Subtract.3 1/3−5enter your answer as a simplified mixed number by filling in the boxes.

If fx = x-4/x^2+13x+36, then the math expression f(x) is increasing for all x > –4 is true.

A mathematical expression is a sentence that combines numbers, variables, and operators to indicate the value of a factor. An equation is a mathematical expression in which two expressions are made equal.

So arrive at the above-stated conclusion:

First, we simplify the expression of the given function:
f (x) = (x - 4) /(x² + 13x +36)

Expand the denominator to get:

f (x) = (x - 4) /(x² + 9x + 4x +36)


Factorize the denominator to achieve:
f (x) = (x - 4) / [x(x + 4) + 9( x+4)

f(x) = (x - 4) / [(x + 9)(x+4)

In this simplified state, it is easy to determine that:

f(x) is increasing for all x > –4

For example
If x = 0 which is > -4, then

f(x) = (0 - 4) / [(0 + 9)(0+4)

= -4/(9*4)

= - 1.11

Where x = 5

f(x) = (5- 4) / [(15+ 9)(5+4)

= 1/216

= 0.0046

Notice that the results are no longer negative hence,

f(x) is increasing for all x > –4

Learn more about math expressions:
https://brainly.com/question/14961928
#SPJ1

Answer:

x = 60.4

Step-by-step explanation:

First, let's remember the three different trigonometric functions: sine, cosine, and tangent. In this case, we would use cosine because the adjacent side to the angle and hypothenuse are used/given.

\(cos(22) = \frac{56}{x}\)

We need to set up a proportion because there is not much else you could do here.

\(\frac{cos(22)}{1} =\frac{56}{x}\)

Then, cross-multiply.

\(cos(22) * x = 56\)

Finally, divide both sides by cos(22). You'll probably need your calculator and make sure it's in degrees mode and not radians!

\(\frac{cos(22) * x}{cos(22)} = \frac{56}{cos(22)}\)

\(x = 60.4\)

Rounded to the nearest tenth, x = 60.4.

Answer:

x = 4; 15 - x > 11

Step-by-step explanation:

Step 1: set up equation

15 - x = 11

- x = 11 - 15

- x = - 4

x = - 4 ÷ - 1

x = 4

For inequality:

15 - x > 11

The minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

In this target game, Malia needs to have the lowest mean distance of all throws to win. The mean distance is calculated by adding up all the distances and dividing by the number of throws.

First, we need to calculate the mean distance of Malia's first 7 throws.

Mean distance = (2 + 3 + 4 + 2 + 5 + 3 + 4) / 7 = 3.14

Now, we know that Malia's mean distance must be less than 3.14 to win the game. Let's call the distance of her last throw x.

The mean distance of all 8 throws will be: (2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8

To find the minimum distance that Malia needs on her last throw to win the game, we can set up an inequality:

(2 + 3 + 4 + 2 + 5 + 3 + 4 + x) / 8 < 3.14

Multiplying both sides by 8 gives us:

2 + 3 + 4 + 2 + 5 + 3 + 4 + x < 25.12

Simplifying gives us:

x < 25.12 - 23

x < 2.12

Therefore, the minimum distance that Malia needs on her last throw to win the game is less than 2.12 meters.

Learn more about distance at https://brainly.com/question/15172156

#SPJ11

scale    1 cm............25 km

            n cm...........280 km

25 x n = 1 x 280

n = 280 : 25

n = 112 cm on the map

Answer:

2. (-3f)

3. (4f)

4. x - 11 (not sure if this one is correct)

Step-by-step explanation:

Move -3 to the left of f = -3f

Move 4 to the left of f = 4f

f(x)=x+11 f ( x ) = x + 11

100 polyps would fit in a row 12 inches long.

The formula for calculating the number of polyps is:

Number of Polyps = 12 in/0.12 in = 100 polyps

To calculate the number of polyps that would fit in a row 12 inches long, we divide 12 (the length of the row) by 0.12 (the diameter of each polyp).

12 in/0.12 in = 100 polyps

This gives us the number of polyps that would fit in a row 12 inches long as 19.7. Thus, approximately 100 polyps would fit in a row 12 inches long

Therefore, 100 polyps would fit in a row 12 inches long.

Learn more about Diameter here:

https://brainly.com/question/5501950

#SPJ4

Answer:

y = \(\frac{-5}{2}\) x + 6

Step-by-step explanation:

We want the form

y = mx + b

5x + 2y =12   Subtract 5x from both side of the equation

2y = -5x + 12  Divide all the way by 2

y = \(\frac{-5}{2}\) x + 6

(a) True. The set {0x: x ∈ {0, 1}^2} can be expressed as {(0, 0), (0, 1), (1, 0), (1, 1)}, which is the Cartesian product of {0, 1} with itself.

(b) False. {0, 1}0 ∪ {0, 1}1 ∪ {0, 1}^2 can be expressed as {00, 01, 10, 11} ∪ {0, 1} ∪ {(0, 0), (0, 1), (1, 0), (1, 1)}, which is not the Cartesian product of sets.

