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Tutors Answer Your Questions about Quadratic Equations (FREE)
Question 152616This question is from textbook Applied Calculus for the Managerial, Life and Social Sciences
: Use the quadratic formula to solve the following equation:
9x^2 - 12x = 4
The answer I worked was:
9x^2 - 12x - 4 = 0
x = -12 +/- sqrt 12^2 - 4(9)(4) / 2 (9)
x = 0/18
x = 0
However, in the book, it shows the answer as:
2/3(1 - sqrt 2); 2/3(1 + sqrt 2)
Can you please explain how I get to this answer? What am I doing wrong?
Thank you sooo much for your help.
This question is from textbook Applied Calculus for the Managerial, Life and Social Sciences
: Use the quadratic formula to solve the following equation:
9x^2 - 12x = 4
The answer I worked was:
9x^2 - 12x - 4 = 0
x = -12 +/- sqrt 12^2 - 4(9)(4) / 2 (9)
x = 0/18
x = 0
However, in the book, it shows the answer as:
2/3(1 - sqrt 2); 2/3(1 + sqrt 2)
Can you please explain how I get to this answer? What am I doing wrong?
Thank you sooo much for your help.
Click here to see answer by Edwin McCravy(1738)  |
Question 152440: Hi,
How would I write the following equations?
Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as:
1. Integers
2. Rational numbers
3. Irrational numbers
Thanks for your help
Jimmy
: Hi,
How would I write the following equations?
Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as:
1. Integers
2. Rational numbers
3. Irrational numbers
Thanks for your help
Jimmy
Click here to see answer by Fombitz(1152) |
Question 152243: 3. In your industrial oven, you bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with 2 scones and 10 cookies.
a) Write an expression that illustrates the total cost of all baked goods in the scenario above using the variable s to represent the cost of scones and the variable c to represent the cost of cookies. Simplify your expression by combining like terms.
b) Suppose you have decided to price the scones at $2.28 each and the cookies at $1.19 each. How much total revenue would result from selling all the scones and cookies baked in the oven at one time?
c) Yesterday your store earned $797.30 just from the sale of cookies. Write and solve an equation that represents how many cookies were sold.
: 3. In your industrial oven, you bake two baking sheets with 12 scones each, two baking sheets with 20 cookies each, and one baking sheet with 2 scones and 10 cookies.
a) Write an expression that illustrates the total cost of all baked goods in the scenario above using the variable s to represent the cost of scones and the variable c to represent the cost of cookies. Simplify your expression by combining like terms.
b) Suppose you have decided to price the scones at $2.28 each and the cookies at $1.19 each. How much total revenue would result from selling all the scones and cookies baked in the oven at one time?
c) Yesterday your store earned $797.30 just from the sale of cookies. Write and solve an equation that represents how many cookies were sold.
Click here to see answer by ankor@dixie-net.com(3845) |
Question 152202: A rectangular swimming pool measures 25m by 6m. It is surrounded by a path of uniform width. If the area of the path is 102m2, find the width of the path. : A rectangular swimming pool measures 25m by 6m. It is surrounded by a path of uniform width. If the area of the path is 102m2, find the width of the path.
Click here to see answer by nerdybill(383) |
Question 152203: The perimeter of a rectangle is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle. : The perimeter of a rectangle is 44cm. The area of the rectangle is 117cm2. Find the length of the shorter side of the rectangle.
Click here to see answer by orca(66) |
Question 151995: A rectangle is twice as long as it is wide. If its length is decreased by 4 and its width is decreased by 2, its area is decreased by 32. Find the original dimensions.: A rectangle is twice as long as it is wide. If its length is decreased by 4 and its width is decreased by 2, its area is decreased by 32. Find the original dimensions.
Click here to see answer by orca(66) |
Question 151911: Using the quadratic formula, solve the following equation for X.
Express your solution both in radical format and as decimals rounded to two decimal places.
3x^2+9x=-4: Using the quadratic formula, solve the following equation for X.
Express your solution both in radical format and as decimals rounded to two decimal places.
3x^2+9x=-4
Click here to see answer by jim_thompson5910(8006) |
Question 151721: What is the actual quadratic formula, and how would you actually get the quation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
This is an any book question. : What is the actual quadratic formula, and how would you actually get the quation itself? All formulas have a reason to how it was made. Such as, a stated theorem.
This is an any book question.
Click here to see answer by ankor@dixie-net.com(3845) |
Question 151645: The equation V=-2000t+20,000 describes the value in dollars of a certain model of car after it is T years old. If a car is worth $12,000 into the equation to find the age of the car.: The equation V=-2000t+20,000 describes the value in dollars of a certain model of car after it is T years old. If a car is worth $12,000 into the equation to find the age of the car.
