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# Recent problems solved by 'Nate'

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 Travel_Word_Problems/35514: I can't figure out these questions. It is approximately 480 miles from Los Angeles, CA, to San Francisco, CA. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. Write a linear function that expresses the distance treveled, d, as a function of time, t. How far have you traveled after 4 hours? Write a linear function that expresses the distance to b e traveled to reach San Francisco, s as a function of time, t.1 solutions Answer 21663 by Nate(3500)   on 2006-04-29 12:07:56 (Show Source): You can put this solution on YOUR website!Write a linear function that expresses the distance treveled, d, as a function of time, t. t=d/60 How far have you traveled after 4 hours? d=60t d=60(4) d=240 miles Write a linear function that expresses the distance to be traveled to reach San Francisco, s as a function of time, t. t=480-60x where x is the hours you already traveled
 expressions/35512: This question is from textbook Beginning Algebra 1. 5(x-3)+ 5= 3(x+2)-4 2. 3/4(x-2)+ 3/5= 1/5(x+1) 3. one-third of sum of a number and seven1 solutions Answer 21662 by Nate(3500)   on 2006-04-29 11:55:56 (Show Source): You can put this solution on YOUR website!1. 5(x-3)+ 5= 3(x+2)-4 original 5x - 15 + 5 = 3x + 6 - 4 distribute 5x - 10 = 3x + 2 2x = 12 x = 6 ............................................ 2. 3/4(x-2)+ 3/5= 1/5(x+1) original (3/4(x-2)+ 3/5= 1/5(x+1))20 multiply the whole equation by 20 to delete fractions 15(x-2) + 12 = 4(x+1) 15x - 30 + 12 = 4x + 4 11x - 18 = 4 11x = 22 x = 2 ........................................... 3. one-third of sum of a number and seven For this equation, what does (1/3)(x+7) equal?
 Graphs/35513: This question is from textbook Beginning Algebra 1. ax + by = c Solve for x. 2. Four less nine times a number is one hundred twenty-two. Find the original number. 1 solutions Answer 21661 by Nate(3500)   on 2006-04-29 11:51:03 (Show Source): You can put this solution on YOUR website!1. ax + by = c Solve for x. ax + by = c original ax = -by + c subtract by from each side x = (-by + c)/a divide each side by 'a' ........................................ 2. Four less nine times a number is one hundred twenty-two. Find the original number 9x-4=122 original equation 9x = 126 add four x = 14 divide by nine on each side
 Polynomials-and-rational-expressions/35511: This question is from textbook Algebra I 7n(n)(n)(n)(n)+7n(n)(n)(n)-3n(n)-6n-31 solutions Answer 21660 by Nate(3500)   on 2006-04-29 11:31:06 (Show Source): You can put this solution on YOUR website!7n^5 + 7n^4 - 3n^2 - 6n - 3
 Graphs/35506: Can someone please help me understand graph's before my final next week. I have 2 questions. 1) It shows a graph given by a quadratic function of the form f(x)=ax^2, which of these 3 functions matches. The graph shows a staight line going thru Y at (-2,2) & (2,2) A)f(x)=2x^2 B)f(x)=3x^2 C)f(x)=1/2x^2 ____________________________________ 2) It shows a graph is froma quadratic function of the form f(x)=(x-h)^2 with a symmetry x=-3 and vertex (-3,0). Which of these 3 matches. A)f(x)=(x-3)^2 B)f(x)=(x+3)^2 C)f(x)=(x+2)^2 Thanks for all your help 1 solutions Answer 21656 by Nate(3500)   on 2006-04-29 11:12:50 (Show Source): You can put this solution on YOUR website!The second is just a lot like the first. f(x)=(x+3)^2 f(-3)=(-3+3)^2 f(-3)=0 (B) is your second answer.
