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jim_thompson5910 answered: 28586 problems
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Graphs/148407: (-2,4) (0,-4) (2.4,-2.6176) Form an equation from these plotted points and answer these questions below: Is the degree of the polynomial odd or even? Is the leading coefficient of the polynomial positive or negative? Number of zeros? 1 solutions Answer 108760 by jim_thompson5910(28598)   on 2008-07-15 18:08:20 (Show Source): You can put this solution on YOUR website! # 26 First let's plot the points Now let's draw a quadratic through these points (let me know if any other type of polynomial needs to be drawn otherwise) If you need the equation of the quadratic, simply set up the system of equations note: let me know if you need help with the setup Now use either your graphing calculator or other software to solve for "a","b", and "c" simultaneously through the use of matrices. The solution that I get is a = 1.04, b = -1.92 and c = -4 So the equation that goes through these points is Is the degree of the polynomial odd or even? Notice how as x approaches negative infinity (ie x goes to the left), then y approaches infinity. Also as x approaches positive infinity (ie x goes to the right), then y approaches infinity. So this tells us that the degree of the polynomial is even. Also, from the equation , we can see that the degree is 2, which is even. Is the leading coefficient of the polynomial positive or negative? Since the parabola is opening upward, this means that the leading coefficient is positive. Also, since the leading coefficient is 1.04, this also tells us that the leading coefficient is positive. Number of zeros? From the graph, we can see that there are two zeros. Also, if you use the quadratic equation on , you'll find that the polynomial has 2 zeros.

Graphs/148406: (-1,2) (0,0)(1,-2) Form an equation from these plots and answer the same questions above: Is the degree of the polynomial odd or even? Is the leading coefficient of the polynomial positive or negative? Number of zeros? 1 solutions Answer 108759 by jim_thompson5910(28598)   on 2008-07-15 18:07:15 (Show Source): You can put this solution on YOUR website! If we plot the points we get Now draw a curve through these points to get the equation: Now if we find the equation of the line through those points, we get the equation note: let me know if you need help with finding the equation of the line. Is the degree of the polynomial odd or even? The degree is odd since one end of the polynomial goes in the positive y direction and the other end goes in the negative y direction. Is the leading coefficient of the polynomial positive or negative? Since the leading coefficient is -2, this means that the leading coefficient is negative. Number of zeros? From the graph, we can see that there is only one zero

Graphs/148405: 24. From the list of plotted points (-5,5) (3,5) (-4, 3/2) (2, 3/2) (-3,-1) (1,-1) (-2, -5/2) (0, -5/2) (-1,-3) Form an equation after plotting these points and then answer the questions below: Is the degree of the polynomial odd or even? Is the leading coefficient of the polynomial positive or negative? Number of zeros 1 solutions Answer 108758 by jim_thompson5910(28598)   on 2008-07-15 18:05:43 (Show Source): You can put this solution on YOUR website! If we plot the points we get Now draw a curve through these points to get the equation: From the graph, we can see that the degree is even (since both ends of the graph go in the same y direction). Also, we can see that the leading coefficient is positive (since the graph opens upward). Finally, we can see that there are two zeros (since there are two x-intercepts). ------------------------------------------------------ Since we have all of this info, we don't need the equation. However, if you do need the equation, this is how you would find it: From the graph, we can see that the vertex is (-1,-3). Start with the general vertex equation. Plug in and Simplify. Now let's plug in another point. Let's plug in (1,-1) Plug in and Add Square 2 to get 4. Add to both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. So this means that the equation is FOIL Distribute Multiply Combine like terms. So the equation that goes through the points is From the equation, we can see that the degree of the polynomial is even. Also, we can see that the leading coefficient is positive since . Finally, if we use the quadratic formula, we'll find that the polynomial has 2 zeros.

Equations/148310: 3x + 4 = 4x -5 3x +4-4= 4x-5-4 3x=4x-1 3x=4x-1 3 = 3 3x=3x 3 =3 x=3 I know i'm doing somthing wrong. I think i miss a step. 1 solutions Answer 108709 by jim_thompson5910(28598)   on 2008-07-15 00:15:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. 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 answer is

Rational-functions/148309: Write in standard form: (3-3i)/(4i) 1 solutions Answer 108708 by jim_thompson5910(28598)   on 2008-07-15 00:09:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by Combine the fractions Distribute and multiply Replace with -1 Multiply Break up the fraction Reduce Rearrange the terms. Now the number is in standard form a+bi where and