Click here to see answer by jim_thompson5910(8006) |
Question 151543: I have answered solved the equation and I believe it is right but I don't know how to check it.
9x^2+24x+15=0
(3x+5)(3x+3)
(3x+5)=0
3x=-5
x= -5/3
or
(3x+3)=0
3x=-3
x=-1
Now when I try to put it in the original equation to check it... my problem is
9(-5/3)^2+24(-5/3)+15 I don't know how to do the fractions with exponents so can you show me how to do the equation to check it? Thanks Dianne: I have answered solved the equation and I believe it is right but I don't know how to check it.
9x^2+24x+15=0
(3x+5)(3x+3)
(3x+5)=0
3x=-5
x= -5/3
or
(3x+3)=0
3x=-3
x=-1
Now when I try to put it in the original equation to check it... my problem is
9(-5/3)^2+24(-5/3)+15 I don't know how to do the fractions with exponents so can you show me how to do the equation to check it? Thanks Dianne
Click here to see answer by jim_thompson5910(8006) |
Question 151487: Word problem help. There is a closet door whose height is 4ft more than its width. To keep the closet closed a cable is attached diagonally from one corner to the other. If the cable measures sqrt194/2 ft, what are the dimensions of the door?
I thought the height would be: h=4+w and width would be w. But from there I am lost. How would I set this equation up? : Word problem help. There is a closet door whose height is 4ft more than its width. To keep the closet closed a cable is attached diagonally from one corner to the other. If the cable measures sqrt194/2 ft, what are the dimensions of the door?
I thought the height would be: h=4+w and width would be w. But from there I am lost. How would I set this equation up?
Click here to see answer by scott8148(2420) |
Question 151469: In a complex number system, any quadratic equation has either one or two solutions. (That is the T/F question)
I believe this is false because I thought they will always have 2 solutions but can someone explain if I am wrong?
: In a complex number system, any quadratic equation has either one or two solutions. (That is the T/F question)
I believe this is false because I thought they will always have 2 solutions but can someone explain if I am wrong?
Click here to see answer by nerdybill(383) |
Question 151467: I am having trouble understanding if some quadratic equations can have one real and one imaginary solution? Is that possible?
: I am having trouble understanding if some quadratic equations can have one real and one imaginary solution? Is that possible?
Click here to see answer by nerdybill(383) |
Question 151472: I am trying to find b^2-4ac and the number of real solutions for the equation 16-24x+9x^2=0.
If I put it in standard form ax^2 + ax + a = 0
a=-9 b=24 c=-16
b^2-4ac= 24^2 - 4(-9)(-16)=576-576= 0
So: when the discriminat equals 0 there should be only one solution correct? But how do I find that 1 solution? : I am trying to find b^2-4ac and the number of real solutions for the equation 16-24x+9x^2=0.
If I put it in standard form ax^2 + ax + a = 0
a=-9 b=24 c=-16
b^2-4ac= 24^2 - 4(-9)(-16)=576-576= 0
So: when the discriminat equals 0 there should be only one solution correct? But how do I find that 1 solution?
Click here to see answer by jim_thompson5910(8006) |
Question 151427: I am very lost on this word problem. I don't even know where to begin. Could someone explain the steps to me?
A battery manufacturing plant spends C dollars per hour to produce "D" size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x)=0.01x^2 - 2.6x + 245. What number of batteries per hour minimizes the cost?
76, 130, 245 or 140 batteries.
Am I supposed to plug the number of batteries into the equation for x and solve? : I am very lost on this word problem. I don't even know where to begin. Could someone explain the steps to me?
A battery manufacturing plant spends C dollars per hour to produce "D" size batteries. An efficiency consultant has determined that C is related to the number of batteries produced per hour, x, according to the equation C(x)=0.01x^2 - 2.6x + 245. What number of batteries per hour minimizes the cost?
76, 130, 245 or 140 batteries.
Am I supposed to plug the number of batteries into the equation for x and solve?
Click here to see answer by scott8148(2420) |
Question 151436: How would you find 2 positive numbers that differ by 2 and have a product of 20? I dont know how to set up the equation in this instance.: How would you find 2 positive numbers that differ by 2 and have a product of 20? I dont know how to set up the equation in this instance.
