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

Discrete uniform distribution, Discrete Uniform Distribution Acme Limit...

Discrete Uniform Distribution Acme Limited is a car manufacturer. The company can paint the car in 3 possible colors: White, Black and Blue. Until the population is sampled, th

Prove that ac2 = ap2 + 2(1+2)bp2, ABC is a right-angled isosceles triangle,...

ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans:    AC = √2AB (Sinc

Question, Hi I have a maths question related to construction as its a cons...

Hi I have a maths question related to construction as its a construction management course...i could send some example sheets too...could it be done?

Second order differential equations, In the earlier section we looked at fi...

In the earlier section we looked at first order differential equations. In this section we will move on to second order differential equations. Just as we did in the previous secti

Slope-intercept form, Slope-intercept form The ultimate special form of...

Slope-intercept form The ultimate special form of the equation of the line is possibly the one that most people are familiar with.  It is the slope-intercept form.  In this if

Geometry, which kind of triangle has no congruent sides ?

which kind of triangle has no congruent sides ?

Time series models, Time Series Models Additive Model Time seri...

Time Series Models Additive Model Time series value = T +S +C +R Whereas S, C and R are expressed in absolute value Additive Model model is best suited where the

Example of least common denominator, Example of Least Common Denominator: ...

Example of Least Common Denominator: Example: Add 1/7 +2 /3 + 11/12 + 4/6 Solution: Step 1:             Find out primes of each denominator. 7 = 7 (already is

Find out the total number people and the total number car, A national park ...

A national park remains track of how many people per car enter the park. Today, 57 cars had 4 people, 61 cars had 2 people, 9 cars had 1 person, and 5 cars had 5 people. What is th

Find the quotient and remainder, Question: Find the quotient and remain...

Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.

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