Rational-functions/148308: Write in standard form: -i+(7+5i)-3(2-3i) 1 solutions Answer 108707 by jim_thompson5910(28598)   on 2008-07-15 00:07:53 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Group like terms Group like terms Now the number is in standard form a+bi where a=1 and b=13

Rational-functions/148307: Write in standard form: (3-2i)^2 1 solutions Answer 108706 by jim_thompson5910(28598)   on 2008-07-14 23:59:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Remember something like . 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. Now the number is in standard form a+bi where a=5 and b=-12

Rational-functions/148306: Solve 4x^2+20=0 1 solutions Answer 108705 by jim_thompson5910(28598)   on 2008-07-14 23:57:19 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Take the square root of both sides. or Break up the expression. or Simplify the square root. So our answers are or

Rational-functions/148305: Write in standard form: (1+i)-(8+3i) 1 solutions Answer 108704 by jim_thompson5910(28598)   on 2008-07-14 23:56:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute Group like terms Combine like terms Now the expression is in standard form where a=-7 and b=-2

Rational-functions/148304: Write in standard form: (5+8i)/(6-i) 1 solutions Answer 108703 by jim_thompson5910(28598)   on 2008-07-14 23:55:15 (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. So the expression is now in standard form where and

Rational-functions/148303: Solve 4x^2+5=-7 1 solutions Answer 108702 by jim_thompson5910(28598)   on 2008-07-14 23:52:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. Take the square root of both sides. or Break up the expression. or Simplify the square root. So our answers are or

Rational-functions/148302: write in standard form: (8+5i)/(6-4i) 1 solutions Answer 108701 by jim_thompson5910(28598)   on 2008-07-14 23:51:24 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by Combine the fractions. FOIL Replace with Multiply Combine like terms. Break up the fraction Reduce So the expression is now in a+bi form where and

Rational-functions/148301: Identify the real and imaginary part: 14+9i 1 solutions Answer 108700 by jim_thompson5910(28598)   on 2008-07-14 23:49:48 (Show Source): You can put this solution on YOUR website! Any complex number of the form a+bi has "a" as the real part and "b" as the imaginary part. So for the complex number 14+9i, the real part is a=14 and the imaginary part is b=9

Rational-functions/148299: (22 pts) Consider the polynomial f(x) = 2x^3 – 3x^2 – 8x – 3. (i) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (ii) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have found them. 1 solutions Answer 108699 by jim_thompson5910(28598)   on 2008-07-14 23:30:26 (Show Source): You can put this solution on YOUR website! i) Any rational zero can be found through this equation where p and q are the factors of the last and first coefficients So let's list the factors of -3 (the last coefficient): Now let's list the factors of 2 (the first coefficient): Now let's divide each factor of the last coefficient by each factor of the first coefficient Now simplify These are all the distinct rational zeros of the function that could occur -------------------------------------------------------- ii) With the help of a graphing calculator, we see that -1 is a zero of note: let me know if you need to find the zeros a different way. So let's set up a synthetic division table by placing the value -1 in the upper left corner and placing the coefficients of the polynomial to the right of -1. -1 | 2 -3 -8 -3 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2) -1 | 2 -3 -8 -3 | 2 Multiply -1 by 2 and place the product (which is -2) right underneath the second coefficient (which is -3) -1 | 2 -3 -8 -3 | -2 2 Add -2 and -3 to get -5. Place the sum right underneath -2. -1 | 2 -3 -8 -3 | -2 2 -5 Multiply -1 by -5 and place the product (which is 5) right underneath the third coefficient (which is -8) -1 | 2 -3 -8 -3 | -2 5 2 -5 Add 5 and -8 to get -3. Place the sum right underneath 5. -1 | 2 -3 -8 -3 | -2 5 2 -5 -3 Multiply -1 by -3 and place the product (which is 3) right underneath the fourth coefficient (which is -3) -1 | 2 -3 -8 -3 | -2 5 3 2 -5 -3 Add 3 and -3 to get 0. Place the sum right underneath 3. -1 | 2 -3 -8 -3 | -2 5 3 2 -5 -3 0 Since the last column adds to zero, this means that -1 is a zero of (this confirms our original claim). Now lets look at the bottom row of coefficients: The first 3 coefficients (2,-5,-3) form the quotient So Basically factors to Now lets find the zeros for . Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the zeros of are , , or

