Friday

January 30, 2015

January 30, 2015

Number of results: 47,190

**math**

What will be the answer of 4x(x-1)+5=0 when i'll use quadratic formula to solve it. Thank you ! ^___^
*September 11, 2014 by ghenny*

**math**

Please solve these using the quadratic formula: 1. 3x^2-4(x-2)=0 2.a^2+2(a++5)=0 3.x^2-3(2x+3)=0 Thank you ^____^
*September 11, 2014 by ghenny*

**Algebra 2 **

How do I solve this using the Quadratic formula and finding the determinant? 1. 5x-6=0 2. x+25=0
*November 12, 2014 by Jessica*

**ALGEBRA**

how do i solve this linear equation: 3x/4 + 6 = -12 (3x over 4 is a fraction) and this quadratic equation..... -4x squared = 0??
*September 10, 2009 by ggift*

**maths**

The following quadratic equation has the integer solutions x^2+5x-6=0 what is the positive solution of the equation
*March 29, 2011 by elizabeth*

**Equation**

-4x (little 2) =0 Not sure what name the technique means. I know this is a Quadratic Equation.
*June 19, 2010 by Lisa*

**Algebra1 HELP PLEASE**

The solutions to a quadratic equation are -1 and 7. What is the equation of its axis of symmetry?
*July 3, 2013 by lisa*

**maths**

quadratic equation solve the equation by factorization 27x^2 - 126x = 0 So x=? or x=?
*August 1, 2013 by gean*

**Algebra**

Please show me how to solve this problem. 8/x^2-16 + 3/4 = 1/x-4 multiply each of the terms by x^2, collect your like terms and bring them all to the left side. You will have a quadratic equation. BTW, since you did not use brackets I will assume your last term is (1/x)-4 and ...
*May 8, 2007 by Marie*

**Algebra help**

Match the equation 4x^6-2x^3+1=0. With a substitution from the column that could be used to reduced the equation to quadratic form: a) u=x^-1/3 b) u=x^1/3 c) u=x^-2 d) u=x^2 e) u=x^-2/3 f) u=x^3 g) u=x^2/3 h) u= x^4
*March 24, 2011 by Miguel*

**Algebra help**

Match the equation 4x^6-2x^3+1=0. With a substitution from the column that could be used to reduced the equation to quadratic form: a) u=x^-1/3 b) u=x^1/3 c) u=x^-2 d) u=x^2 e) u=x^-2/3 f) u=x^3 g) u=x^2/3 h) u= x^4
*March 24, 2011 by Miguel*

**math,help,algebra I**

I need help can someone help me get unstuck and let me know if i am correct.thank you. solve by completing the square. 4x^2+2x-3=0 this is what i am doing: i used the quadratic equation. so where i am is in this step: x = (-2 (+-) sqrt (-44))/(8) from this point i am stuck: ...
*April 14, 2007 by jasmine20*

**algebra II**

Can you please help me with the these problems. 8.Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 11x^2, but which has its vertex at (2, 9). 10. Use the vertex and intercepts to sketch the graph of the quadratic function. y + 3...
*October 13, 2007 by Ashley*

**Chemistry**

Water is added to 4.267 grams of UF6. The only products are 3.730 grams of a solid containing only uranium, oxygen and fluorine and 0.970 gram of gas. The gas is 95.0% flourine, and the remainder is hydrogen. From data determine the empirical formula of the gas. What fraction ...
*January 9, 2011 by deanna*

**chemistry**

Water is added to 4.267 grams of UF6. The only products are 3.730 grams of a solid containing only uranium, oxygen and fluorine and 0.970 gram of gas. The gas is 95.0% flourine, and the remainder is hydrogen. From data determine the empirical formula of the gas. What fraction...
*January 9, 2011 by Deanne*

**algebra2**

If the discriminant of a quadratic equation is equal to zero, how many real solutions does the equation have? A. 0 B. 1 C. 2 D. 3 please help!!
*June 25, 2012 by laltk*

**algebra1please look over THANK YOU**

The solutions to a quadratic equation are -1 and 7. What is the equation of its axis of symmetry? I GOT 3 is that right
*July 3, 2013 by lisa*

**quadratic equation**

what's the positive root of the following equation x(square)=7x+8
*February 8, 2012 by tanya*

