Phil's shadow is half as long as Phil is tall. If he were 4 inches taller and his shadow were 3 inches

shorter, his height times his shadow's length would be 100 square inches. How tall is Phil? How

long is his shadow?

Phil is 16 inches tall and his shadow is 8 inches tall

Step-by-step explanation:

this is an algebra word problem.

1. Find the unknown and label it x.

Let Phil's shadow be x inches.

2. find other unknown quantities and define them with

Phil's height= 2x (phil is shadow is half as long as Phil is tall)

3. FInd the equation

if he was 4 inches taller (2x+4)

and his shadow was three inches shorter (x-3)

his height ( 2x+4) times the shadow's height (x-3) would be 100 square inches.

(2x+4) ×(x-3)=100

(2x+4)(x-3)=100

this is a quadratic equation and there are a number of ways to solve these. the two main ways are

1. quadratic equation

2. expanding and factorising

3. graphing

we will use 2. expanding and factorising for this problem. We need to make the right hand side = 0 by first factorising then rearranging.

(2x*x)+(2x*-3)+(x*4) +(4*-3)=100

2x^2 -6x+4x-3x-12=100

2x^2 -2x=112

2x^2 -2x-112=0

once factorised take out the common factor of 2

2(x^2-x-56)=0

now factorise what's in the brackets ( two numbers multiply to make 56 but add to make -1.

2(x-8)(x+7)=0

x-8=0 =>   x=8

x+7=0        x=-7 not possible

the shadow is 8 inces long. Phil is 16 inches tall.

Hope this is of help :)

15

step-by-step explanation:

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows: