For the function f(x) = x2 + 4x - 12 solve the following.
f(x) < 0

Answer:

(-6,2)

Step-by-step explanation:

[tex]f(x)<0[/tex]

We are given [tex]f(x)=x^2+4x-12[/tex].

So we need to solve:

[tex]x^2+4x-12<0[/tex]

First let's find when the expression on the left is 0.

[tex]x^2+4x-12=0[/tex].

The expression on the left is factorable.

Given the coefficient of [tex]x^2[/tex] is 1, all we have to do is see if there are two numbers that multiply to be -12 and add to be 4.

Those numbers are 6 and -2 so the factored form is:

[tex](x+6)(x-2)=0[/tex]

So the solutions can be found be solving the following linear equations:

[tex]x+6=0[/tex] and [tex]x-2=0[/tex].

First equation, you just need to subtract 6 on both sides. [tex]x=-6[/tex]

Second equation, you just need to add 2 on both sides. [tex]x=2[/tex]

So draw a number line with those on it and test the intervals they divide.

--------(-6)--------(2)----------

So we need to test three intervals.

*Plug in a number before -6 to see if that piece of the function is above the x-axis or below. We are looking for below since we want [tex]f(x)<0[/tex].

Let's plug in x=-8

[tex]f(x)=(x+6)(x-2)[/tex] or use [tex]f(x)=x^2+4x-12[/tex].

[tex]f(-8)=(-8+6)(-8-2)[/tex]

[tex]f(-8)=(-2)(-10)[/tex]

[tex]f(-8)=20[/tex] so this piece is above since 20 is positive and not negative.

So we will not include this interval in our answer.

*Plug in a number between -6 and 2 like 0.

[tex]f(x)=(x+6)(x-2)[/tex]

[tex]f(0)=(0+6)(0-2)[/tex]

[tex]f(0)=(6)(-2)[/tex]

[tex]f(0)=-12[/tex] so this piece is under since -12 is negative and not positive.

So our solution includes the interval (-6,2).

*Plug in a number after 2 like 5.

[tex]f(x)=(x+6)(x-2)[/tex]

[tex]f(5)=(5+6)(5-2)[/tex]

[tex]f(5)=(11)(3)[/tex]

[tex]f(5)=33[/tex] so this piece is above since 33 is positive and not negative.

The answer only includes the interval (-6,2).

Answer the question below

A store owner wants to advertise his store in magazines that most of his shoppers are likely to read. He takes a survey to determine the ratio of females to males that shop at his store each day.

The chart below represents the number of females and males that shop at his store on average each day.



Which statement identifies the ratio of females to males that shop at his store and who he should focus his advertising on?
He should focus on males because the ratio of females to males is 3:5.
He should focus on females because the ratio of females to males is 5:2.
He should focus on females because the ratio of females to males is 5:3.
He should focus on males because the ratio of females to males is 2:5.

(05.01)
The graph of a system of equations with the same slope and the same y-intercepts will
have no solutions. (1 point)
O Always
Sometimes
O Never
Help ASAP

You have 5814 meters of rope you need to cut into 27 sections how many 27 meters secton of rope will you be able to create and how much rope will be left over as waste

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what is the probability that an integer selected at random from the interval 1

A) 1/6

B) 1/5

C) 3/10

D) 1/3

E) 7/10

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Find the value of f(-7).

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Standard form

5
Which list shows these numbers in order from least to greatest?
37
26
-5.17, 133,
6
5
37
А
26
5
-5.17,
33
B -5.17,
26
5
37
6
33
C
26
S
-5.17)
133,
37
6
D
-5.17, 252
133,
37
6
5

due now help please !!!!!!!!!!!!!!!!!!!!

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