How many inches is the smaller dimension of the decreased, Mathematics

Assignment Help:

A photographer decides to decrease a picture she took in sequence to fit it within a certain frame. She requires the picture to be one-third of the area of the original. If the original picture was 4 inches through 6 inches, how many inches is the smaller dimension of the decreased picture if each dimension changes the same amount?

Let x = the amount of reduction.  Then 4 - x = the width of the decreased picture and 6 - x = the length of the decreased picture. Since area is length times width, and one-third of the old area of 24 is 8, the equation for the area of the decreased picture would be (4 - x)(6 - x) = 8. Multiply the binomials by using the distributive property:  24 - 4x - 6x + x2 = 8; combine like terms: 24 - 10x + x2 = 8. Subtract 8 from both sides: 24 - 8 - 10x + x2 = 8 - 8. Simplify and place in standard form: x2 - 10x + 16 = 0. Factor the trinomial into 2 binomials: (x - 2)(x - 8) = 0. Set each factor equal to zero and solve: x - 2 = 0 or x - 8 = 0; x = 2 or x = 8. The solution of 8 is not reasonable because it is greater than the original dimensions of the picture. Accept the solution of x = 2 and the smaller dimension of the reduced picture would be 4 - 2 = 2 inches.

 


Related Discussions:- How many inches is the smaller dimension of the decreased

Example of 3-d coordinate system, Example of 3-D Coordinate System Exam...

Example of 3-D Coordinate System Example: Graph x = 3 in R, R 2 and R 3 .   Solution In R we consist of a single coordinate system and thus x=3 is a point in a 1-D co

Shiites muhammad''s flight from mecca to medina, The first year of the Isla...

The first year of the Islamic calendar marks the following event: The birth of Muhammad The Qu'ran is assembled into a single sacred text The division of the Sunnis and the Shiites

If 1/x+2, if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5...

if 1/x+2, 1/x+3, 1/x+5 are in AP find x Ans 1/x+2,1/x+3, 1/x+5 are in AP find x. 1/x+3 - 1/x+2 = 1/x+5-1/x+3 =>  1/x 2 +5x+6  = 2/ x 2 +8x +15 =>  On solving we get x

Integration, how to learn integration?easier

how to learn integration?easier

Find the maxima or minima and green theorem, 1) find the maxima and minima ...

1) find the maxima and minima of f(x,y,z) = 2x + y -3z subject to the constraint 2x^2+y^2+2z^2=1 2)compute the work done by the force field F(x,y,z) = x^2I + y j +y k in moving

Diffrence between integers and rational numbers, Q. Give basic Diffrence be...

Q. Give basic Diffrence between Integers and Rational Numbers? Ans. Integers The integers are positive and negative whole numbers. The integers are closed under ad

Greatest common factor, x 4 - 25 There is no greatest common factor her...

x 4 - 25 There is no greatest common factor here.  Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2   - (5) 2 Thus, we can employ

Recursively, Let a 0 , a 1 ::: be the series recursively defined by a 0 =...

Let a 0 , a 1 ::: be the series recursively defined by a 0 = 1, and an = 3 + a n-1 for n ≥ 1. (a) Compute a 1 , a 2 , a 3 and a 4 . (b) Compute a formula for an, n ≥ 0.

Combined mean and standard deviation -illustration, Combined mean Assu...

Combined mean Assume m be the combined mean Assume x 1 be the mean of first sample Assume x 2 be the mean of the second sample Assume n 1 be the size of the 1 st

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd