11. Determine the solutions to the inequality in interval notation.
(x - 1)(x + 3) < 0
a. (-0, -3) U (1,0)
b. (-3,1)
c. (-0, -1) U (3)
d. [-3,1]

Answer/Step-by-step explanation:

Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.

f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not

the same as g ◦ f. (This means that composition is not commutative).

f ◦ g ◦ h is the composition that composes f with g with h.

Since when we combine functions in composition to make a new function, sometimes we

define a function to be the composition of two smaller function. For instance,

h = f ◦ g (1)

h is the function that is made from f composed with g.

For regular functions such as, say:

f(x) = 3x

2 + 2x + 1 (2)

What do we end up doing with this function? All we do is plug in various values of x into

the function because that’s what the function accepts as inputs. So we would have different

outputs for each input:

f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)

f(0) = 3(0)2 + 2(0) + 1 = 1 (4)

f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)

When composing functions we do the same thing but instead of plugging in numbers we are

plugging in whole functions. For example let’s look at the following problems below:

Examples

• Find (f ◦ g)(x) for f and g below.

f(x) = 3x + 4 (6)

g(x) = x

2 +

1

x

(7)

When composing functions we always read from right to left. So, first, we will plug x

into g (which is already done) and then g into f. What this means, is that wherever we

see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).

g(x) = x

2 +

1

x

(8)

f(x) = 3x + 4 (9)

f( ) = 3( ) + 4 (10)

f(g(x)) = 3(g(x)) + 4 (11)

f(x

2 +

1

x

) = 3(x

2 +

1

x

) + 4 (12)

f(x

2 +

1

x

) = 3x

2 +

3

x

+ 4 (13)

Thus, (f ◦ g)(x) = f(g(x)) = 3x

2 +

3

x + 4.

Let’s try one more composition but this time with 3 functions. It’ll be exactly the same but

with one extra step.

• Find (f ◦ g ◦ h)(x) given f, g, and h below.

f(x) = 2x (14)

g(x) = x

2 + 2x (15)

h(x) = 2x (16)

(17)

We wish to find f(g(h(x))). We will first find g(h(x)).

h(x) = 2x (18)

g( ) = ( )2 + 2( ) (19)

g(h(x)) = (h(x))2 + 2(h(x)) (20)

g(2x) = (2x)

2 + 2(2x) (21)

g(2x) = 4x

2 + 4x (22)

Thus g(h(x)) = 4x

2 + 4x. We now wish to find f(g(h(x))).

g(h(x)) = 4x

2 + 4x (23)

f( ) = 2( ) (24)

f(g(h(x))) = 2(g(h(x))) (25)

f(4x

2 + 4x) = 2(4x

2 + 4x) (26)

f(4x

2 + 4x) = 8x

2 + 8x (27)

(28)

Thus (f ◦ g ◦ h)(x) = f(g(h(x))) = 8x

2 + 8x.

Answer:

[tex]x=\frac{2}{3}, -4[/tex]

Step-by-step explanation:

hope this helps!

Answer:

• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier

Step-by-step explanation:

• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closing of the frontier• The closin[tex]\sqrt{x} 67[/tex]g of the frontier

Answer:

14 × (19 + 6)

hope it helps

The expression represents the total number of cans of beans Mr. Jenkins is, (19+6)×14, So Option B is correct.

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

Mr. Jenkins has 19 cases of beans

He also has 6 cases of beans in the stock room

There are 14 cans of beans in each case

Expression for total number of beans = ?

Total number of beans  = Total number of cases ×beans in each case

Total number of beans = (beans in grocery store+beans in stock room)×14

Total number of beans = (19 +6) × 14

Hence, the expression is  (19 +6) × 14

To know more about Expressions check:

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Answer:

x = 30

Step-by-step explanation:

well from the theorem we have

[tex]\frac{15}{3}=\frac{x}{6}[/tex]

yes i know you could say that the right way is

[tex]\frac{3}{15}=\frac{6}{x}[/tex]

well if you notice they are the same only that in my way the x is in the numerator which means it will be far easier to know it's value :)

so

[tex]\frac{15}{3}=\frac{x}{6}\\\\5=\frac{x}{6}\\\\6[5]=6[\frac{x}{6}]\\\\30=x[/tex]

Answer:

60 %

Step-by-step explanation:

multiply .90 * 150

Answer:

60%

Step-by-step explanation:

hope this helps <3

Answer:

the last one is true

Step-by-step explanation:

sin R=PQ/PR=TS/TR

The answer is 53 degrees

Answer:

Geography? You mean middle school math? But anyways, the measure of angle 6 is 143 degrees.

Step-by-step explanation:

So, all the angles that measure 37 degrees are 1, 4, 5, and 8. First, you know that 37 + x = 180. Now, do 180 - 37. You should get 143, you are welcome.