Rational-functions/148297: Use synthetic division to divide the polynomial 2x^3 – 7x + 10 by x + 3, and write the quotient polynomial and the remainder. 1 solutions Answer 108698 by jim_thompson5910(28598)   on 2008-07-14 23:17:30 (Show Source): You can put this solution on YOUR website! Let's simplify this expression using synthetic division Start with the given expression First lets find our test zero: Set the denominator equal to zero Solve for x. so our test zero is -3 Now set up the synthetic division table by placing the test zero in the upper left corner and placing the coefficients of the numerator to the right of the test zero.(note: remember if a polynomial goes from to there is a zero coefficient for . This is simply because really looks like -3 | 2 0 -7 10 | Start by bringing down the leading coefficient (it is the coefficient with the highest exponent which is 2) -3 | 2 0 -7 10 | 2 Multiply -3 by 2 and place the product (which is -6) right underneath the second coefficient (which is 0) -3 | 2 0 -7 10 | -6 2 Add -6 and 0 to get -6. Place the sum right underneath -6. -3 | 2 0 -7 10 | -6 2 -6 Multiply -3 by -6 and place the product (which is 18) right underneath the third coefficient (which is -7) -3 | 2 0 -7 10 | -6 18 2 -6 Add 18 and -7 to get 11. Place the sum right underneath 18. -3 | 2 0 -7 10 | -6 18 2 -6 11 Multiply -3 by 11 and place the product (which is -33) right underneath the fourth coefficient (which is 10) -3 | 2 0 -7 10 | -6 18 -33 2 -6 11 Add -33 and 10 to get -23. Place the sum right underneath -33. -3 | 2 0 -7 10 | -6 18 -33 2 -6 11 -23 Since the last column adds to -23, we have a remainder of -23. This means is not a factor of Now lets look at the bottom row of coefficients: The first 3 coefficients (2,-6,11) form the quotient and the last coefficient -23, is the remainder, which is placed over like this Putting this altogether, we get: So which looks like this in remainder form: remainder -23

Functions/148258: John increased the area of his garden by 120 ft^2. The original garden was 12 ft. by 14 ft., and he increased the length and the width by the same amount. Find the exact dimensions of the new garden and approximate the dimensions in feet and inches. 1 solutions Answer 108657 by jim_thompson5910(28598)   on 2008-07-14 16:41:14 (Show Source): You can put this solution on YOUR website! Let x=amount he increased the dimensions of his garden, =area of original garden and =area of new garden Since the original garden is 12 ft by 14 ft, this means that the area of the original garden is So which means that the area of the original garden is 168 ft^2 Because the area of the new garden is 120 ft^2 larger than the original garden, this means that Plug in Add So the area of the new garden is 288 ft^2 Now since he increased the dimensions by some unknown amount, this means that the area of the new garden is equal to: Plug in FOIL Subtract 288 from both sides. Combine and rearrange the terms. Let's use the quadratic formula to solve for x Start with the quadratic formula Plug in , , and Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the possible answers are or However, since a negative length is not possible, this means that he increased his garden by 4 feet. Now simply add 4 to each dimension 12 and 14 to get: 12+4=16 by 14+4=18 So the dimensions of the new garden are 16 ft by 18 ft note: the approximate answers are the same as the exact answers since there are no square roots, fractions, decimals, etc. in the answer

Functions/148253: The velocity of sound is given by . Find the temperature when the velocity is 348 m/s 1 solutions Answer 108651 by jim_thompson5910(28598)   on 2008-07-14 16:24:34 (Show Source): You can put this solution on YOUR website! Start with the given equation. Plug in Divide both sides by 20. Square both sides. Square 17.4 to get 302.6 Divide both sides by 273. Take the 6th root of both sides to isolate t. Take the 6th root of 1.10842 to get 1.0173 Now round to the nearest degree So when the temperature is 1 degree Celcius, then the approximate velocity of sound is 348 meters per second

Linear-equations/148220: 31. e^ln(3) = s. 1 b. 2 c. 0 d. e Can someone help me out with this? Eddie 1 solutions Answer 108622 by jim_thompson5910(28598)   on 2008-07-14 12:46:04 (Show Source): You can put this solution on YOUR website! Let y=ln(3). So this means that e^y=3 So e^(ln(3))=e^y=3 So the answer is 3. I don't see "3" as an answer. So make sure that you wrote the problem correctly.

Equations/148216: Which of the following cannot be a base for exponential and logarithmic functions? 0.1 π 1 e 1 solutions Answer 108621 by jim_thompson5910(28598)   on 2008-07-14 12:43:18 (Show Source): You can put this solution on YOUR website! The previous solution is correct, but there's more to this solution. Let's say that you could have a base of 1. So this means that can be written as by use of the property ===> Now using the change of base formula, we can rewrite as . However, which means that becomes . Since you cannot divide by zero, this means that a base of 1 is not possible for a logarithmic function.

