 and the opposite leg is 4.
 Exponents/681986: (a^-3/b)^-11 solutions Answer 422914 by jim_thompson5910(28476)   on 2012-11-17 16:43:32 (Show Source): You can put this solution on YOUR website!(a^-3/b)^-1 [(a^-3)^(-1)]/[(b)^-1] (a^3)/(b^(-1)) a^3b^1 a^3b So (a^-3/b)^-1 simplifies to a^3b
 percentage/681922: What is 92% off of $36?1 solutions Answer 422912 by jim_thompson5910(28476) on 2012-11-17 16:42:31 (Show Source): You can put this solution on YOUR website!92% of$36 is (92/100)*36 = 0.96*36 = 33.12 Subtract this from 36 to get 36 - 33.12 = 2.88 So after taking 92% off of $36, you only have to pay$2.88. This is quite a discount, which makes sense given that 92% is a very large percentage (when it comes to discounts).
 Polynomials-and-rational-expressions/681876: Expand: (2x^2 + 4x + 5)(3x^2 - 6x + 7)1 solutions Answer 422911 by jim_thompson5910(28476)   on 2012-11-17 16:40:37 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Distribute. Multiply. Now combine like terms. So expands to . In other words, .
 Numeric_Fractions/681919: (10-2)4+81 solutions Answer 422910 by jim_thompson5910(28476)   on 2012-11-17 16:39:19 (Show Source): You can put this solution on YOUR website!Follow PEMDAS (10-2)4+8 (8)4+8 32+8 40 So (10-2)4+8 = 40
 Coordinate-system/681891: y=4/3x + 3 y=-2/3x + -3 1 solutions Answer 422909 by jim_thompson5910(28476)   on 2012-11-17 16:38:26 (Show Source): You can put this solution on YOUR website!Hint: y=4/3x + 3 -2/3x - 3 = 4/3x + 3 -2x - 9 = 4x + 9 ... Multiply everything by 3 to clear out the fractions. I'll let you finish.
 Exponential-and-logarithmic-functions/681880: Graph the function y=5(1/2)^x+4.1 solutions Answer 422908 by jim_thompson5910(28476)   on 2012-11-17 16:35:08 (Show Source): You can put this solution on YOUR website!If you want to graph , then you will get If you want to graph , then you will get Here are both graphs plotted on the same xy axis ( in green and in blue) Both graphs can be found using a graphing calculator.
 Exponential-and-logarithmic-functions/681881: Graph the function y=4(1/6)^x+2 ((x+2) is the entire exponent.)1 solutions Answer 422906 by jim_thompson5910(28476)   on 2012-11-17 16:32:42 (Show Source): You can put this solution on YOUR website!Use a graphing calculator to get Note: the green curve gets closer and closer to the x-axis, but it will never cross or touch it (regardless of how it looks above)
 test/681882: 1 solutions Answer 422905 by jim_thompson5910(28476)   on 2012-11-17 16:31:24 (Show Source): You can put this solution on YOUR website!Problem missing. Please post the full problem. Thanks.
 Angles/681886: 2x+y=230 & y-x=5..find value of y1 solutions Answer 422904 by jim_thompson5910(28476)   on 2012-11-17 16:30:55 (Show Source): You can put this solution on YOUR website!Hint: y-x=5 -x = 5 - y x = y - 5 ------------------------------------------------------- 2x+y=230 2(y-5)+y=230 2y - 10 + y = 230 3y - 10 = 230 I'll let you finish.
 Linear-equations/681976: x/3-y/8=11 solutions Answer 422903 by jim_thompson5910(28476)   on 2012-11-17 16:28:53 (Show Source): You can put this solution on YOUR website!If you want to get this into slope intercept form, then x/3-y/8=1 -y/8 = -x/3 + 1 y = 8/3x - 8
test/681947: 4b^2-7b-15
1 solutions

Answer 422902 by jim_thompson5910(28476)   on 2012-11-17 16:27:41 (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 :
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60

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

These factors pair up and multiply to .
1*(-60) = -60
2*(-30) = -60
3*(-20) = -60
4*(-15) = -60
5*(-12) = -60
6*(-10) = -60
(-1)*(60) = -60
(-2)*(30) = -60
(-3)*(20) = -60
(-4)*(15) = -60
(-5)*(12) = -60
(-6)*(10) = -60

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

First NumberSecond NumberSum
1-601+(-60)=-59
2-302+(-30)=-28
3-203+(-20)=-17
4-154+(-15)=-11
5-125+(-12)=-7
6-106+(-10)=-4
-160-1+60=59
-230-2+30=28
-320-3+20=17
-415-4+15=11
-512-5+12=7
-610-6+10=4

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 .

In other words, .

Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).

