How can you tell whether a solution to a rational equation is extraneous?

What are the solutions of the equation x^4-5x-^2-14=0

ohaa [14]

So you want to start to factor so you get (x²+2)(x²-7) = 0. Now set each () to 0, so you get (x²+2) = 0 and (x²-7)=0. The first ends with +√2i and -√2i, the second ends with +√7 and -√7

8 0

3 years ago

The height of a rocket launched upward from a 160 foot cliff is modeled by the function h(t)= -16t^2+48t+160, where h is height

aliina [53]

Answer:

5 seconds

Step-by-step explanation:

In order to find the time when it landed, we will have to find the x-intercepts.

Equation given to us : -16t² + 48t + 160

Let's take the GCD, which is -16.

-16( t² - 3t - 10 )

Factoring what's inside the brackets, we get the x-intercepts.

What multiples to -10 but adds up to -3? The numbers are -5 and 2

-16 ( t - 5 ) ( t - 2 )

X-intercepts are t - 5 and t - 2

Which is 5 and 2 seconds. But one of this is an extraneous solution and that is 2.

If we substitute the value of 2 in the equation, we will not get 0.

During the x-intercept, the x has a value and y is 0. If we substitute 5 ans x. we will get y as 0.

Hence, the answer is 5 seconds.

6 0

3 years ago

Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Ksenya-84 [330]

Part a) Use a system of inequalities to model the scenario

Let

x-------> represent babysitting hours

y-------> represent tutoring hours

we know that

$x+y \leq20$ --------> inequality $1$

$6x+10y \geq 75$ --------> inequality $2$

Part b) Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week

we know that

$x+y \leq20$ --------> inequality $1$

This inequality represent Jeanne’s possible number of hours worked this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N $1$

$6x+10y \geq 75$ --------> inequality $2$

This inequality represent Jeanne’s probable income earned this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N $2$

Part c) Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model

we have the system of inequalities

$x+y \leq20$ --------> inequality $1$

$6x+10y \geq 75$ --------> inequality $2$

the solution of the system of inequalities is the shaded area

using a graph tool

see the attached figure N $3$