Mathematics: Let s start form the product `x^{2}+11x+30,` and get back to the binomials we started with. Show your steps.

Let s start form the product `x^{2}+11x+30,` and get

Ответ:

cherry12345627

25.04.2021

Then, the polynomial $x^{2}+11\cdot x + 30$ is equal to the product of the binomials (x+5) and (x+6) .

Step-by-step explanation:

The polynomial $x^{2}+11\cdot x + 30$ is a polynomial of the form $x^{2} - (r_{1}+r_{2})\cdot x + r_{1}\cdot r_{2} = (x-r_{1})\cdot (x-r_{2})$ , where $r_{1}$ and $r_{2}$ are the roots of the polynomial. Then, we find the following system of equations:

$-r_{1}-r_{2} = 11$ (1)

$r_{1}\cdot r_{2} = 30$ (2)

After some algebraic handling, the solution of this system is $r_{1} = -5$ and $r_{2} = -6$ .

Then, the polynomial $x^{2}+11\cdot x + 30$ is equal to the product of the binomials (x+5) and (x+6) .

0,0(0 оценок)

Ответ:

cicilee49

23.05.2023

Mathematics

Part A) x + y=125, y = x +45

Part B) 85 minutes

Part C) Not possible

Step-by-step explanation:

Given that Angela plays soccer and golf for a total of 125 minutes everyday.

Number of minutes she plays golf = x minutes

Number of minutes she plays soccer = y minutes

Part A:

Total time she plays golf and soccer is 125 minutes.

x+y=125 ...... (1)

Angela plays Soccer for 45 minutes longer than she plays golf i.e.

y = x+45 ....... (2)

The pair of linear equations are:

x + y=125, y = x +45

Part B:

Let us solve the linear equations (1) and (2):

Putting value of y from equation (2) into equation (1):

$x+x+45=125 \\\Rightarrow 2x+45=125\\\Rightarrow 2x=80\\\Rightarrow x=40$

Putting value of x in equation (2):

$y = 40 +45 = 85\ minutes$

Angela plays golf for 85 minutes daily.

Part C:

Given that

Angela spends 80 minutes on soccer.

Total Time = 125 minutes

$\Rightarrow$ Time spent on golf = 125 - 80 = 45 minutes

Time spent on soccer longer than golf = 80 - 45 = 35 minutes $\neq$ 45 minutes

Hence, it is not possible for Angela to have spent 80 minutes playing soccer if she plays for a total of exactly 125 minutes and plays soccer for 45 minutes longer than she plays golf.

So, the answers are:

Part A) x + y=125, y = x +45

Part B) 85 minutes

Part C) Not possible

0,0(0 оценок)

Let's start form the product `x^{2}+11x+30,` and get back to the binomials we started with. Show your steps.

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question