(c) True. The set {0x: x ∈ B}, where B = {0, 1}^0 ∪ {0, 1}^1 ∪ {0, 1}^2, can be expressed as {0^0, 0^1, 1^0, 1^1, 0^00, 0^01, 0^10, 0^11, 1^00, 1^01, 1^10, 1^11}, where ^ represents concatenation.

(d) True. The set {xy: where x ∈ {0} ∪ {0}^2 and y ∈ {1} ∪ {1}^2} can be expressed as {01, 011, 001, 0001}, which is the Cartesian product of {0} with {1, 11, 1, 0001}.

In summary, statements (a) and (d) are true, while statement (b) is false. Statement (c) is true, given the definition of B.

To learn more about Cartesian product click here: brainly.com/question/30340096

#SPJ11

Answer:

1 and 19

Step-by-step explanation:

I believe this is a factoring problem.

Example:

If we have the equation x^2-2x-3

We can find two numbers that multiply to -3 that add to -2

The two numbers are -3 and 1

(x-3)(x+1)= So x=3 and x=1

Answer:

1 and 19

Explanation:

1x19=19

1+19=20

Answer:

24 pots 2 plates

Step-by-step explanation:

Answer:

24 pots and 2 plates

Step-by-step explanation:

Answer:

x>8

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

               6*x-20-(3*(2-x)+6*x-2)>0

6x - 20) -  ((3 • (2 - x) +  6x) -  2)  > 0

3x - 24  =   3 • (x - 8)

3 • (x - 8)  > 0

   x > 8

Answer:

135 degrees

Step-by-step explanation:

It is on a straight line so that equals 180 degrees. Since there is already a 45 degree angle do 180-45. This leaves you with 135 degrees for the angle RUP

Answer:

1. 23x/10

2. 13x/10

Step-by-step explanation:

explanation: find the common denominator and then go from there. i suck at in depth explanations but as long as you get the gist of it youre good

Answer:

B is the correct option dear .

Step-by-step explanation:

Good luck ^_^

Answer:

I think its B

Step-by-step explanation:

Answer:

x = 5

Step-by-step explanation:

The diagram shows that the rhombus is split into two isosceles triangles, LKM and NMK.  

Thus, the three angles in triangle LKM are 110, (8x - 5), and (8x - 5).

Thus, we can solve for x by setting the sum of the measures of the three angles in triangle LKM equal to 180:

(8x - 5) + (8x - 5) + 110 = 180

(8x + 8x) + (-5 - 5 + 110) = 180

16x + 100 = 180

16x = 80

x = 5

Thus, x = 5

Optional step:

We can check that we've correctly solved for x by plugging in 5 for x in (8x - 5) twice for both angles, adding the result to 110, and seeing if we get 180 on both sides of the equation:

(8(5) - 5) + (8(5) - 5) + 110 = 180

(40 - 5) + (40 - 5) + 110 = 180

35 + 35 + 110 = 180

70 + 110 = 180

180 = 180

Thus, x = 5 is correct.

Answer:

There are 7 quarters and 9 nickels.

Explanation:

Let the number of quarters = x

Let the number of nickels = y

There are a total of 16 coins, therefore:

• 1 Quarter = $0.25

• 1 Nickel =$0.05

Since the total value in the cup is $2.20, we have that:

We substitute x in the first equation into the second one.

Recall: x=16-y

Therefore:

There are 7 quarters and 9 nickels.

Mathematically, if a space of 2m can comfortably fit 6 students in a standing position, the maximum number of students that can be sent to stand in the naughty corner that is 36m² during devotion is 108.

The maximum number can be determined using the mathematical operation of multiplication and division.

Multiplication and division operations are two of the four basic mathematical operations, including addition and subtraction.

The area of the naughty corner = 36m²

The space that can comfortably fit 6 students in a standing position = 2m

The maximum number of students that can occupy 36m² in a standing position = 108 (36/2 x 6).

Learn more about mathematical operations at https://brainly.com/question/28294142 and https://brainly.com/question/4721701

#SPJ1

The lengths of the legs of a right triangle, where one acute angle measures 65 degrees and the hypotenuse measures 12, are approximately 10.88 and 5.07.

To find the lengths of the legs of a right triangle, we can use the trigonometric functions sine and cosine. Since we know one acute angle and the hypotenuse, we can use the following formulas:

sin(65) = opposite/hypotenuse

cos(65) = adjacent/hypotenuse

Plugging in the known values and solving for the unknowns, we get:

sin (65) = opposite/12

opposite = 12sin (65) ≈ 10.88

cos (65) = adjacent/12

adjacent = 12cos (65) ≈ 5.07

Therefore, the lengths of the legs of the right triangle are approximately 10.88 and 5.07.

Learn more about trigonometric functions here: https://brainly.com/question/25618616.

#SPJ11

Answer:

take a actual picture maby

Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is

1 - 1.9287 x 10⁻²².

It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.

We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.

Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.

Poisson distribution gives the probability of occurrence of any event in a given time interval.

Let the average number of event per year in 30 years of period is λ.