 Exponents-negative-and-fractional/35504: I need help with this ....please!!!! (5^-1+x^-1)/(x^2-25^-1)1 solutions Answer 21654 by Nate(3500)   on 2006-04-29 10:58:35 (Show Source): You can put this solution on YOUR website!(5^-1+x^-1)/(x^2-25^-1) (5+x)^-1/(x^2-25^-1) 1/((5+x)(x^2-(1/25))) 1/(x^3-(x/25)+5x^2-(1/5))
 Functions/35505: This question is from textbook Let f(x) = 2x + 1 and g(x) = x^2 - 4 and find the following: (fg)(x) (g of f)(x)1 solutions Answer 21652 by Nate(3500)   on 2006-04-29 10:54:42 (Show Source): You can put this solution on YOUR website!f(x) = 2x + 1 g(x) = x^2 - 4 ........................................................................ (fg)(x)=(2x+1)(x^2-4)=2x^3+x^2-8x-4 ................................... (g of f)(x) = (2x+1)^2 - 4 = (2x+1)(2x+1) - 4 = 4x^2 + 4x + 1 - 4 = 4x^2 + 4x - 3
 Functions/35507: This question is from textbook For the following problems, y varies directly with x If y is -3 when x is 5, find y when x is -10.1 solutions Answer 21649 by Nate(3500)   on 2006-04-29 10:50:25 (Show Source): You can put this solution on YOUR website!y/x=y/x (-3)/(5)=y/(-10) 6=y
 Polynomials-and-rational-expressions/35509: Can someone help me solve this for X sqrtx+7 = x+11 solutions Answer 21647 by Nate(3500)   on 2006-04-29 10:49:08 (Show Source): You can put this solution on YOUR website!(x+7)^(1/2)=(x+1) (x+7)=(x+1)^2 x+7=x^2+2x+1 x^2+x-6=0 (x+3)(x-2)=0 x=-3 and x=2 If you plug in the -3, you get 2=-2 .... so -3 isn't an answer. However, 2 is a right answer, so the answer is x=2.
 Functions/35508: This question is from textbook For the following problems y varies inversely with the square of x. If y is 4 when x is 5, find y when x is 2. 1 solutions Answer 21645 by Nate(3500)   on 2006-04-29 10:45:50 (Show Source): You can put this solution on YOUR website!yx^(2)=yx^(2) 4(5^2)=y(2^2) 4(25)=y(4) y=25
 Functions/35503: This question is from textbook Let f(x) = 2x^2 - 4x + 1 and g(x) = 3x + 2 and evaluate each of the following: g(f) f[g(0)] f[g(1)]1 solutions Answer 21642 by Nate(3500)   on 2006-04-29 10:39:28 (Show Source): You can put this solution on YOUR website!g(x) = 3x + 2 f(x) = 2x^2 - 4x + 1 ............................................................... g(f) = 3(2x^2 - 4x + 1) + 2 g(f) = 6x^2 - 12x + 3 + 2 g(f) = 6x^2 - 12x + 5 ................................ f[g(0)]=3(0) + 2=2 f(2)=2(4) - 4(2) + 1=1 ................................ f[g(1)]=3(1) + 2=5 f(5)=2(25) - 4(5) + 1 = 50 - 20 + 1 = 31
 logarithm/35404: Hi! I need help with two problems. (^ means exponent follows) 2e^2x = 5^x+1 and... log(x+1)-log(x)=2 thanks!1 solutions Answer 21585 by Nate(3500)   on 2006-04-28 23:12:38 (Show Source): You can put this solution on YOUR website!2e^(2x) = 5^(x+1) e^(2x) = 5^(x+1)/2 2x = (x+1)ln(5)-ln(2) 2x = 1.6x + 1.6 - 0.69 0.4x = 0.91 x=2.275 The number is about 2.275 ............................................................................. log(x+1)-log(x)=2 log((x+1)/x))=2 (x+1)/(x)=100 x+1=100x 1=99x x=(1/99)
 Graphs/35475: For the function, y=1/(x-2) a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer: Show work in this space. b) Using these points, draw a curve. Show graph here. 1 solutions Answer 21584 by Nate(3500)   on 2006-04-28 23:06:06 (Show Source): You can put this solution on YOUR website!y=1/(x-2) (-2,-.25),(-1,-.333333),(0,-.5),(1,-1),(2,undefined) Since I do not know how to show this graph, just connect the dots on a cartesian coordinate plane. It should look like an exponential growth.