 Miscellaneous_Word_Problems/681959: 1 solutions Answer 422901 by jim_thompson5910(28476)   on 2012-11-17 16:27:12 (Show Source): You can put this solution on YOUR website!Problem missing.
 Exponents/681926: -x^2 - 61 solutions Answer 422900 by jim_thompson5910(28476)   on 2012-11-17 16:26:31 (Show Source): You can put this solution on YOUR website!If you want to graph, then using a graphing calculator will give you
 expressions/681894: 3p(q-r^2) p=-1 q=-3 r=5 What is the solution? I got -66, but in class the teacher says its 84. 3(-1)(-3-5^2) -3(-3+25) -3(22) -66 How do you get 84?1 solutions Answer 422899 by jim_thompson5910(28476)   on 2012-11-17 16:25:14 (Show Source): You can put this solution on YOUR website!Your work 3(-1)(-3-5^2) -3(-3+25) <<<<------ It should be -25 since -5^2 = -25 -3(22) -66 ======================================================= Corrected work 3p(q-r^2) 3(-1)(-3-5^2) 3(-1)(-3-25) 3(-1)(-28) -3(-28) 84 So 3p(q-r^2) = 84 when p = -1, q = -3 and r = 5
 Linear-equations/681884: y=3/2x+121 solutions Answer 422898 by jim_thompson5910(28476)   on 2012-11-17 16:22:48 (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 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
Quadratic_Equations/681794: Help explain why this expression cannot be factored
40a^2+21a-2
1 solutions

Answer 422798 by jim_thompson5910(28476)   on 2012-11-16 21:09:56 (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 :
1,2,4,5,8,10,16,20,40,80
-1,-2,-4,-5,-8,-10,-16,-20,-40,-80

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

These factors pair up and multiply to .
1*(-80) = -80
2*(-40) = -80
4*(-20) = -80
5*(-16) = -80
8*(-10) = -80
(-1)*(80) = -80
(-2)*(40) = -80
(-4)*(20) = -80
(-5)*(16) = -80
(-8)*(10) = -80

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

First NumberSecond NumberSum
1-801+(-80)=-79
2-402+(-40)=-38
4-204+(-20)=-16
5-165+(-16)=-11
8-108+(-10)=-2
-180-1+80=79
-240-2+40=38
-420-4+20=16
-516-5+16=11
-810-8+10=2

From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.

===============================================================

Answer:

So doesn't factor at all (over the rational numbers).

So is prime.

 Miscellaneous_Word_Problems/681787: what is the formula to add 40% to any given amount of money, say, add 40% to $67.50. and visa versa whats the formula to subtract 40% of any given amount of money. Thank you, wendears@yahoo.com really! 1 solutions Answer 422796 by jim_thompson5910(28476) on 2012-11-16 21:09:10 (Show Source): You can put this solution on YOUR website!Take 40% of 67.50 to get 0.4*67.50 = 27 So 40% of$67.50 is $27. Add this to the original amount ($67.50) to get 67.50 + 27 = 94.50 ======================================================= Doing it in general If you want to add 40% to any amount, call it x dollars, then take 40% of x to get 0.4x Then add it to the original amount x to get x + 0.4x You can combine like terms to get 1.4x Notice how 1.4 times 67.50 gives you the same answer as before.
 test/681781: Factor. Check by multiplying x2-5x1 solutions Answer 422782 by jim_thompson5910(28476)   on 2012-11-16 20:17:02 (Show Source): You can put this solution on YOUR website!x^2-5x = x(x-5) To check, just distribute back again.
 Polynomials-and-rational-expressions/681683: If possible, evaluate the expression for the given value of the variable. 9/x^2-7x + 12 x = -3 1 solutions Answer 422747 by jim_thompson5910(28476)   on 2012-11-16 16:05:30 (Show Source): You can put this solution on YOUR website! So when x = -3
 Polynomials-and-rational-expressions/681684: simplify the espression. n^2 - n/n^2 - 4n I came up with n - n/n - 4 just want to check if that is correct. If not can you please provide correct answer? Thanks!1 solutions Answer 422745 by jim_thompson5910(28476)   on 2012-11-16 15:52:24 (Show Source): You can put this solution on YOUR website!n^2 - n = n(n-1) n^2 - 4n = n(n-4) So the two 'n' terms outside the parenthesis cancel leaving you with this final answer:
 Numeric_Fractions/681606: -3/8 + 5/8=1 solutions Answer 422736 by jim_thompson5910(28476)   on 2012-11-16 14:59:20 (Show Source):
 Linear_Algebra/681636: -4(3x-4)=2(4x-24) 1 solutions Answer 422735 by jim_thompson5910(28476)   on 2012-11-16 14:58:09 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 . Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Quadratic-relations-and-conic-sections/681672: need to understand how to get center and radius and then graph this equation? x squared + y squared=11 solutions Answer 422734 by jim_thompson5910(28476)   on 2012-11-16 14:56:03 (Show Source): You can put this solution on YOUR website!x^2 + y^2 = 1 can be rewritten as (x-0)^2 + (y-0)^2 = 1^2 and that is in the form (x-h)^2+(y-k)^2=r^2, which is a circle with radius r and center (h,k) Since h = 0, k = 0 and r = 1, the center of x^2 + y^2 = 1 is (0,0) and it has a radius of 1 unit. This is a special circle known as the unit circle (which you'll use a lot in trigonometry). The graph looks like this
 Trigonometry-basics/681671: Is sinA > cosA always? why and how?1 solutions Answer 422732 by jim_thompson5910(28476)   on 2012-11-16 14:54:14 (Show Source): You can put this solution on YOUR website!no, if A = 0, then sin(A) > cos(A) sin(0) > cos(0) 0 > 1 which is FALSE So sin(A) > cos(A) is not always true.