3. Write f(x) = x3 – 2x² – 15x in factored form. What are the zeros?

Answer please show steps please

erik [133]

Answer:

25 girls

Step-by-step explanation:

Let

x denote number of boys

and

y denote number of girls

According to the statement that total 45 people came,

x+y = 45 => Eqn 1

And total paid amount was 175

So,

5x + 3y = 175 => Eqn 2

For solving, We will use the substitution method

So, from eqn 1

x = 45-y

Putting value of x in eqn 2

5(45-y) +3y = 175

225 - 5y + 3y = 175

-2y+225 = 175

-2y = 175-225

-2y = -50

2y = 50

y = 25

Putting y =25 in eqn 1

x+25 = 45

x = 45 - 25

x = 20

As y= 25

So, 25 girls came to the dance ..

6 0

2 years ago

A food packet is dropped from a helicopter and is modeled by the function f(x) = −15x2 + 6000. The graph below shows the height

melisa1 [442]

General Idea:

Domain of a function means the values of x which will give a DEFINED output for the function.

Applying the concept:

Given that the x represent the time in seconds, f(x) represent the height of food packet.

Time cannot be a negative value, so

$x\geq 0$

The height of the food packet cannot be a negative value, so

$f(x)\geq 0$

We need to replace $-15x^2+6000$ for f(x) in the above inequality to find the domain.

$-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0$

The possible solutions of the above inequality are given by the intervals $(-\infty , -2], [-2,2], [2,\infty )$ . We need to pick test point from each possible solution interval and check whether that test point make the inequality $(x+200)(x-200)\leq 0$ true. Only the test point from the solution interval [-200, 200] make the inequality true.