How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … (a) There are no other restrictions. (b) xi ≥ 3 for i = 1, 2, 3, 4, 5, 6 (c) 3 ≤ x1 ≤ 10 (d) 3 ≤ x1 ≤ 10 and 2 ≤ x2 ≤ 7

The equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a non-negative integer and … Will have:

(a) 6 solutions where there are no other restrictions.

(b) 4 Solutions for xi ≥ 3 for i = 1, 2, 3, 4, 5, 6(x3 + x4 +x5 + x6 = 25)

(c) 4 Solutions for 3 ≤ x1 ≤ 10

( x3 + x4 + x5 + x6 = 25)

(d) 5 Solutions for 2 ≤ x2 ≤ 7

Step-by-step explanation:

The equation have 6 unknown variables . This means it will have 6 solutions when no condition is imposed as in (a) above. The number of unknown variables in the equation will give the numbers of solutions

When the conditions are imposed, the numbers of unknown variables will give the number of solutions.

In (b) and (c), the equation will reduce to x3 + x4 +x5 + x6 = 25) and the unknown variables are 4, giving 4 solutions

In (d), the equation will reduce be 5 unknown variables(x2 + x3 + x4 +x5 + x6 = 25) and the solution is 5

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: