If a student gets an A on a final exam, then the student will pass the course.

Find all the zeros of the equation. -x^3-x^2=11x+11

anyanavicka [17]

Answer:

x= -1 , i(sqrt11) , -i(sqrt11)

Step-by-step explanation:

subtract 11x from both sides

-x^3 - x^2 - 11x = 11

subtract 11 from both sides

-x^3 - x^2 - 11x - 11 = 0

Factor the left side of the equation

- (x - 1)(x^2 + 11) = 0

Set both factors to zero and solve for x

x + 1 = 0 x^2 + 11 = 0

-1 -11

x^2 = -11

x = -1 x = +/- i(sqrt11)

7 0

3 years ago

Simplify (write without the absolute value sign): 120+x, if x <- 120

Tju [1.3M]

Answer:

Step-by-step explanation:

hello :

120+x, if x <- 120

given : x <- 120 add 120 x+120<- 120+120

x+120< 0

8 0

3 years ago

Please help me find the y-intercept! :(

zvonat [6]

5 inches

Explanation: y = Mx + b, m is your slope (1/2), b is your y-intercept (5 inches)

Equation would be y= (1/2)x + 5

4 0

3 years ago

Use complete sentences to describe why √-1 ≠ -√1

tekilochka [14]

Well let's say that to compare these two numbers, we have to start with the definition first.

Definition

$\displaystyle \large{ {y}^{2} = x} \\ \displaystyle \large{ y = \pm \sqrt{x} }$

Looks like we can use any x-values right? Nope.

The value of x only applies to any positive real numbers for one reason.

As we know, any numbers time itself will result in positive. No matter the negative or positive.

Definition II

$\displaystyle \large{ {a}^{2} = a \times a = |b| }$

Where b is the result from a×a. Let's see an example.

Examples

$\displaystyle \large{ {2}^{2} = 2 \times 2 = 4} \\ \displaystyle \large{ {( - 2)}^{2} = ( - 2) \times ( - 2) = | - 4| = 4}$

So basically, their counterpart or opposite still gives same value.

Then you may have a question, where does √-1 come from?

It comes from this equation:

$\displaystyle \large{ {y}^{2} = - 1}$

When we solve the quadratic equation in this like form, we square both sides to get rid of the square.

$\displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{ - 1} }$

Then where does plus-minus come from? It comes from one of Absolute Value propety.

Absolute Value Property I

$\displaystyle \large{ \sqrt{ {x}^{2} } = |x| }$

Solving absolute value always gives the plus-minus. Therefore...

$\displaystyle \large{ y = \pm \sqrt{ - 1} }$

Then we have the square root of -1 in negative and positive. But something is not right.

As I said, any numbers time itself of numbers squared will only result in positive. So how does the equation of y^2 = -1 make sense? Simple, it doesn't.

Because why would any numbers squared result in negative? Therefore, √-1 does not exist in a real number system.

Then we have another number which is -√1. This one is simple.

It is one of the solution from the equation y^2 = 1.

$\displaystyle \large{ {y}^{2} = 1} \\ \displaystyle \large{ \sqrt{ {y}^{2} } = \sqrt{1} } \\ \displaystyle \large{ y = \pm \sqrt{1} }$

We ignore the +√1 but focus on -√1 instead. Of course, we know that numbers squared itself will result in positive. Since 1 is positive then we can say that these solutions exist in real number.

Conclusion

So what is the different? The different between two numbers is that √-1 does not exist in a real number system since any squared numbers only result in positive while -√1 is one of the solution from y^2 = 1 and exists in a real number system.

5 0

3 years ago

Read 2 more answers

Bly makes fleece scarves and sells them for $11 each. The supplies cost her $5 per scarf. Last month, Bly had a profit of $139.

seraphim [82]

Bly sold 29 scarves last month

Solution:

Let "x" be the number of scarves sold

Bly made 7 more scarves than she sold

Then, number of scarves made = x + 7

Bly makes fleece scarves and sells them for $11 each

Thus for selling "x" scraves , he will get 11x dollars

Total sales revenue = 11x

number of scarves made = x + 7

The supplies cost her $5 per scarf

Therefore, cost for scarves made = 5(x + 7)

Therefore,

profit = Total sales revenue - cost for scarves made

profit = 11x - 5(x + 7)

profit = 11x - 5x - 35

profit = 6x - 35

Last month, Bly had a profit of $139

139 = 6x - 35

6x = 174

x = 29

Thus Bly sold 29 scarves last month

5 0

3 years ago