\(\lambda = \frac{1500}{30}\)

λ = 50

Let, the occurrence of an earthquake is a random variable x.

Then the probability that at least an earthquake occur in next 30 years is calculated as:

P(x ≥ 1) = 1 - P(x<1)

P(x ≥ 1) = 1- P(x=0)   -----(1)

PDF of Poisson distribution with parameter λ is given as:

\(P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}\)

So, in this case

\(P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}\)

\(P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}\)

\(P(x=0)={1.9287 \times 10^{-22}\)

Substitute this value in equation (1)

P(x ≥ 1) = 1 - 1.9287 x 10⁻²²

Hence, the probability of an earthquake in next 30 years is

1 - 1.9287 x 10⁻²².

Learn more about Poisson distribution here:

https://brainly.com/question/30388228

#SPJ4

Answer:

((x)h)g

Step-by-step explanation:

Hope this helps and if this is wrong then please comment the right answer and I will edit it thanks :)

To find the absolute maximum and absolute minimum values of f on the given interval, f(x) = xe−x2/128, [−2, 16].Here, f(x) = xe−x2/128, [−2, 16]Let's find the absolute maximum and absolute minimum value for the given function by taking the derivative of the function and equating it to zero.

The first derivative of f(x) is: f'(x) = e−x2/128 (1−x2/64)The critical points occur where f'(x) = 0 and where f'(x) is undefined. f'(x) = 0 when e−x2/128 (1−x2/64) = 0 ⇒ 1−x2/64 = 0 or e−x2/128 = 0.Now, 1−x2/64 = 0 when x2 = 64 ⇒ x = ±8.e−x2/128 = 0 when x = ±∞ since e−∞ = 0 and e∞ = ∞.

Therefore, the critical points in the interval [−2, 16] are x = −8 and x = 8. To find the nature of critical points, we take the second derivative. f"(x) = (1/64) (3x2−32)e−x2/128.The second derivative is positive for x < −4 and 4 < x, so x = −8 is a local maximum, and x = 8 is a local minimum.

However, we need to verify whether the critical points are absolute maximum or absolute minimum values. Now, we evaluate the function at the critical points and at the endpoints of the interval to determine the absolute maximum and minimum values. At x = −8, f(−8) = −8e−2 < 0.At x = 8, f(8) = 8e−2 > 0.At x = −2, f(−2) = −2e−1/8 > 0.At x = 16, f(16) = 16e−8/2 < 0.The maximum value of the function occurs at x = 8 and is f(8) = 8e−2.Conversely, the minimum value of the function occurs at x = 16 and is f(16) = 16e−8/2.

Therefore, the absolute maximum value of the function is 8e−2 and the absolute minimum value is 16e−8/2 on the interval [−2, 16].We are given f(x) = xe−x2/128, [−2, 16]. We are to determine the absolute maximum and absolute minimum value of the function on the interval [−2, 16]. The first step to finding the absolute maximum and minimum value of the function is to find the critical points.

To find the critical points, we take the derivative of the function and equate it to zero. We getf'(x) = e−x2/128 (1−x2/64) = 0.The critical points occur where f'(x) = 0 and where f'(x) is undefined. f'(x) = 0 when e−x2/128 (1−x2/64) = 0 ⇒ 1−x2/64 = 0 or e−x2/128 = 0. We find x = ±8. However, we need to verify whether the critical points are absolute maximum or absolute minimum values.

To determine this, we evaluate the function at the critical points and at the endpoints of the interval. Now, we take the second derivative to determine the nature of the critical points.

f"(x) = (1/64) (3x2−32)e−x2/128. The second derivative is positive for x < −4 and 4 < x, so x = −8 is a local maximum, and x = 8 is a local minimum. However, we need to verify whether the critical points are absolute maximum or absolute minimum values.

At x = −8, f(−8) = −8e−2 < 0. At x = 8, f(8) = 8e−2 > 0. At x = −2, f(−2) = −2e−1/8 > 0. At x = 16, f(16) = 16e−8/2 < 0. The maximum value of the function occurs at x = 8 and is f(8) = 8e−2. Conversely, the minimum value of the function occurs at x = 16 and is f(16) = 16e−8/2.

Thus, the absolute maximum value of the function is 8e−2 and the absolute minimum value is 16e−8/2 on the interval [−2, 16]..

Therefore, we can conclude that the absolute maximum value of the function is 8e−2 and the absolute minimum value is 16e−8/2 on the interval [−2, 16].

Learn more about derivative visit:

brainly.com/question/29020856

#SPJ11

Answer:

8b - 136

Step-by-step explanation:

Answer:

C is your Answer

Step-by-step explanation:

Answer:

a or b i will help no further

Answer:

x² - 6x + 9

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

Step 1: Define

x² + 6x + 9

Step 2: Find Roots α and β

Step 3: Solve

Answer

He earned 35

Step-by-step explanation:

He earned 35 because if you multiply $7 with 5 hours it equals $35, therefore the answers is $35

Hope this helped ;)

Answer:

Step-by-step explanation:

1+1

2/555