Exponential-and-logarithmic-functions/148215: Determine x for 10^2x + 1 = 1000^x - 1 a. x = -2 b. x = 4 c. x = 9 d. No solution 1 solutions Answer 108614 by jim_thompson5910(28598)   on 2008-07-14 12:30:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Rewrite 1000 as Multiply the exponents. Distribute. Since the bases are equal, this means that the exponents are equal. 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 answer is

Graphs/148210: IN NEED OF HELP. I CANT SEEM TO GET THESE CAN ANYONE HELP? FIND THE SLOPE AND y-INTERCEPT OF THE GIVEN LINE. 1. 5y-2x+8=0 A. m = B. y-intercept 2. x=-9 A. m = B. y-intercept 3. 2x-7y=8 A. m = y-intercept D.y=5 A. m= B. y-intercept 1 solutions Answer 108612 by jim_thompson5910(28598)   on 2008-07-14 12:27:34 (Show Source): You can put this solution on YOUR website! I'll do the first two to get you started. # 1 Start with the given equation. Add to both sides. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Break up the fraction. Now the equation is in slope intercept form where the slope is and the y-intercept is # 2 Since the equation x=-9 is not in slope intercept form, this means that the slope is undefined and there is no y-intercept (the line is parallel to the y-axis).

Polynomials-and-rational-expressions/148208: For all x=0 and y=0, (3x^3y^3)/xy=? Multiple choose answers are A. 9x^3y^8 B. 9y^4/x C. 9y^4/x^2 D. 9y^5/x^5 E. 9y^7/x^5 What is the right answer 1 solutions Answer 108610 by jim_thompson5910(28598)   on 2008-07-14 12:22:12 (Show Source): You can put this solution on YOUR website! Start with the given expression. Expand. Remember, Highlight the common terms. Cancel out the common terms. Simplify. Regroup. So simplifies to . I don't see this as an answer choice so double check the problem

Equations/148209: What is the domain of standard exponential functions? a. x (0, ∞) b. x (-∞, ∞) c. x [0, ∞) d. x (0, 1) (1, 2) (2, 3) (3, 4) (4, 5) ..... 1 solutions Answer 108608 by jim_thompson5910(28598)   on 2008-07-14 12:19:18 (Show Source): You can put this solution on YOUR website! If you graph a standard exponential function like , you get From the graph, we can see that x can be any number. So the domain is b. x (-∞, ∞)

Equations/148207: If log a ≈ 0.250 and log b ≈ 0.644, then log b/a ≈ a. 2.576 b. 0.161 c. 0.394 d. There is insufficient information for a meaningful answer 1 solutions Answer 108607 by jim_thompson5910(28598)   on 2008-07-14 12:18:02 (Show Source): You can put this solution on YOUR website! log (b/a)=log(b)-log(a)=0.644-0.250=0.394 So log (b/a)≈0.394

Equations/148206: Which of the following is a logarithmic function? a. f(x) = x^2 b. L(t) = 1 - e^-t c. g(q) = q^-2 d. R(x) = 4 ln(x) 1 solutions Answer 108606 by jim_thompson5910(28598)   on 2008-07-14 12:16:47 (Show Source): You can put this solution on YOUR website! Remember, ln(x) is the natural log of x. So this means that d)R(x) = 4 ln(x) is a logarithmic function.

Equations/148205: Which of the following represents the numerical solution of: log2((4^2)(2^3) a. 5 b. 12 c. 7 d. There is no numerical solution; this expression cannot be resolved 1 solutions Answer 108605 by jim_thompson5910(28598)   on 2008-07-14 12:15:52 (Show Source): You can put this solution on YOUR website! Start with the given expression. Rewrite as Multiply the exponents. Multiply the terms by adding the exponents. Rewrite the expression using the identity . Evaluate to get 1 Multiply So