 Graphs/35474: 3) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour. a) Write a linear function that expresses the distance traveled, d, as a function of time, t. Answer: b) How far have you traveled after 4 hours? Answer: Show work in this space. c) Write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t. Answer: Show work in this space. d) How far will I need to travel to reach San Francisco after I have traveled 3 hours? Answer: Show work in this space:1 solutions Answer 21583 by Nate(3500)   on 2006-04-28 23:01:30 (Show Source): You can put this solution on YOUR website!a.) Write a linear function that expresses the distance traveled, d, as a function of time, t. d=60t b.) How far have you traveled after 4 hours? d=60t d=60(4) d=240 c.) Write a linear function that expresses the distance to be traveled to reach San Francisco as a function of time, t. t=480/s where s is your speed d.) How far will I need to travel to reach San Francisco after I have traveled 3 hours? 480 - (3*60) = d 300=d
 Graphs/35468: This question is from textbook algebra for college students I need help with this too, Please: Find the vertex, focus, and directrix of the given parabloa and sketch it's graph: Find the equation of the parabloa that has it's vertex at (2,-3) and it's focus at (2,-5).1 solutions Answer 21582 by Nate(3500)   on 2006-04-28 22:48:13 (Show Source): You can put this solution on YOUR website!distance from vertex to focus (p=1/4a units) 2=1/(4a) 8a=1 a=(1/8) Directrix: y=-1 Latus Rectum: 1/(A) = (8) units long use: y=a(x-h)^2+k where the vertex is (h,k) y=a(x-2)^2-3 also, use the point(-2,-5) -5=a(-2-2)^2-3 -5=a(-4)^2-3 -2=16a a=(-1/8) y=(-1/8)(x-2)^2-3
 Graphs/35469: This question is from textbook algebra for college students I need help with this too, Please: Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph: 4x squared + y squared - 8y + 4y + 4 = 01 solutions Answer 21580 by Nate(3500)   on 2006-04-28 22:36:56 (Show Source): You can put this solution on YOUR website!4x^2 + y^2 - 8y + 4y + 4 = 0 4x^2 - 8x + y^2 + 4y = -4 4(x^2 - 2x) + (y^2 + 4y) = -4 4(x - 1)^2 + (y + 2)^2 = 4 ((x - 1)^2) + ((y + 2)^2)/4 = 1 center (1,-2) has a vertical major axis a(length of major axis) = 2 b(length of minor axis) = 1 c^2 = a^2 - b^2 c^2 = 4 - 1 c = 3^(1/2) or -3^(1/2) length cannot be negative so the c is 3^(1/2) foci: (1+3^(1/2),-2) and (1-3^(1/2),-2)
 Exponential-and-logarithmic-functions/35470: I'm really struggling with this problem: The amount of radioactive material, in grams, present after t days is modeled by A(t)=500e to the -0.05t (-0.05t is the exponent) a)What is the initial amount of material? b)How much material is left after 10 days? c)Find the half-life of the material.1 solutions Answer 21578 by Nate(3500)   on 2006-04-28 22:28:13 (Show Source): You can put this solution on YOUR website!a.)A(t)=500e^(-0.05t) A(0)=500(1) Initially, the amount was 500 grams. b.)A(t)=500e^(-0.05t) A(10)=500e^(-0.5) Since I do not have a calculator with 'e', I'll let you solve the rest. c.)250=500e^(-.05t) the end result is half of the initial (500) so (250) .5 = e^(-.05t) ln .5 = -.05t take the natural log of each side (ln .5)/(-.05) = t The time for half life of the radioactive element is about 13.86 days.