Click here to see answer by jim_thompson5910(8006) |
Question 151429: I am trying to find the vertex for the function: f(x)=x^2 + x - 2. I believe the axis of symmetry is -1/2 since x= -b/2(a)(which should be the x-coordinate) but when I plug it in to find y I am coming up with - 3/2 which doesnt seem correct. Where am i going wrong, and what would be the vertex? : I am trying to find the vertex for the function: f(x)=x^2 + x - 2. I believe the axis of symmetry is -1/2 since x= -b/2(a)(which should be the x-coordinate) but when I plug it in to find y I am coming up with - 3/2 which doesnt seem correct. Where am i going wrong, and what would be the vertex?
Click here to see answer by jim_thompson5910(8006) |
Question 151432: Will the quadratic equation work on an equation such as x^2 - 3=0? : Will the quadratic equation work on an equation such as x^2 - 3=0?
Click here to see answer by jim_thompson5910(8006) |
Question 151404: How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)?
The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck.: How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)?
The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck.
Click here to see answer by jim_thompson5910(8006) |
Question 151337: Thank you for your help on this one
skydiving If a skydiver jumps from an airplane at a height of 8256 feet, then for the first five seconds her height above the earth is approximated by the formula h=- 16t^2 + 8256. How many seconds does it take her to reach 8000 feet?
I am thinking 8000= -16t^2 + 8256 16t^2 =256 t^2=16 t=4
so it takes 4 seconds to fall 256 feet is this right? My husband says this can't be right because skydivers fall much faster than that. Thanks Dianne: Thank you for your help on this one
skydiving If a skydiver jumps from an airplane at a height of 8256 feet, then for the first five seconds her height above the earth is approximated by the formula h=- 16t^2 + 8256. How many seconds does it take her to reach 8000 feet?
I am thinking 8000= -16t^2 + 8256 16t^2 =256 t^2=16 t=4
so it takes 4 seconds to fall 256 feet is this right? My husband says this can't be right because skydivers fall much faster than that. Thanks Dianne
Click here to see answer by stanbon(17617) |
Question 151319This question is from textbook 
: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be?This question is from textbook
: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be?
Click here to see answer by stanbon(17617) |
Question 151319This question is from textbook
: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be?This question is from textbook
: Width of border: rectangular flower bed 9' by 5'. 2 colors in the bed, one in center, one for border of the same width on all sides. If she has enough plants to cover 24 ft^2 for the border, how wide can the border be?
Click here to see answer by scott8148(2420) |
Question 151151: A restaurant's aquarium is destroyed in an earthquake. the insurance company is willing to replace the aquarium with one of the same dimensions. The owner can only remember that the diagonal of the front was 45 inches, the length was 9 inches more than the height of the front, and the depths was the same as the height of the front. Find the dimensions of the aquarium.: A restaurant's aquarium is destroyed in an earthquake. the insurance company is willing to replace the aquarium with one of the same dimensions. The owner can only remember that the diagonal of the front was 45 inches, the length was 9 inches more than the height of the front, and the depths was the same as the height of the front. Find the dimensions of the aquarium.
Click here to see answer by ankor@dixie-net.com(3845) |
Question 151227: 1. Find the variation constant and an equation of variation where y varies directly as x and y=12 when x=6.
2. Divide... (35b^3+18b^2+37b+41)/(5b+4)
3. Solve for x... 4x(x-1)-5x(x)=3
4. A 15 in. TV set also has a width of 12 inches. What is it's height?: 1. Find the variation constant and an equation of variation where y varies directly as x and y=12 when x=6.
2. Divide... (35b^3+18b^2+37b+41)/(5b+4)
3. Solve for x... 4x(x-1)-5x(x)=3
4. A 15 in. TV set also has a width of 12 inches. What is it's height?
Click here to see answer by stanbon(17617) |
Question 151224: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect.
x^2 - 4x - 60 = 0
: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect.
x^2 - 4x - 60 = 0
Click here to see answer by jojo14344(271) |
Question 151224: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect.
x^2 - 4x - 60 = 0
: Can someone please show me how this is done. The way I am doing it the teacher says is incorrect.
x^2 - 4x - 60 = 0
Click here to see answer by jim_thompson5910(8006) |
Question 151131: The baton twirler releases the baton into the air when it is 5 feet above the ground. The initial velocity of the baton is 30 feet per second. The twirler will catch the baton when it falls back to a height of 6 feet. How many seconds is the baton in the air?: The baton twirler releases the baton into the air when it is 5 feet above the ground. The initial velocity of the baton is 30 feet per second. The twirler will catch the baton when it falls back to a height of 6 feet. How many seconds is the baton in the air?
