Achild launches a toy rocket from the top of a slide at the park. suppose the equation -16t^2+28t+8=0 can be used to find how many seconds it will take for the rocket to hit the ground. a)write the equation in factored form. b)use the zero product property to solve the equation. show all the steps needed to find both answers. c)explain how the solution relates to this situation.

A) The equation in factored form is (4t + 1)(t - 2) = 0

B) The solutions of the equation are t = -1/4 and t = 2

C) It will take 2 seconds for the rocket to hit the ground

Step-by-step explanation:

* Lets study the information in the problem

- A child launches a toy rocket from the top of a slide

- The equation of the motion is -16² + 28t + 8 = 0, where t is the time

 of rocket to hit the ground

* Now lets solve the problem

- At first simplify the equation

∵ -16t² + 28t + 8 = 0

∵ Al the terms have a factor 4

- Divide all terms by 4

∴ -4t² + 7t + 2 = 0 ⇒ multiply all terms by -1

∴ 4t² - 7t - 2 = 0

- Lets factorize

∵ 4t² = 4t × 1t ⇒ 1st term in the 1st bracket × 1st term in the 2nd bracket

∵ -2 = 1 × -2 ⇒ 2nd term in the 1st bracket × 2nd term in the 2nd bracket

∵ 4t + -2 = -8t ⇒ product of the extremes

∵ 1t × 1 = 1t ⇒ product of means

∵ -8t + 1t = -7t ⇒ middle term

∴ The factorization of 4t² - 7t - 2 is (4t + 1)(t - 2)

∴ (4t + 1)(t - 2) = 0

A) The equation in factored form is (4t + 1)(t - 2) = 0

- Lets use the zero product property to solve the equation

∵ (4t + 1)(t - 2) = 0

- Equate each factor by 0

∵ 4t + 1 = 0 ⇒ subtract 1 from both sides

∴ 4t = -1 ⇒ divide both sides by 4

∴ t = -1/4

OR

∵ t - 2 = 0 ⇒ add 2 for both sides

∴ t = 2

B) The solutions of the equation are t = -1/4 and t = 2

C) We can not accept the answer t = -1/4 because there is no negative

    value for the time

∴ The answer is t = 2 only

* It will take 2 seconds for the rocket to hit the ground

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer

the correct answer is

c. 4

step-by-step explanation:

the given polynomial is

the degree of the polynomial is the highest exponent which is 4.

the -4 is called the leading coefficient.

this polynomial has only one term so it is a monomial.

the correct answer is option c.