**quadriatic equation**

solve and check each of the following quadratic equation (1)x^+x-6=0 (2)x^+8x+15=0 (3)x^+2x+1=0 (4)x^-3x-4=0 (5)x^-4x-32=0
*February 15, 2012 by tanya*

**algebra**

Hi Dear Jiskha team, I have Algebra homework and I will need some help. The homework is following: Suppose you are using a computer to draw a face on a coordinate plane. The eyes are at (–3, 3) and (3, 3). The tip of the nose is at the origin. To make a smiling mouth, you are ...
*February 22, 2012 by Lily*

**SAT math**

1. x>15-2x / -3 Solve the linear inequality. Write the solution in set builder notation. So, -3x>15-2x, x<-15..? And how do I write it in set builder notation? 2. y+x=9 and 3y=2x + 8. How do I solve this system of equations? 3. Find the maximum y- value of the ...
*June 1, 2013 by mysterychicken*

**Chemistry**

Dilute H3PO4(aq) and NaOH(aq) are mixed in chemically equivalent quantities. Write the formula equation for the reaction
*April 30, 2011 by Donna*

**math**

is these answers correct? solve the equation: 2x^2 +8x - 17=(x +2)^2= x=-7,3 solve (v-5)^2-63=0, where v is a real number, simplify answer as much as possible. v=3 square root 7+5,-3 square root7+5 v``12.93725, -2.937254 use the quadratic formula to solve for x. 4x^2x-4=0 =x=1...
*October 31, 2010 by lee*

**PHYSICS**

A DAREDEVIL JUMPS A CANYON 12 METERS WIDE. TO DO SO HE DRIVES A CAR UP A 15 DEGREE INCLINE. a. WHAT IS THE MINIMUM SPEED HE MUST ACHIEVE IN ORDER TO CLEAR THE CANYON? B. IF THE DAREDEVIL JUMPS AT THIS MINIMUM SPEED WHAT WILL HIS SPEED BE WHRN HE REACHES THE OTHER SIDE? Write ...
*November 1, 2006 by Jill Hefner*

**math**

Can someone explain how to label the vertex of this equation. f(x)= -(1/2)x^2. i know how to do these question but when it actually has the other components to the quadratic equation.
*April 6, 2010 by jen*

**Intermediate Algebra**

If the discriminant of a quadratic equation has the given value, determine the number and type of solutions of the equation. A.48 B.0
*April 21, 2012 by Ralph*

**College Math**

For questions 1-2, apply the quadratic formula to find the roots of the given function, and then graph the function. 1. f(x) = x2 + 4 (6 points) g(x) = x2 - x – 12 For questions 3-4, factor the quadratic expression completely, and find the roots of the expression. 1. (3 ...
*December 12, 2010 by jennie*

**Chem**

Complete the table below: Note: Make simplifying assumptions, do not use the quadratic formula. What is the pH of the solution created by combining 1.90 mL of the 0.10 M NaOH(aq) with 8.00 mL of the 0.10 M HCl(aq)? with 8.00 mL of the 0.10 M HC2H3O2(aq)? mL NaOH: 1.90 pH w/HCl...
*May 7, 2012 by Jenna*

**college**

Solve; 5X2 - 8 X + 3 = 0 using the quadratic formula the 2 is to the second power a. X = 1 and X = 3/5 b. X = -1 and X = 1/5 c. X = 1 and X = - 2/5 d. X = 3 and X = - 1/3
*April 16, 2009 by deirra*

**math**

Solve; 5X2 - 8 X + 3 = 0 using the quadratic formula . the 2 is second power
*April 16, 2009 by Minnie*

**math**

how to find the values of x?? x^2 - 3x - 7 = 0 tried quadratic formula and completing the square what else can i do??
*October 21, 2010 by john*

**pre cal**

using formula v=-b/2a, 4ac-b^2/4a graph the quadratic function f(x)=x^2-6x+5
*February 3, 2011 by heather*

**college algebra**

find the real solutions, if any. use the quadratic formula 2/3x^2 - x -3=0
*January 23, 2012 by kathy*

**math**

solve(x-1)^2=-4..... i used the quadratic formula but got stock ... please help thank you
*May 16, 2012 by devon*

**math**

1/2x^2=x/4+1 how can i solve that with quadratic formula?plz i need the solution fast.
*January 28, 2013 by Riana*