Click here to see answer by ankor@dixie-net.com(3845) |
Question 151131: The baton twirler releases the baton into the air when it is 5 feet above the ground. The initial velocity of the baton is 30 feet per second. The twirler will catch the baton when it falls back to a height of 6 feet. How many seconds is the baton in the air?: The baton twirler releases the baton into the air when it is 5 feet above the ground. The initial velocity of the baton is 30 feet per second. The twirler will catch the baton when it falls back to a height of 6 feet. How many seconds is the baton in the air?
Click here to see answer by stanbon(17617) |
Question 151087: 1. Rewrite with a rational exponent...
√(7&23)
2. Factor out the greatest common factor...
2x^6-10x^5+14x^4
3. Factor Completely...
24-11r+r^2
4. Find the x-intercepts...
24-11r+r^2
: 1. Rewrite with a rational exponent...
√(7&23)
2. Factor out the greatest common factor...
2x^6-10x^5+14x^4
3. Factor Completely...
24-11r+r^2
4. Find the x-intercepts...
24-11r+r^2
Click here to see answer by checkley77(1452) |
Question 151013: A snake can lay either white eggs or brown eggs. Three white eggs and two brown eggs weigh 13 grams, while five white eggs and four brown eggs weigh 24 grams. Find the weight of a brown egg and a white egg.: A snake can lay either white eggs or brown eggs. Three white eggs and two brown eggs weigh 13 grams, while five white eggs and four brown eggs weigh 24 grams. Find the weight of a brown egg and a white egg.
Click here to see answer by jojo14344(271) |
Question 151058: please help me solve this problem using the quadratic root formula:  : please help me solve this problem using the quadratic root formula:
Click here to see answer by jim_thompson5910(8006) |
Question 151048: Word Problem
A student is given this formula to calculate their grade for the term
Course Grade is determined as follows:
Course Grade = 0.30(Quiz Avg) + 0.10(Participation) + 0.15(Exam 1) + 0.15(Exam 2) + 0.30(Final Exam
.30(Quiz Average) + .10 ( Participation) + .15 (Exam 1) + .15 (Exam 2) + .30 ( Final exam) equals the final grade.
Given this information what is the expected grade?
Quiz Average=84
Participation=120
Exam 1=50
Exam 2=90
Final exam=30: Word Problem
A student is given this formula to calculate their grade for the term
Course Grade is determined as follows:
Course Grade = 0.30(Quiz Avg) + 0.10(Participation) + 0.15(Exam 1) + 0.15(Exam 2) + 0.30(Final Exam
.30(Quiz Average) + .10 ( Participation) + .15 (Exam 1) + .15 (Exam 2) + .30 ( Final exam) equals the final grade.
Given this information what is the expected grade?
Quiz Average=84
Participation=120
Exam 1=50
Exam 2=90
Final exam=30
Click here to see answer by Fombitz(1152) |
Question 151026: (1) x+3y=6 (2) x=2 (3) y=-1 (4)Determine wether graphs of pairs of line are parallel x+11=y and y-x=-7 (5) Determine wether the graph of the pair of lines are parallel 3x+6=y and 2y=6x-5 yes or no (6) same question as (5) but this equation as a perpendicular 2x-3y=7 and 2y=3x=3 yes or no (7) Find the slope-intercept equation of the line that has the given characterctics slope 3 and y-intercpt (0,6) The slope-intersept equation is y= (8) As question as (7) bt this equation Slope 1.7 and y-intercept (0,-2) Th slope-intercept equation y= (9) Find an equation of line having the given slope and containing the given point m=7(8,3) The equation of lines is y= (10) find an equation of the line having the given slope and containing the given point m=6/7,(5,-5) The equation of the lines is y= (11) Find an equation of the line containing the given pair of points. Express your answer in the form x=b,or y=mx+b What is an equation of the line? y= Simiplify the answer (12) Find an equation of the line conatining the given of points (-3,-4) and (-7,-5) The equation of the line is y= simifily the answer. Use integers or fraction or any number expression.(13) Find an equation of the line containing the given pair of points (1/4,1/2 and 3/4,5 What is the equation of the line y= Simpifly the answer. Type answer in the form y=mx+b using integers or fraction (14) Wrie an equation of the line containing thegiven point and parallel to line givn Express answer in the form y=mx+b (6,8);x+7y The eqation of line is y= Simipfily, use integers or fraction for number in expression (15) Write an equation of the line containing the given points and parallel to given line express the answer in form of y=mx+b (-3,6);3x=4y+7 Line y= (16) write an equation of the line containing the given point and perpendicular to given line (4,5);6x+y=4 (17)same as (16) but perpendicular (8,-7);4x+7y=3 y= (18)Media Services charges $30. for the phone and $20./month for its economy plan cost, C(t) of operating a Media Services phone for (t)months. C(t)= (19) The table list data regarding the average salaries of serveral professional athletes in the years 1991 and 2001. a) Use