21 the speed of a certain chemical reaction is expressed by the equation y = 120 - 4x + x², where y is the…

21 the speed of a certain chemical reaction is expressed by the equation y = 120 - 4x + x², where y is the number of seconds needed to complete the reaction and x is the temperature, in degrees celsius, at which the reaction occurs. the reaction is complete in 141 seconds. at what negative temperature, in degrees celsius, could the reaction have occurred? 22 the equation y = x² - 5x + 41 models the earnings of a company, where y is the revenue in millions of dollars and x is the number of years since the company was founded. after how many years are the companys earnings $77 million?

21 the speed of a certain chemical reaction is expressed by the equation y = 120 - 4x + x², where y is the number of seconds needed to complete the reaction and x is the temperature, in degrees celsius, at which the reaction occurs. the reaction is complete in 141 seconds. at what negative temperature, in degrees celsius, could the reaction have occurred? 22 the equation y = x² - 5x + 41 models the earnings of a company, where y is the revenue in millions of dollars and x is the number of years since the company was founded. after how many years are the companys earnings $77 million?

Answer

Explanation:

Step1: Substitute values into the equation for problem 21

Given $y = 120-4x + x^{2}$ and $y = 141$. So, $141=120 - 4x+x^{2}$.

Step2: Rearrange the equation to standard quadratic form

$x^{2}-4x + 120 - 141=0$, which simplifies to $x^{2}-4x - 21 = 0$.

Step3: Factor the quadratic equation

$(x - 7)(x+3)=0$.

Step4: Solve for $x$

Setting each factor equal to zero gives $x - 7=0$ or $x+3 = 0$. So $x = 7$ or $x=-3$. We want the negative value, so $x=-3$.

Step5: Substitute values into the equation for problem 22

Given $y=x^{2}-5x + 41$ and $y = 77$. So, $77=x^{2}-5x + 41$.

Step6: Rearrange the equation to standard quadratic form

$x^{2}-5x+41 - 77=0$, which simplifies to $x^{2}-5x - 36=0$.

Step7: Factor the quadratic equation

$(x - 9)(x + 4)=0$.

Step8: Solve for $x$

Setting each factor equal to zero gives $x - 9=0$ or $x+4=0$. So $x = 9$ or $x=-4$. Since $x$ represents the number of years since the company was founded, we discard the negative value. So $x = 9$.

Answer:

For problem 21: -3 For problem 22: 9