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 Equations/620975: I need to solve this problem for "a" 2a-b=ac+3b Thanks!1 solutions Answer 390480 by jim_thompson5910(28476)   on 2012-06-14 18:39:22 (Show Source):
 Numeric_Fractions/620978: how do i simplify 7(x-4)=?1 solutions Answer 390479 by jim_thompson5910(28476)   on 2012-06-14 18:38:12 (Show Source): You can put this solution on YOUR website!7(x-4) 7x-7*4 7x-28
 Numeric_Fractions/620976: how do i simplify 3x+7-2x?1 solutions Answer 390476 by jim_thompson5910(28476)   on 2012-06-14 18:29:36 (Show Source): You can put this solution on YOUR website!3x+7-2x (3x-2x)+7 x+7 So 3x+7-2x simplifies to x+7
 Numeric_Fractions/620969: how do i solve for 10-6y+4y+9?1 solutions Answer 390475 by jim_thompson5910(28476)   on 2012-06-14 18:20:14 (Show Source): You can put this solution on YOUR website!You can't solve, but you can simplify 10-6y+4y+9 -2y+19 So 10-6y+4y+9 simplifies to -2y+19
Numeric_Fractions/620953: x2 – 5x – 6
1 solutions

Answer 390473 by jim_thompson5910(28476)   on 2012-06-14 17:56:22 (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 :
1,2,3,6
-1,-2,-3,-6

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

These factors pair up and multiply to .
1*(-6) = -6
2*(-3) = -6
(-1)*(6) = -6
(-2)*(3) = -6

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

First NumberSecond NumberSum
1-61+(-6)=-5
2-32+(-3)=-1
-16-1+6=5
-23-2+3=1

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

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

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).