**math**

solve for x in the following expression using the quadratic formula 3x^2 + 29x - 8.5=0
*February 19, 2013 by Anonymous*

**math**

f(x)=-16t^2-22t+220 Solve using quadratic formula
*October 8, 2014 by spud*

**math**

a patrol boat took 2.5 hours for a round trip 12km upriver and 12km back. the speed of the current was 2 km/h. what was the speed of the boat in still water? ps: i just need to know how to make equations from the question above. it's supposed to create equation, then use the ...
*October 15, 2010 by lawrence*

**Algebra**

Suppose a market research company finds that at a price (y) of $30, they would sell x =10 t-shirts. If they lower the price to y = $20, then more people would purchase the t-shirts, and they can expect to sell x = 30 t-shirts. Find the equation of the line for the demand ...
*March 30, 2012 by Gurlredneck*

**Math(Please answer, thank you)**

(4.44e-2 - x) (8.06e-2 - x) / (0.331 + 2x)^2 = 1.80e-2 I need to rearrange this equation so that I can get a,b, and c, for the quadratic equation but I am not sure how to do this. Thank you for the help.
*March 24, 2012 by Hannah*

**MATH**

(2,14),(1,-1),(3,35) Find the quadratic function y=ax^2+bx+c 1) 4a+2b+c=14 2) a+b+c=-1 3) 9a+3b+c= 35 equation 1&2 = 3a + b = 13 equation 1&3 = -5a +5b = -21
*May 12, 2009 by Sarah*

**Equation**

Solve the quadratic equation. 12x2 + 23x + 10 = 0 A.5/4,2/3 B. 5/12, 1/5 C. 5/4, 2/3 D. 5/4, 2/3
*June 28, 2010 by Lisa D*

**Algebra**

Use the quadratic equation to solve the equation: 4k(k+13)=13
*April 26, 2012 by Jay*

**8th grade math**

Your uncle is three years older than your aunt. The product of their ages is 3190. What are their ages? I know the answer is 55 and 58. But I can't come up with the correct formula or equation to get the answer. I've tried 3(A+3)=3190. It doesn't come up with the right answer ...
*February 7, 2008 by KL*

**Algebra**

1)Solve by factoring:5x^2=4-19x answer=-4,1/5 2)Which quadratic equation has roots 7 and -2/3? answer=A A.2x^2-11x-21=0 B.3x^2-19x-14=0 C.3x^2+23x+14=0 D.2x^2+11x-21=0 3)To solve 4x^2-28x+49=25 by using the square root property,you would first rewrite the equation as answer=(...
*August 12, 2007 by Marissa*

**MATH**

The perimeter of a rectangle is 540ft. Let x represent the width of the rectangle. Write a quadratic function for the area of rectangle in terms of its width. Find the vertex of the graph of the quadratic function and interpret its meaning in the context of the problem.
*June 8, 2014 by Anonymous*

**Calculus**

Find the slope-predictor formula and write an equation for the line tangent to (a, f(a)) for f(x) = x2 - 6x + 4. Make sure you detail the process.
*December 16, 2010 by Brian Meredith*

**trig**

write an equation expressing: cos37cos99 as a sum Review question. I know the formula. Having trouble with working it out.
*November 6, 2011 by Gaile*

**Quadratic Equations and Functions**

I started having trouble on part (c), and I need to know this before I can go onto the other problems. Plz help! The parabola shown at the right (no picture, sorry) is of the form y=x^2+bx+c. The graph's y-intercept is (0,2), the axis of symmetry is -2.5 and the two points ...
*February 4, 2007 by Emily*

**math**

Theses are just some problems i did not understand how to do so if you could please explain and write the answer(: anything helps thank you(: 2. Simplify ---(3x^11z^5)^3 b. (3x^5)^ -3 / 2x-5(3y)^4 c.3x^5)^ -3 / 2x ^ -5(3y)^4 (same as b but - 5 is the exponent) 3a.x^2 / 5 + x-5...
*March 14, 2010 by Alyssa Pacheco*

**algebra**

Solve using the quadratic formula and leave the answer in radical form: y^2+6y-1=0
*March 10, 2011 by mimi*

**Precalculus**

Solve for x, 0<x<2pi 3sin^2x - sinx -2=0 Its not factorable, do I use quadratic formula?
*January 31, 2012 by jake*

