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Polynomials-and-rational-expressions/294611: 2
y +13y+40=0
(y+13)=0 (y+ )=0
y+13=0
y=-13
1 solutions

Answer 212547 by jim_thompson5910(28715)   on 2010-04-21 11:35:18 (Show Source):
You can put this solution on YOUR website!
 Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for y: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=13, and c=40 Square 13 to get 169 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

Quadratic_Equations/294772: 9) Solve by using quadratic formula x2 + 2x – 4 = 0

1 solutions

Answer 212546 by jim_thompson5910(28715)   on 2010-04-21 11:34:23 (Show Source):
You can put this solution on YOUR website!
9)

 Solved by pluggable solver: Quadratic Formula 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=2, and c=-4 Square 2 to get 4 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 Now break up the fraction or Simplify or So the solutions are: or

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

10)

 Solved by pluggable solver: Quadratic Formula 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=-3, and c=-10 Negate -3 to get 3 Square -3 to get 9 (note: remember when you square -3, 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 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

 Expressions-with-variables/294721: f(3) if f(x) = 2x + 61 solutions Answer 212545 by jim_thompson5910(28715)   on 2010-04-21 11:33:19 (Show Source): You can put this solution on YOUR website!Just replace each 'x' with 3 and compute to get . So
 Linear_Equations_And_Systems_Word_Problems/294733: The cost in millins of dollars for a company to manufacture x thousand automobiles is given by the function C(x)= 4x^2-16x+32. Find the number of automobiles that must be produced to minimize the cost Tried to factor out the four then simpliy. Stuck. Help!1 solutions Answer 212543 by jim_thompson5910(28715)   on 2010-04-21 11:31:41 (Show Source): You can put this solution on YOUR website!The minimum is the C(x) value that is the smallest (ie it is the smallest cost value). This minimum occurs at the vertex (h,k) where In this case, and meaning that . In other words, if 2 thousand autos are produced, then the cost will be at a minimum. Simply plug this value into the function to get: which means that . So the minimum cost is 16 million dollars (when 2 thousand autos are manufactured). So the vertex is the point (2,16). What this means is that if we graph , the lowest point on the graph is (2,16)
Problems-with-consecutive-odd-even-integers/294753: Find two consecutive odd integers such that the sum of their reciprocals is 12/35.I have been trying for three days to write a problem out for this question and I am for some reason not able to come up with an answer. Thank you
1 solutions

Answer 212542 by jim_thompson5910(28715)   on 2010-04-21 11:25:14 (Show Source):
You can put this solution on YOUR website!
Consecutive odd integers follow the pattern: x, x+2, ...

So adding their reciprocals to get means that

Multiply EVERY term by the LCD to clear out the fractions.

Distribute

Combine like terms.

Get every term to one side.

Combine like terms.

 Solved by pluggable solver: Quadratic Formula 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=12, b=-46, and c=-70 Negate -46 to get 46 Square -46 to get 2116 (note: remember when you square -46, 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 12 to get 24 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

Since we're only looking for integer values of 'x', we can ignore .

So the only answer is which means that the two consecutive odd integers are 5 and 7.

Notice how which confirms our answer.

