Afireworks rocket is launched from a hill above a lake. the rocket will fall into the lake after exploding at its maximum height. the rocket's height above the surface of the lake is given by g(x)= -16x2 + 64x + 80. how long will it take the rocket to hit the lake? a) 5 seconds b) 8 seconds c) 12 seconds d) 10 seconds

It would take 5 seconds for the rocket to hit the lake.

An equation is used to show the relationship between two or more variables and numbers.

Let g(x) represent the height of the rocket at time x seconds. Given that:

g(x)= -16x² + 64x + 80

The rocket touches the lake, when the height is 0. Hence:

0 = -16x² + 64x + 80

x = 5 seconds.

It would take 5 seconds for the rocket to hit the lake.

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A.  5 seconds

Step-by-step explanation:

This quadratic (second degree polynomial) models parabolic motion.  The vertex of the function is the projectile's max height.  When the height of the object is 0 is when it hits the water.  Set the function equal to 0 then and factor.  I used the quadratic formula on my calculator, but if you need to, stick it into the quadratic formula and do it long hand.  The values of x (which is actually time here) are -1 and 5.  The two things in math that will never ever be negative are distance measurements and time, so we can disregard the -1 and say that it takes 5 seconds for the rocket to hit the water.

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:

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