**algebra**

Can you use algebra to find a quadratic equation if your know the coordinates of just ONE point on its graph? Can you use algebra to find a quadratic equation if your know the coordinates of just TWO points on its graph? If so, what information is needed?
*October 6, 2011 by Sejul*

**math 116**

a. Write an equation in the “y = mx + b” format for the canal that runs through the Toaster Company property. Solve for “m” and “b” in the “y = mx + b” formula. The canal crosses the x-axis at -16 and crosses the y-axis at 3. See the chart for a visual. ( b. Write an equation ...
*November 1, 2010 by dwayne*

**math 116**

a. Write an equation in the “y = mx + b” format for the canal that runs through the Toaster Company property. Solve for “m” and “b” in the “y = mx + b” formula. The canal crosses the x-axis at -16 and crosses the y-axis at 3. See the chart for a visual. ( b. Write an equation ...
*November 1, 2010 by dwayne*

**Honors Chemistry**

I need someone to check these questions. I know its a lot of questions. 2NH3 + Ag+ Ag(NH3)2+ a. What is the Lewis acid in this equation? [Ag+] b. What is the Lewis base in this equation? [NH3] Given H2SO4 is sulfuric acid, HNO3 is nitric acid, and H3PO4 is phosphoric acid, ...
*May 7, 2012 by Elizabeth*

**Math**

(2,14),(1,-1),(3,35) Find the quadratic function y=ax^2+bx+c 1) 4a+2b+c=14 2) a+b+c=-1 3) 9a+3b+c= 35 equation 1&2 = 3a + b = 13 equation 1&3 = -5a +5b = -21 i know you take those two equations now 3a + b = 13 -5a - 5b = -21 multiply the top by 5 and the bottom equation by 3 ...
*May 12, 2009 by Sarah*

**math**

Algebraically analyze the graph of the function f(x)= -6x^2+5x+2 . Find the vertex, axis of symmetry, range, minimum or maximum value, increasing and decreasing intervals, and zeros. Write the Quadratic equation in standard form. [Standard form is: f(x)=a(x-h)^2+k ]
*September 30, 2008 by shannon*

**College Math**

Another question which is confusing. The position of an object moving in a straight line is give by s=2t^2-3t, where is s in metres and t is the time in seconds the object has been in motion.. how long will it is take the object to move 6 meters? I first used the simplfying ...
*September 29, 2011 by HM*

**math,help**

on one of last week homeworks i got this one wrong can someone explain to me what is the correct format. The demand supply equations for a certain item are given by: D= -5p+40 S=-p^2+30p-8 The correct answer was: $1.43 how do you get to this answer because i've tried it and it...
*April 19, 2007 by jasmine20*

**Chemistry**

Sulfur dioxide gas is bubbled through sodium hydroxide solution Write the balanced formula equation for this reaction
*April 12, 2011 by Janie*

**Math**

Football Lesson 5.1 1. y= -0.035x^2 + 1.4x + 1, where x is the distance (in yards) and y is the height (in yards) a. Does the graph open up or down? b. Does the graph have a Maximum value or a minimum value? c. graph the quadratic function. (i'll graph it just write it in the ...
*November 11, 2007 by Monte'*

**chem help**

i just don't know where to begin/how a) Write a balanced chemical equation for: potassium carbonate + magnesium chloride b) Write a balanced chemical equation for: sulfuric acid + calcium carbonate c) Write a balanced chemical equation for: sodium sulfate + calcium nitrate d) ...
*January 15, 2013 by thad*

**math**

(a) Complete the square by writing in the form . Note: the numbers and can be positive or negative. x^2-14x-17=(x-7)^2+ (b) Solve the equation by completing the square or using the quadratic formula. If there is more than one correct answer, enter your answers as a comma ...
*September 6, 2012 by Anonymous*

**College Algebra**

Solve 2x(squared)-3x-2=0 using the quadratic formula. Can someone explain this to me please?
*November 18, 2007 by Alicia*

**Math**

Solve; 5X2 - 8 X + 3 = 0 using the quadratic formula the 2 is second power can someone explain
*April 16, 2009 by Tracy*

**Algebra**

Do you know a site with some practice problems for a quadratic formula (ax^2 + bx + c) for my test tomorrow? Thank you so much!
*May 28, 2009 by Gemma*