 Quadratic_Equations/294603: Which values of b and c would make x to the 2nd power + bx + c a perfect square trinomial? a) b = 2, c = 6 b) b = 6, c = 12 c) b = 8, c = 16 d) b = 10, c = 100 1 solutions Answer 212401 by jim_thompson5910(28715)   on 2010-04-20 21:09:47 (Show Source): You can put this solution on YOUR website!Hint: is a perfect square trinomial when
 Proportions/294190: How do you solve this proportion: z is to 7, as 16 is to 56 It must be solved with algebra.1 solutions Answer 212202 by jim_thompson5910(28715)   on 2010-04-19 21:34:56 (Show Source): You can put this solution on YOUR website!Hint: The phrase "z is to 7, as 16 is to 56 " simply translates to the equation . I'll let you solve the equation.
 Radicals/294178: √(18yz^2 ) Rewrite in simplified radical form, ssume that all variables represent positive real numbers1 solutions Answer 212197 by jim_thompson5910(28715)   on 2010-04-19 21:17:44 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Rearrange and multiply the terms. ================================================== Answer: So simplifies to In other words, where every variable is non-negative.
 Quadratic_Equations/294173: √(12z^10 ) Rewrite in simplified radical form, assume that all variables represent positive real numbers1 solutions Answer 212195 by jim_thompson5910(28715)   on 2010-04-19 21:15:27 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Rewrite into Break up the square root using the identity . Take the square root of to get . Take the square root of to get and rearrange the terms. ================================================== Answer: So simplifies to In other words, where .
 Quadratic_Equations/294169: √8 Rewrite the following in simplified radical form1 solutions Answer 212192 by jim_thompson5910(28715)   on 2010-04-19 21:08:05 (Show Source): You can put this solution on YOUR website!Hint: Factor 8 into 4*2 and use the property
 Sequences-and-series/294166: 16, –4, 1, –14.... What is the next term in the geometric sequence?1 solutions Answer 212191 by jim_thompson5910(28715)   on 2010-04-19 21:07:25 (Show Source): You can put this solution on YOUR website!Hint: You are dividing each term by -4 to get the next term.
 Pythagorean-theorem/294162: the sides of a right triangle are x,x+32,and x+32 units long. What is the length of the hypotenuse?1 solutions Answer 212190 by jim_thompson5910(28715)   on 2010-04-19 21:03:22 (Show Source): You can put this solution on YOUR website!Since 'x' is positive, this means that . Also, because we have two sides of length x+2, this means that the legs are x+2 units long leaving the hypotenuse to be 'x' units long. That's where the problem lies: the hypotenuse cannot be shorter than either leg. So either there's a typo, or something is missing.
2x^2-11x+12
1 solutions

Answer 212182 by jim_thompson5910(28715)   on 2010-04-19 20:25:11 (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 :
1,2,3,4,6,8,12,24
-1,-2,-3,-4,-6,-8,-12,-24

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

These factors pair up and multiply to .
1*24 = 24
2*12 = 24
3*8 = 24
4*6 = 24
(-1)*(-24) = 24
(-2)*(-12) = 24
(-3)*(-8) = 24
(-4)*(-6) = 24

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

First NumberSecond NumberSum
1241+24=25
2122+12=14
383+8=11
464+6=10
-1-24-1+(-24)=-25
-2-12-2+(-12)=-14
-3-8-3+(-8)=-11
-4-6-4+(-6)=-10

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).

 Equations/294143: 5(3x-2)=x-41 solutions Answer 212181 by jim_thompson5910(28715)   on 2010-04-19 20:23:53 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. 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 which approximates to .
 Probability-and-statistics/294145: The digits 0, 1, 2, 3,and 4 are to be used in a three-digit ID card. How many different cards are possible if repetitions are NOT allowed? I don't know how to do this!1 solutions Answer 212180 by jim_thompson5910(28715)   on 2010-04-19 20:23:01 (Show Source): You can put this solution on YOUR website!Number of choices for first digit * Number of choices for second digit * Number of choices for third digit = 5 * 4 * 3 = 60 Note: Notice how the number of digit choices decreases (since repetitions are not allowed) So there are 60 possible 3-digit ID card combinations.
 Quadratic_Equations/293896: I need help in factoring this equation! I also need it to be shown to me step by step because I dont know how to solve it! 1 solutions Answer 212054 by jim_thompson5910(28715)   on 2010-04-19 12:21:57 (Show Source): You can put this solution on YOUR website! Start with the given equation Pair off the terms into two groups Factor out the GCF from the first group. Factor out the GCF from the second group. The goal is get a common term between the two groups. Factor out the GCF from the entire left side. Factor to get using the difference of squares formula. I'll let you take it from here.
 Triangles/293894: Can you please solve this problem The sum of the measures of the angles in any triangle is 180 degrees. In triangle ABC angles A and B have the same measure while angle c is 9 degrees larger than each of the other two angles. Find the measure of angle C Please show work. Thanks1 solutions Answer 212053 by jim_thompson5910(28715)   on 2010-04-19 12:18:32 (Show Source): You can put this solution on YOUR website!Hint: Let 'x' be the measure of angles A and B (since they are equal) and 'y' be the measure of angle C. Because "angle c is 9 degrees larger than each of the other two angles", we know that (just add 9 to the measure of 'x' to get 'y') Now recall that the three angles of a triangle add to 180 degrees. So this means that: angle A + angle B + angle C = 180 which then means that . From here, plug in to get and you can remove the parenthesis to get . I'll leave it to you to solve for 'x'. Once you have the value of 'x', plug it into to find 'y', which is the measure of angle C.
Polynomials-and-rational-expressions/293740: Factor: tsquared+3t-10
1 solutions