 Graphs/35472: This question is from textbook algebra for college students I need help with this too, Please: Find the vertices, the endpoints of the minor axis, and foci of the given ellipse, and sketch it's graph: (x+5) squared + 4(y-4) squared = 161 solutions Answer 21577 by Nate(3500)   on 2006-04-28 22:22:12 (Show Source): You can put this solution on YOUR website!(x+5)^2 + 4(y-4)^2 = 16 original ((x+5)^2)/16 + ((y-4)^2)/4 = 1 divide by 16 to get the side to equal 1 the major axis is the highest value (16)^(1/2) the major axis is 4 units long, and the major axis is horizontal the minor axis, on the other hand, is the lower value (4)^(1/2) the minor axis is 2 units long the center is found by: ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1 where a is the length of the minor axis and b is the length of the minor axis and (h,k) is the center the center is (-5,4) ................................................................... To Graph: go to the point (-5,4) and make points 4 units left and right of that point....also, go 2 units up and down from the center....connect the dots (excluding the center) to make an ellipse
 real-numbers/35471: This question is from textbook Beginning Algebra -37-(-18)+51 solutions Answer 21575 by Nate(3500)   on 2006-04-28 22:15:25 (Show Source): You can put this solution on YOUR website!-37-(-18)+5 -37+18+5 -37+23 -14
 logarithm/35274: In a town whose population is 2000, a disease creates an epidemic. The number of people (N) infected (t) days after the disease has begun is given by the function N(t)=2000/(1+19e^-0.6t) a. how many are initially infected with the disease (t=0)? b. how many infected after 2,5,8,12, and 16 days?1 solutions Answer 21574 by Nate(3500)   on 2006-04-28 22:14:28 (Show Source): You can put this solution on YOUR website!N(t)=2000/(1+19e^-0.6t) N(0)=2000/(1+19(1)) N(0)=2000/(20) N(0)=100 Initially, 100 people were infected. -------------------------------------------- N(t)=2000/(1+19e^-0.6t) N(2)=2000/(1+19e^(-1.2)) I do not have a calculator on me, so I will let you solve the rest of the equation. Also, all you have to do is plug in the numbers into your calculator, and you will have it all solved. I'll let you finish.
 absolute-value/35464: This question is from textbook algebra for college students Can anyone tell me how to: Find an equation of the circle with center (4,-3) and radius 5. I need to express the final equation in the form x squared + y squared + Dx + Ey + F = 01 solutions Answer 21570 by Nate(3500)   on 2006-04-28 22:05:48 (Show Source): You can put this solution on YOUR website!the equation for a circle is: (x-h)^2 + (y-k)^2 = r^2 where center is (h,k) and r is the radius with center (4,-3) and radius 5 (x - 4)^2 + (y + 3)^2 = 25 x^2 - 8x + 16 + y^2 + 6y + 9 - 25 = 0 x^2 + y^2 - 8x + 6y = 0
 Linear-equations/35463: Need help!!!!! Solve for x. 3x – 2y = 61 solutions Answer 21568 by Nate(3500)   on 2006-04-28 22:01:29 (Show Source): You can put this solution on YOUR website!3x – 2y = 6 original 3x - 2y + 2y = 6 + 2y add 2y to each side 3x = 6 + 2y combine (3x)/3 = (6 + 2y)/3 divide each side by 3 x = 2 + (2/3)y
 Polynomials-and-rational-expressions/35425: Perform the indicated operation (-3x^4 + 4x^2 - 7x + 10) - (-2x^3 + 6x^2 - 5x + 3)1 solutions Answer 21562 by Nate(3500)   on 2006-04-28 21:56:36 (Show Source): You can put this solution on YOUR website!-3x^4 + 4x^2 - 7x + 10 + 2x^3 - 6x^2 + 5x - 3 -3x^4 + 2x^3 - 2x^2 - 2x + 7
 Polynomials-and-rational-expressions/35319: This question is from textbook Algebra I need help with this Equation: 4 over x+1 minus 1 over x equals 1 Thank you1 solutions Answer 21560 by Nate(3500)   on 2006-04-28 21:54:37 (Show Source): You can put this solution on YOUR website!4/(x+1) - 1/x = 1 multiply by x(x+1) 4x - x - 1 = x^2 + x x^2 -2x + 1 = 0 (x-1)(x-1) = 0 x=1
 Equations/35383: Here what the used was only the symbol of pi but I don't know how to write that using the keyboard so I wrote the actual word "pi." Classify the given number as real and rational, real and irrational, or complex. pi1 solutions Answer 21553 by Nate(3500)   on 2006-04-28 21:43:48 (Show Source): You can put this solution on YOUR website!pi: real and irrational all numbers are real, and pi doesn't repeat nor does it terminate .... so pi is irrational
Graphs/35420: I need to solve the equation 4x + y > 4 then determine the half plane which I would show on the graph. I am lost at how to do this.