**Algebra 2 URGENT**

Solve by using the quadratic formula. Please Show All Work! 4x(x+3)=15
*November 18, 2009 by Trisan*

**Algebra**

Use the quadratic formula to find the real solutions: 2x/x-3 + 2/x = 3 I know I multiply both sides by x(x-3), but I don't know how to do that.
*August 22, 2010 by Aless*

**Math**

1/4=3-2x-1/x+2..so far i have 8x^2-19x+4=0 do i use quadratic formula to solve the rest of the way?
*September 21, 2010 by Roger*

**Algebra 1**

X^2-14x+3=-10 Ineed to know how to find the discriminant quadratic formula and by tabe and graph it Please help me
*June 1, 2011 by David*

**Algebra1 HELP PLEASE**

Solve 7⋅x = x2 - 6 by using the Quadratic Formula. Round to the nearest tenth.
*July 5, 2013 by lisa*

**Algebra**

Quadratic formula x^2+6x+8-0 (solve by factoring) (second Problem) 5w^2-3=0 Please show steps
*May 29, 2014 by tbell*

**Math - Solving equation (check )**

7 = (210+88t)/(2(sqrt(210t+44t^2))) Is t= 1.0479....? I got the denominator multiplied by 7 and squared both sides to eliminate the sqrt and then simplified, used the quadratic formula to find the values but since the questions is about squirrels growth it can not be a ...
*October 22, 2010 by Anonymous*

**Quadratic Functions**

Please explain to me how to do the following problems, I dont understand them. Thanks! Find the x-intercepts (if any) for the graph of the quadratic function. 1.f(x) = (x + 2)2 - 4 Find the y-intercept for the graph of the quadratic function. 5.y + 9 = (x + 3)2 Find the domain...
*October 13, 2007 by Carmen*

**math**

If an object is fired upward from the top of a tower at a velocity of 80 feet per second, the tower is 200 ft high, the formula is h(t)=-16t^2+80t+200, t is time h is height, how long after it is fired does the object reach the max height? It is like a quadratic equation
*October 23, 2007 by shila*

**math (please help)**

1. Write the equation for the horizontal line that contains point G(-8, 8). 2. What is an equation for the line that passes through points (-1, -4) and (1, 4)? Write the equation in slope-intersect form. 3. Write an equation for the vertical line that contains point E(10, -3).
*October 31, 2013 by kaitlyn*

**algebra (quadratic formula0**

or the period 1990-2003, the amount of biscuits, pastas, and noodles y (in thousands of metric tons)imported into the united states ca be modeled by the function y=1.36(xsquared)+ 27.8x+304 where x is the number of year since 1990. a.write and solve an equation that you can ...
*March 22, 2011 by Bri*

**math**

2.Define the shape of the rectangular area by establishing a relationship between the length and width of the rectangle. For example, L = 2W + 5, or W = 3L – 4. Be sure to include the appropriate units (inches, feet, yards, miles, or meters). 3.Using the fact that A = LW, ...
*October 11, 2011 by Anonymous*

**chemistry**

For the electrolysis of molten potassium bromide: (a) write the equation for the reaction at cathode. (b) write the equation for the reaction at anode. (c) write the equation for the overall reaction.
*September 10, 2014 by Shane*

**chemistry**

when propane gas C3H8, is burned with oxygen, the products are carbon dioxide and water. Write an unbalanced formula equation for the reaction.
*February 3, 2009 by kate*

**maths**

1. write a linear equation to model the situation. you have walked 4 miles on a trail. you continue to walk at a rate of 3 miles per hour for 5 hours. 2. write an equation of the line that passes through the point and has the given slope. write the equation in slope-intercept ...
*October 16, 2009 by lovers*

**College algebra**

Given a quadratic equation in the form y = ax2 +bx +c , and four choices of graphs representing that equation, how can you tell which choices could be eliminated right away by looking at the equation and looking at the graphs and doing some minimal calculations and not ...
*June 6, 2011 by Belle*

**MATH**

Sketch the graph of a quadratic function for which the related quadratic equation has only one solution. Then, sketch one that has two solutions. Explain how you know by looking at the graph the number of solutions there are.
*September 15, 2009 by Anonymous*