Answer:

23

Step-by-step explanation: hope this helps

Answer:

Length of rectangle = 64 inches

Width of rectangle = 32 inches

Step-by-step explanation:

Perimeter of rectangle = 192 in

Length = x

Width = [tex]\frac{1}{2}x[/tex]

We need to find the length and width.

The formula used is: [tex]Perimeter\:of\:rectangle=2(Length+Width)[/tex]

Putting values and finding value of x

[tex]Perimeter\:of\:rectangle=2(Length+Width)\\192=2(x+\frac{x}{2} )\\192=2(\frac{2x+x}{2} )\\192=2(\frac{3x}{2} )\\192=3x\\x=\frac{192}{3}\\x=64[/tex]

So, we get x = 64

The length of rectangle x = 64

The width of rectangle = [tex]\frac{1}{2}x[/tex] = [tex]\frac{64}{2} = 32[/tex]

So, Length of rectangle = 64 inches

Width of rectangle = 32 inches

Answer:

Length of rectangle = 64 inches

Width of rectangle = 32 inches

Step-by-step explanation:

Answer:

9.25

Step-by-step explanation:

No problem..

Answer:

A and D are the answers for the question and

Step-by-step explanation:

please mark me as brainlest

Answer:

You done it right

Step-by-step explanation:

Step-by-step explanation:

Arrow JK=360-54-130-110=66

arrow MK=66+54=120

Angle L=120/2=60

3a=60

a=30

Answer:

661 is for the first 308 for second 849 for last

Step-by-step explanation:

Answer:

1/52

Step-by-step explanation:

The probability that the card is a 4 in a pack of cards is 1 /13.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A card is selected from a pack of 52 cards. A favorable outcome is getting 4 since there are four 4 in a pack of cards. Thus,

When a card is selected from a pack of 52 cards the number of possible outcomes is 52 i.e., the sample space contains 52 elements

Therefore there are 52 points in the sample space.

Let E be the event in which the card drawn is an ace.

Since there are 4 aces in a pack of 52 cards n(E)=4

∴P(E)=  [tex]\frac{Totalnumberofpossibleoutcomes}{Numberofoutcomesfavourableto}[/tex]

E = [tex]\frac{n(S)}{n(E)}[/tex]

E = 4/52 = 1/13

​Therefore, In a deck of cards, there is a 1 in 13 chance that the card is a 4.

Learn more about probability here:

https://brainly.com/question/11234923

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​

Answer: The probability is 0.083

Step-by-step explanation:

First, let's find the individual probabilities:

The probability that the outcome of the red number cube is even:

This will be equal to the quotient between the number of outcomes that are even (3) and the total number of outcomes for this dice (6)

Then the probability is:

p = 3/6 = 1/2.

The probability that the outcome of the blue number cube is a 5.

Similar to the above case, here the probability will be the quotient between the number of outcomes that are 5 (only one) and the total number of outcomes.

q = 1/6

And the joint probability will be equal to the product of the individual probabilities, then he probability that the outcome of the red number cube is even and the outcome of the blue number cube is a 5 is equal to:

P = p*q = (1/2)*(1/6) = 1/12 = 0.083

Answer:

If you have two points, (x1, y1) and (x2, y2), you can define the exponential function that passes through these points by substituting them in the equation y = abx and solving for a and b. In general, you have to solve this pair of equations: y1 = abx1 and y2 = abx2, .

Answer:

I think d sorry if I get it wrong

Answer:

Step-by-step explanation:

How are you feeling in your home

Slope is -1/4

Y intercept is 5

Answer:

y = 2x+11

Step-by-step explanation:

Answer:B

Step-by-step explanation:

Answer:

Hop. Answer ur question the answer is 13

Step-by-step explanation:

yeah hope i helped

12/10

6/5

It’s simple by Dividing

Well since it's better to teach you than answer, I'll give you an explanation using #1.

Answer:

6.88

Step-by-step explanation:

In the parentheses, 1.6 has one decimal place, and so does 4.3. (count number of digits after decimal point.) So a total of 2 decimal places. (1) + (1) = (2)

Next, ignore the decimal points for now and multiply 16 × 43 = 688.

Add in the 2 decimal places, 6.88, there is your answer!

9514 1404 393

Answer:

  x = 0

Step-by-step explanation:

You can eliminate parentheses and subtract 50.

  5(2x +10) = 50

  10x +50 = 50 . . . . use the distributive property

  10x = 0 . . . . . . . . . subtract 50 from both sides

  x = 0 . . . . . . . . . . . divide by 10

__

Check

  5(2·0 +10) = 50

  5(10) = 50 . . . . true

Answer:

x < 88

Step-by-step explanation:

ΔCED and ΔCEF

DE = EF      CE = CE      CF < CD

∠FEC < ∠DEC

x - 13 < 75

x < 88