1 solutions

Answer 21550 by Nate(3500)   on 2006-04-28 21:39:51 (Show Source):
You can put this solution on YOUR website!
put into y=mx+b where m is the slope and b is the y-intercept
4x + y > 4
y > -4x + 4
slope is -4
y-intercept is 4
*The answer is all numbers higher than the line*
 Solved by pluggable solver: DESCRIBE a linear EQUATION: slope, intercepts, etc Equation describes a sloping line. For any equation ax+by+c = 0, slope is .X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. 4/4 = 1.Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is 4/1 = 4.Slope is -4/1 = -4. Equation in slope-intercept form: y=-4*x+4.

 Graphs/35459: Please help. I go to college online and I have to submit this answer by Sat. night.Heres the question: x -2 -1 0 1 2 y .0625 .25 1 4 16 Given the table above, graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. Graph: Graph Type: Explanation: Domain: Range: 1 solutions Answer 21538 by Nate(3500)   on 2006-04-28 20:46:32 (Show Source): You can put this solution on YOUR website!the numbers decrease as the x-values go lower....but the y-values never are equal to or lower than 0 .... so it must be an exponential function! use y=(a)(b^x) y=(a)(b^x) 1=a(b^0) a=1 so: y=b^x 4=b^1 b=4 so your final equation is: y=4^x ------------------------------------ the domain and range are the same as in the graph as they are in your list domain: all real number range: y>0 sorry, I do not know how to plot an exponential growth equation to show you
 Triangles/35424: hello I have 2 questions i was assigned to draw and label each figure a. an isooscelees traingle with area equal to 32 square inches. b. A trapezoid with area equal to 50 square inches. may you please help me thank you1 solutions Answer 21536 by Nate(3500)   on 2006-04-28 20:39:20 (Show Source): You can put this solution on YOUR website!a.)the area fora circle is (1/2)(l)(w) (1/2)(l)(w)=32 (1/2)x^2=32 the sides are equal x^2=64 x = 8 or -8 a side cannot be negative so the sides are 8 inches while the hypontenuse is (8192)^(1/2) which is about 90.5 inches b.)((parallel + parallel)/2)h = area of trapezoid ((parallel + parallel)/2)h = 50 depends on what you want the length of the parallel lines let us say that the top parallel line is 30 and the bottom parallel line is 20 (((20)+(30))/2)h = 50 (25)h = 50 h = 2
 Parallelograms/35458: This question is from textbook Geometry The area of a parallelogram is 2x^2 + 9x + 4 cm^2 If the length of the base is 2x + 1 cm, find the length of the altitude. 1 solutions Answer 21534 by Nate(3500)   on 2006-04-28 20:27:13 (Show Source): You can put this solution on YOUR website!the area of a parallelogram is the base times height a=lh here, we want to find h so: h=a/l h=(2x^2 + 9x + 4)/(2x + 1) h=(x + 4)
 Volume/35431: How do I find the volume of a cone that has a circumfrence at the base of 100 feet and its height is 14 feet high. 1 solutions Answer 21533 by Nate(3500)   on 2006-04-28 20:21:21 (Show Source): You can put this solution on YOUR website!The equation to find the volume for a cone is: V=(1/3)(area of base)(height) 100=2(3.14)(x) where x is the radius for the cirmuference of the base (100)/((2)(3.14))=x the radius is about 15.92 V=(1/3)(area of base)(height) V=(1/3)((15.92)^2(3.14))(14)) V=3,717.38 feet cubed
 Geometric_formulas/35442: If possible, descibe a geometric figure that can be transformed into itself by each of the following: reflection rotation translation glide reflection1 solutions Answer 21532 by Nate(3500)   on 2006-04-28 20:10:21 (Show Source): You can put this solution on YOUR website!Won't a circle fit all the required options.