 Numeric_Fractions/620960: how do i solve for 8n-7y-12n+5-3y? 1 solutions Answer 390472 by jim_thompson5910(28476)   on 2012-06-14 17:55:33 (Show Source): You can put this solution on YOUR website!You can't solve, but you can simplify 8n-7y-12n+5-3y (8n-12n)+(-7y-3y)+5 -4n-10y+5 So 8n-7y-12n+5-3y simplifies to -4n-10y+5
 Numeric_Fractions/620955: 2(x – 5) = –111 solutions Answer 390471 by jim_thompson5910(28476)   on 2012-06-14 17:54:32 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Travel_Word_Problems/620952: jim drive 70 miles in 2 hours. if he can keep the same pace , how long will it take him to drive 630 miles?1 solutions Answer 390468 by jim_thompson5910(28476)   on 2012-06-14 17:19:08 (Show Source): You can put this solution on YOUR website!70/2 = 630/x 70x = 2*630 70x = 1260 x = 1260/70 x = 18 So it will take him 18 hours to drive 630 miles (if he keeps the same pace).
 Probability-and-statistics/620938: Please help? I'm so lost on this problem. Can anyone help? A sample of 140 golfers showed that their average score on a particular golf course was 93.38 with a standard deviation of 4.36. Answer each of the following (show all work and state the final answer to at least two decimal places.): (A) Find the 90% confidence interval of the mean score for all 140 golfers. (B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 95 golfers instead of a sample of 140. (C) Which confidence interval is smaller and why? 1 solutions Answer 390465 by jim_thompson5910(28476)   on 2012-06-14 16:59:29 (Show Source): You can put this solution on YOUR website!I'll do part A) to get you going. A) Lower Bound: LB = xbar - z*sigma/sqrt(n) LB = 93.38 - 1.64485*4.36/sqrt(140) LB = 93.38 - 1.64485*4.36/11.8321596 LB = 93.38 - 7.171546/11.8321596 LB = 93.38 - 0.606106 LB = 92.773894 ----------------------- Upper Bound: LB = xbar + z*sigma/sqrt(n) LB = 93.38 + 1.64485*4.36/sqrt(140) LB = 93.38 + 1.64485*4.36/11.8321596 LB = 93.38 + 7.171546/11.8321596 LB = 93.38 + 0.606106 LB = 93.986106 So the 90% confidence interval of the mean score for all 140 golfers is (92.774, 93.986) Note: I rounded to three places because it said to round to "at least two decimal places", so I just picked one number higher Another note: The value z = 1.64485 is the value of z such that 90% of the distribution under the standard normal curve is between z = -1.64485 and z = 1.64485. Use a calculator or a table to find this value.
 Polynomials-and-rational-expressions/620940: Name two monomials whose product is 54x^2y^31 solutions Answer 390462 by jim_thompson5910(28476)   on 2012-06-14 16:25:27 (Show Source): You can put this solution on YOUR website!54 = 27*2 x^2 = x*x and y^3 = y^2*y So the two monomials 27xy^2 and 2xy multiply to 54x^2y^3
 Equations/620939: Help me solve 3(x-1)-5x = 12-(6x-7)1 solutions Answer 390461 by jim_thompson5910(28476)   on 2012-06-14 16:24:23 (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. Add to 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
 Probability-and-statistics/620707: Solve: 73x is congruent to(the three line equal symbol) 115 (mod 971). I know you can change this to (73x-115)/971, but I'm not sure how to solve the rest of this.1 solutions Answer 390349 by jim_thompson5910(28476)   on 2012-06-14 00:54:02 (Show Source): You can put this solution on YOUR website!73x = 1 (mod 971) 971 | (73x - 1) 971y = 73x - 1 -73x + 971y = -1 73x - 971y = 1 971 = 13*73 + 22 ----> 22 = 971 -13*73 73 = 3*22 + 7 ----> 7 = 73 - 3*22 22 = 3*7 + 1 ----> 1 = 22 - 3*7 1 = 22 - 3*7 1 = 22 - 3*(73 - 3*22) 1 = 22 - 3*73 + 9*22 1 = 971 -13*73 - 3*73 + 9*(971 - 13*73) 1 = 971 - 13*73 - 3*73 + 9*971 - 117*73 1 = 10*971 - 13*73 - 3*73 - 117*73 1 = 10*971 - 133*73 Since 1 = 10*971 - 133*73, this means that for 73x = 1 (mod 971), the solution is x = -133 = 838 (mod 971) So 73x = 1 (mod 971) 73*838 = 1 (mod 971) Now multiply both sides by 115 73*838 = 1 (mod 971) 115*73*838 = 115*1 (mod 971) 73*(115*838) = 115*1 (mod 971) 73*(115*838) = 115 (mod 971) 73*96370 = 115 (mod 971) 73*241 = 115 (mod 971) So the solution for x in 73x = 115 (mod 971) is x = 241
 Radicals/620690: Darla is building a new desk. To make sure she had made a square corner, she measures 6ft. from the corner along one edge and 3ft. from the corner along the other edge. How long should the diagonal be between those two points if the corner is a right angle? Diagonal = ? ft. (Round to the nearest thousandth)1 solutions Answer 390335 by jim_thompson5910(28476)   on 2012-06-13 22:06:01 (Show Source): You can put this solution on YOUR website!D = sqrt( L^2 + W^2 ) D = sqrt( 6^2 + 3^2 ) D = sqrt( 36 + 9 ) D = sqrt( 45 ) D = 6.7082 D = 6.708 So the diagonal should be roughly 6.708 feet
 Coordinate-system/620689: true or false, the graph of 2x-3y=6 is a line, for all real numbers x and y1 solutions Answer 390334 by jim_thompson5910(28476)   on 2012-06-13 22:01:06 (Show Source): You can put this solution on YOUR website!This is true as it's in the standard form for a line.
 Volume/620684: what is the density of a rock with a mass of 450 grams and a volume of 225 cm cubed1 solutions Answer 390333 by jim_thompson5910(28476)   on 2012-06-13 21:59:51 (Show Source): You can put this solution on YOUR website!D = m/v D = 450/225 D = 2 g/cm^3
 Average/620683: Going into a 15% of overall grade final I have 7 9%. I had 64% on the final. What is my grade now1 solutions Answer 390332 by jim_thompson5910(28476)   on 2012-06-13 21:59:04 (Show Source): You can put this solution on YOUR website!15% of 64% + 85% of 79% 0.15*0.64 + 0.85*0.79 0.096 + 0.6715 0.7675 So your overall grade is a 76.75%