Geometry_proofs/148202: Verify the identity. a)(csc(-t)-sin(-t))/(sin(-t))=cot^(2)t b)ln cotx= -ln tanx 1 solutions Answer 108603 by jim_thompson5910(28598)   on 2008-07-14 12:12:06 (Show Source): You can put this solution on YOUR website! a) Note: I'm only algebraically manipulating the left side. I'm showing the right side for comparison. (csc(-t)-sin(-t))/(sin(-t))=cot^(2)t ... Start with the given equation (1/sin(-t)-sin(-t))/(sin(-t))=cot^(2)t .... Replace csc(-t) with 1/sin(-t) -(-1/sin(t)+sin(t))/(sin(t))=cot^(2)t .... Replace each sin(-t) with -sin(t) (1/sin(t)-sin(t))/(sin(t))=cot^(2)t .... Simplify (1/sin(t)-sin^2(t)/sin(t))/(sin(t))=cot^(2)t ... Rewrite sin(t) as sin^2(t)/sin(t) ((1-sin^2(t))/sin(t))/(sin(t))=cot^(2)t ... Combine the fractions in the numerator ((1-sin^2(t))/sin^2(t)=cot^(2)t ... Divide the fractions (cos^2(t))/sin^2(t)=cot^(2)t ... Replace 1-sin^2(t) with cos^2(t) cot^2(t)=cot^(2)t .... Replace (cos^2(t))/sin^2(t) with cot^2(t) So this verifies the identity. -------------------------------------------------- b) Note: I'm only algebraically manipulating the left side. I'm showing the right side for comparison. ln(cot(x))= -ln(tan(x)) ... Start with the given equation. ln(1/tan(x))= -ln(tan(x)) ... Rewrite cot(x) as 1/tan(x) ln((tan(x))^(-1))= -ln(tan(x)) ... Rewrite 1/tan(x) as (tan(x))^(-1) -1*ln(tan(x))= -ln(tan(x)) ... Rewrite the left side using the identity -ln(tan(x))= -ln(tan(x)) .... Multiply So this verifies the identity.

Graphs/148204: solve the inequality 6+3y<4(3-x) for y and graph the solution. Please show me this step by step because I think I went wrong somewhere down the line, and I need to see where. Thanks in advance! 1 solutions Answer 108601 by jim_thompson5910(28598)   on 2008-07-14 12:05:31 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . Break up the fraction. Reduce ---------------------------------------------------------------------- Answer: So the answer is Now let's graph the equation (replace the inequality sign with an equals sign) Graph of Now plug in a test point (0,0) into the inequality Start with the given inequality. Plug in and Evaluate and simplify. Since the inequality is true, this means that we shade the entire region that contains the point (0,0) In other words, we simply shade the entire region that is below the line. Graph of with the shaded region in green note: the boundary should be a dotted line.

Angles/148176: Please try to help me on this question: If the measure of an angle is (7x-13)degree and the measure of its supplement is (5x-11)degree, find x. 1 solutions Answer 108599 by jim_thompson5910(28598)   on 2008-07-14 11:43:56 (Show Source): You can put this solution on YOUR website! Since the two angles are supplementary, this means that the two angles add to 180 degrees. So this means that Start with the given equation. Combine like terms on the left side. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is

Linear-systems/148199: Write the equation of a line whose slope is 6 and whose y intercept is -3. 1 solutions Answer 108597 by jim_thompson5910(28598)   on 2008-07-14 11:39:12 (Show Source): You can put this solution on YOUR website! Since the equation has a y intercept of -3, this means that the equation goes through the point (0,-3). If you want to find the equation of line with a given a slope of which goes through the point (0,-3), you can simply use the point-slope formula to find the equation: ---Point-Slope Formula--- where is the slope, and is the given point So lets use the Point-Slope Formula to find the equation of the line Plug in , , and (these values are given) Rewrite as Distribute Multiply and to get Subtract 3 from both sides to isolate y Combine like terms and to get ------------------------------------------------------------------------------------------------------------ Answer: So the equation of the line with a slope of which goes through the point (0,-3) is: which is now in form where the slope is and the y-intercept is Notice if we graph the equation and plot the point (0,-3), we get (note: if you need help with graphing, check out this solver) Graph of through the point (0,-3) and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (0,-3), this verifies our answer.

Graphs/148201: 1. Line j contains the points (-2,3) and (1,5). a) Determine the slope of the line.---I got that part. slope=2/3 b) Write an equation for the line. y=2/3x+ ??? I need help right there. 1 solutions Answer 108595 by jim_thompson5910(28598)   on 2008-07-14 11:36:24 (Show Source): You can put this solution on YOUR website! First let's find the slope of the line through the points and Start with the slope formula. Plug in , , , , , 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 Add 3 to both sides. Rewrite as . Combine the fractions. So the equation that goes through the points and is Notice how the graph of goes through the points and . So this visually verifies our answer. Graph of through the points and