the data points to find a linear function that fits the data. b) Use the function to perdict the average salary in 2005 and 2010. Data year 1991 average salary $252,000. and 2001 $1,470,000 A linear function that fits the data is S(x)= Let x= the number of years since 1990, and let S= the average salary x yeras from 1990. (20) In 1920 the record for a certain race was 46.6 sec. In 19940, it was 46.0 sec. Let R(t)= the record in the race and t= the number of year since 1920 a) Find a linear function that fits the data b) Use the function in(a) to perdict the record in 203 and 2006. c) Find the year when the record will be 43.8 sec. Find a linear function that fts the data R(t)= Round to the nearest Hundreth (21)In 1995, the life expectancy of males in a certain county was 71.9 years. in 1999, it was 75.8 years. let E represent the life expectancy in year (t) and let (t) represent the number of years since 1995 The linear function E (t) that fits the data is E(t)= answer (t)+ answer round to nearest tenth: (1) x+3y=6 (2) x=2 (3) y=-1 (4)Determine wether graphs of pairs of line are parallel x+11=y and y-x=-7 (5) Determine wether the graph of the pair of lines are parallel 3x+6=y and 2y=6x-5 yes or no (6) same question as (5) but this equation as a perpendicular 2x-3y=7 and 2y=3x=3 yes or no (7) Find the slope-intercept equation of the line that has the given characterctics slope 3 and y-intercpt (0,6) The slope-intersept equation is y= (8) As question as (7) bt this equation Slope 1.7 and y-intercept (0,-2) Th slope-intercept equation y= (9) Find an equation of line having the given slope and containing the given point m=7(8,3) The equation of lines is y= (10) find an equation of the line having the given slope and containing the given point m=6/7,(5,-5) The equation of the lines is y= (11) Find an equation of the line containing the given pair of points. Express your answer in the form x=b,or y=mx+b What is an equation of the line? y= Simiplify the answer (12) Find an equation of the line conatining the given of points (-3,-4) and (-7,-5) The equation of the line is y= simifily the answer. Use integers or fraction or any number expression.(13) Find an equation of the line containing the given pair of points (1/4,1/2 and 3/4,5 What is the equation of the line y= Simpifly the answer. Type answer in the form y=mx+b using integers or fraction (14) Wrie an equation of the line containing thegiven point and parallel to line givn Express answer in the form y=mx+b (6,8);x+7y The eqation of line is y= Simipfily, use integers or fraction for number in expression (15) Write an equation of the line containing the given points and parallel to given line express the answer in form of y=mx+b (-3,6);3x=4y+7 Line y= (16) write an equation of the line containing the given point and perpendicular to given line (4,5);6x+y=4 (17)same as (16) but perpendicular (8,-7);4x+7y=3 y= (18)Media Services charges $30. for the phone and $20./month for its economy plan cost, C(t) of operating a Media Services phone for (t)months. C(t)= (19) The table list data regarding the average salaries of serveral professional athletes in the years 1991 and 2001. a) Use the data points to find a linear function that fits the data. b) Use the function to perdict the average salary in 2005 and 2010. Data year 1991 average salary $252,000. and 2001 $1,470,000 A linear function that fits the data is S(x)= Let x= the number of years since 1990, and let S= the average salary x yeras from 1990. (20) In 1920 the record for a certain race was 46.6 sec. In 19940, it was 46.0 sec. Let R(t)= the record in the race and t= the number of year since 1920 a) Find a linear function that fits the data b) Use the function in(a) to perdict the record in 203 and 2006. c) Find the year when the record will be 43.8 sec. Find a linear function that fts the data R(t)= Round to the nearest Hundreth (21)In 1995, the life expectancy of males in a certain county was 71.9 years. in 1999, it was 75.8 years. let E represent the life expectancy in year (t) and let (t) represent the number of years since 1995 The linear function E (t) that fits the data is E(t)= answer (t)+ answer round to nearest tenth
Click here to see answer by Fombitz(1152) |
Question 151017: Determine the type of solution the quadratic equation x^2=16 has, and then solve the equation.: Determine the type of solution the quadratic equation x^2=16 has, and then solve the equation.
Click here to see answer by jojo14344(271) |
Question 150991: 1. Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?: 1. Some students planned for a get-together. The budget for food was $500. Five of the students failed to come because of the distance and therefore the cost of food for each member increased by $5. How many students attended the get-together?
Click here to see answer by mducky2(41) |
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