 test/620687: Going into a 15% overall final I have 79%. I received 64% on final what is my overall grade1 solutions Answer 390330 by jim_thompson5910(28476)   on 2012-06-13 21:58:24 (Show Source): You can put this solution on YOUR website!15% of 64% + 85% of 79% 0.15*0.64 + 0.85*0.79 0.096 + 0.6715 0.7675 So your overall grade is a 76.75%
 Polynomials-and-rational-expressions/620678: x^2-x=561 solutions Answer 390326 by jim_thompson5910(28476)   on 2012-06-13 21:29:28 (Show Source): You can put this solution on YOUR website! Now use the quadratic formula to solve for x or or or or So the solutions are or
 test/620672: What is the solution to the equation x squared minus 6x equals 0?1 solutions Answer 390322 by jim_thompson5910(28476)   on 2012-06-13 21:17:11 (Show Source): You can put this solution on YOUR website!x^2-6x=0 x(x-6)=0 x=0 or x-6=0 x=0 or x=6 So the solutions are x=0 or x=6
 Expressions-with-variables/620674: It says, Simplify each expression. Show any factoring and canceling 10y-30/y^2-1 I have 10(y-3) / (y-1) (y+1).. Is that right am I missing any steps?? Thank you! 1 solutions Answer 390321 by jim_thompson5910(28476)   on 2012-06-13 21:16:21 (Show Source): You can put this solution on YOUR website!That is correct. You have the right steps. Since there are no common terms, there's nothing to cancel. So either it doesn't simplify or there's a typo.
 Exponents/620675: please help me solve this equation: 3(x+1)-5 > 5(x+4) 1 solutions Answer 390320 by jim_thompson5910(28476)   on 2012-06-13 21:15:08 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left 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 . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is
 Rational-functions/620613: I know X= 1/2 y= -1 Z= 2 6x(y^2 z) so I substitute and i get this.. 6(1/2)(-1^2 2) my answer is 6.. but how did i get there1 solutions Answer 390294 by jim_thompson5910(28476)   on 2012-06-13 17:50:36 (Show Source): You can put this solution on YOUR website!6(1/2)((-1)^2*2) (6/2)(1*2) 3*2 6 So 6(1/2)((-1)^2*2) = 6
 Miscellaneous_Word_Problems/620606: There are 40 dogs in a kennel. 15 are lab, 16 are bulldog, 7 are terrier, 4 are unknown type. There are also collies. There are 3 lab/bulldog, 2 terrier/lab, 0 bulldog/terrier. There are 2 lab/collie, 1 bulldog/collie, & no terrier/collie mixes. The unknowns are unknown so they cannot be classified as lab, bulldog, or terrier. Draw a venn diagram.1 solutions Answer 390293 by jim_thompson5910(28476)   on 2012-06-13 17:48:48 (Show Source): You can put this solution on YOUR website!Hint: Draw a venn diagram like the one shown below Note: the region ABD for instance represents the region where the sets A, B and D overlap. Relabel sets A, B, C, and D with the dog breeds (and the "unknown") if you need to.
 Numbers_Word_Problems/620604: The dimEnsions of a sheet of paper can be represented by consecutive odd integers. If the area of the paper is 143 square centimeters, what is the perimeter of the sheet of paper?1 solutions Answer 390289 by jim_thompson5910(28476)   on 2012-06-13 17:26:22 (Show Source): You can put this solution on YOUR website!Hint: Solve (2x+1)*(2x+3) = 143
 test/620603: 1 solutions Answer 390285 by jim_thompson5910(28476)   on 2012-06-13 17:15:33 (Show Source): You can put this solution on YOUR website!Problem missing.
 Triangles/620598: The measures of the angles in a triangle are x, 2x, and 3x. The triangle is? 1 solutions Answer 390275 by jim_thompson5910(28476)   on 2012-06-13 16:59:40 (Show Source): You can put this solution on YOUR website!Hint: x+2x+3x = 180
 Length-and-distance/620573: What is the equation of a line in slope intercept form that has the endpoints of (3,6)and (7,-2)? 1 solutions Answer 390254 by jim_thompson5910(28476)   on 2012-06-13 16:07:17 (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 6 to both sides. Combine like terms. So the equation that goes through the points and is
 Polynomials-and-rational-expressions/620574: Subtract. (5a^3+2b^3)-(3a^3+5a^2b-2ab^2+2b^3)1 solutions Answer 390246 by jim_thompson5910(28476)   on 2012-06-13 15:54:07 (Show Source): You can put this solution on YOUR website!(5a^3+2b^3)-(3a^3+5a^2b-2ab^2+2b^3) 5a^3+2b^3-3a^3-5a^2b+2ab^2-2b^3 Now combine like terms
 Miscellaneous_Word_Problems/620568: A globe is 41.198 feet in diameter. Find its exact circumference (distance around) and then approximate its circumference using 3.14 for pi1 solutions Answer 390239 by jim_thompson5910(28476)   on 2012-06-13 15:41:58 (Show Source): You can put this solution on YOUR website!C = pi*d C = pi*41.198 C = 3.14*41.198 C = 129.36172 So the exact circumference is 41.198pi feet and the approximate circumference is 129.36172 feet
 Unit_Conversion_Word_Problems/620569: Patient is 6'2" and weighs 205 what is the height in inches and the weight in kg. how do i solve this 1 solutions Answer 390238 by jim_thompson5910(28476)   on 2012-06-13 15:40:30 (Show Source): You can put this solution on YOUR website!1 ft = 12 in 6 ft = 72 in 6'2" = 6'+2" = 72"+2" = 74" So 6'2" = 74" ------------------------------------------------------- I'm assuming the patient weighs 205 pounds 1 pound = 0.45359237 kilograms 205 pound = 92.98643585 kilograms
 Rectangles/620567: What are the dimensions of the largest rectangular pen that can be enclosed with 48 meters of fence? 14 m by 10 m 12 m by 12 m 8 m by 16 m 15 m by 9 m None of these1 solutions Answer 390237 by jim_thompson5910(28476)   on 2012-06-13 15:38:04 (Show Source): You can put this solution on YOUR website!Multiply each pair of dimensions to find the area. The one with the largest area is your answer.