Answer 211967 by jim_thompson5910(28715)   on 2010-04-18 22:21:18 (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 :
1,2,5,10
-1,-2,-5,-10

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

These factors pair up and multiply to .
1*(-10) = -10
2*(-5) = -10
(-1)*(10) = -10
(-2)*(5) = -10

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

First NumberSecond NumberSum
1-101+(-10)=-9
2-52+(-5)=-3
-110-1+10=9
-25-2+5=3

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).

 expressions/293701: 12-(2x+5)=-2+(x-3)1 solutions Answer 211962 by jim_thompson5910(28715)   on 2010-04-18 21:21:39 (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. 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
 Exponents/293645: if f(x)=x^2+2x find f(a+3)1 solutions Answer 211932 by jim_thompson5910(28715)   on 2010-04-18 19:19:49 (Show Source): You can put this solution on YOUR website! Start with the given function. Plug in FOIL Distribute. Combine like terms.
 Distributive-associative-commutative-properties/293640: use the distrubutive property to multiply 5(b+8) plz list the steps on how to get it1 solutions Answer 211927 by jim_thompson5910(28715)   on 2010-04-18 19:15:36 (Show Source): You can put this solution on YOUR website!Recall that the distributive property is . So this means that .
 Graphs/293607: write the equation of the line that passes through the following points (5, -3),(8,4)1 solutions Answer 211902 by jim_thompson5910(28715)   on 2010-04-18 18:17:03 (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 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 Rewrite as Distribute Multiply Subtract 3 from both sides. Combine like terms. note: If you need help with fractions, check out this solver. So the equation that goes through the points and is
 Quadratic_Equations/293599: How do you do a quadratic equation not ending in zero? The problem on my worksheet is 3xsquared + 3x = 4 ? I dont know what to do.1 solutions Answer 211899 by jim_thompson5910(28715)   on 2010-04-18 18:04:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract 4 from both sides. Now you just need to solve . Does that help?
 Trigonometry-basics/293596: how do you undo rcis theta? if you have a problem such as 4(cos pi/4 + i sin pi/4) how would you put that back into a +bi? im not asking for an answer, rather the method to do the problem1 solutions Answer 211898 by jim_thompson5910(28715)   on 2010-04-18 18:03:05 (Show Source): You can put this solution on YOUR website!Hint: For any polar number in the form , where 'r' is the magnitude and 'x' is the angle, it can be converted into rectangular form using the following equations: 1) (this can be seen if you draw out a triangle with sides 'a', 'b', and hypotenuse 'r') 2) (again this can be seen with a drawing of the triangle) Note: since 'b' is the vertical side, this is the side opposite from the angle 'x' So in this case, and meaning that and . You'll then find that you'll have two equations and two unknowns which means that you can solve for both 'a' and 'b'.
 Equations/293591: Solve the equation algebraically for all values of x. We've been trying to solve this problem for hours, but it can't be factored at all.1 solutions Answer 211894 by jim_thompson5910(28715)   on 2010-04-18 17:50:00 (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 Now factor to get (difference of squares) So factors to In other words, This basically means that is equivalent to . I'll let you take it from here.