**math**

Sketch the graph of a quadratic function for which the related quadratic equation has only one solution. Then, sketch one that has two solutions. Explain how you know by looking at the graph the number of solutions there are.
*July 7, 2011 by candy*

**chem**

Complete the table below: Note: Make simplifying assumptions, do not use the quadratic formula. What is the pH of the solution created by combining 1.00 mL of the 0.10 M NaOH(aq) with 8.00 mL of the 0.10 M HCl(aq)? with 8.00 mL of the 0.10 M HC2H3O2(aq)? table 1: mL NaOH=1.00 ...
*May 1, 2012 by Heather*

**Math **

Suppose a scientist on Earth throws a baseball upward. The scientist lets go of the ball 2 meters above the ground with an initial velocity of 10 meters per second. How long does it take for the ball to hit the ground (H=0)? (Use the quadratic formula to solve this problem, ...
*July 24, 2011 by A.S. *

**add maths**

Given that the quadratic equation is (2m+3)x^2+(4m-2)x-(m+1)=0.Find the value of m,if •one of the root of the equation is negative •one of the root of the equation is reciprocal of the other
*February 2, 2014 by mandy*

**questions**

1.) Why are there usually two solutions in quadratic equations? 2.) Under what situation would one or more solutions of a rational equation be unacceptable? If putting the found "solution" cannot be put back into the original equation without violating fundamental math rules...
*August 8, 2005 by leleirvin*

**Quadratic equation...**

Hi Can anyone help me solve the quadratic equation for the following:- The motion of a two stage rocket is stated by it height y in metres above the ground since t seconds since launch. Flies vertically Ist stage burns for 5 seconds and cuts out. 2nd stage rocket is under ...
*December 1, 2007 by Leo*

**Math**

We are studying Quadratic formula: A football player punts a ball. The path of the ball can be modeled by the equation y=-0.004x(squared) + x + 2.5, where x is the horizontal distance, in feet, the ball travels and y is the height, in feet, of the ball. How far from the ...
*February 27, 2012 by Jane*

**math **

Suppose that a market research company finds that at a price of p = $30, they would sell x = 36 tiles each month. If they lower the price to p = $15, then more people would purchase the tile, and they can expect to sell x = 41 tiles in a month’s time. Write two ordered pairs ...
*July 31, 2011 by jean*

**algebra**

Solve each quadratic by using the wuadratic formula and round the answer to the nearest hundredth, if possible. 1. x^2 = 9 2. 0 = 3x^2 - 8
*January 19, 2011 by Clammyson*

**algebra**

Use the quadratic formula to find the zeros of the function. Round to tenths if necessary. y = 17x^2 - 21
*October 20, 2011 by tracy*

**math-calculus**

using quadratic formula solve |x^2-2x-6| = 4. and answer have to be 1+-sqrt3, 1+-sqrt11 i just not get how to get this.
*January 18, 2012 by Shreya*

**calculus**

Find a formula for a quadratic function whose graph has a y-intercept at y = 21 and only one zero at x = –28.
*January 31, 2012 by Anonymous*

**Desperate to understand ionic/net equa.-Chemistry**

When the following solutions are mixed together, FeSO4 (aq) + Csl (aq): What precipitate if any will form, Write the balanced equation, write the complete ionic equation and write the net ionic equation?
*April 13, 2012 by ASA*

**Math**

One student studied for 8 years in college and her tuition bills are recorded. Years. One semester tuition 1. 4680 2. 4960 3. 5510 4. 6060 5. 6845 6. 7600 7. 8435 8. 9250 Construct the scatter plot for the data with the scales.choose 3 points,find a quadratic equation in ...
*December 15, 2012 by Praphul*

**CHEMISTRY**

Write the formulas for the following substances as they would appear in a total ionic equation: a) Aqueous acetic acid b) solid lithium carbonate c) Aqueous ammonia d) Aqueous sodium dihydrogen phosphate I don't know, do we have to write the formula [like ammonia is NH3] Or ...
*May 13, 2012 by DAN*

**Pre-Calculus**

The population of a particular type of bacteria doubles in number every 12 hours. a)if there are 8 bcteria initially, write an equation that models the number of bacteria present after x 12 hours. b)How many bacteria will be present after 5 days? by using this formula N(t)=N0(...
*December 21, 2009 by Amy*

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