Find
f '(a).
f(x) = 3 − 4x

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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Answer:

(0,2)

(3,0)

Step-by-step explanation:

Answer: 344.7

Explanation:

344.7∣234

  (Cut ^off point at the line)

The digit to the right of the cut of the point is less than 5. So the digit to its left (the 7) is not changed and all those to the right are changed to 0 gives you:

344.7000

Written as 344.7

Hope this helps and hope you have a wonderful day :)

Answer:

10

Step-by-step explanation:

2x5=10

Answer:

The least common denominator is 10

Number 1 Not similar

Number 2: not similar since 9/8 different from 15/10

Number 3: they are similar since they are issoceles triangles with the same exact angles: A A A is the theorem that supports the similarity

Number 4: Not imilar since 12/9 is different from 9/6

Number 5: Yes, they are similar since 24/12 = 18/9 = 10/5 all have rate of 2/1 Use S S S

Number 6: Yes, they are similar since 10/8 = 5/4 and they share a same angle. so this is S A S

Answer:

12.1 seconds

Step-by-step explanation:

84.7/7 = 12.1

Answer:

12.1

Step-by-step explanation:

Divide the 84.7 by the # of people on team (7)

The rate of change of the Distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

The rate of change of the distance between the planes, we need to determine how the distance between them changes over time.

the distance between the two planes is represented by the variable D, and time is represented by the variable t.

At noon, the southbound plane starts flying and continues for 4 hours until 4 pm. During this time, the plane covers a distance of 900 km/h * 4 hours = 3600 km due south.

Meanwhile, the eastbound plane is also traveling towards the airport. It starts from a distance of 2000 km away from the airport at 4 pm.

To find the distance between the planes at any given time, we can use the Pythagorean theorem, as the planes are moving at right angles to each other. The distance D between the planes can be calculated as:

D^2 = (2000 km)^2 + (3600 km)^2

Simplifying the equation:

D^2 = 4000000 km^2 + 12960000 km^2

D^2 = 16960000 km^2

Taking the square root of both sides:

D = sqrt(16960000) km

D = 4120 km

Now, we can find the rate of change of the distance between the planes by calculating the derivative of the distance equation with respect to time

dD/dt = 0

Since the distance between the planes is constant, the rate of change is zero.

Therefore, the rate of change of the distance between the planes is zero. This means that the distance between the planes remains constant throughout their respective flights.

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Answer:

x = 21

Step-by-step explanation:

the equation is 2x + 10 = 52

2x = 42

x = 21

Answer:

56 inches

Step-by-step explanation:

4 feet in inches is 48

48+8=56

Answer:

56

4 times 12 is 48

48 + 8 = 56

Answer:

  b ≈ 101.52

Step-by-step explanation:

Given two sides and the angle between, the Law of Cosines is useful.

  b^2 = a^2 +c^2 -2ac·cos(B)

  b^2 = 105^2 +9^2 -2·105·9·cos(65°) ≈ 10307.251

  b ≈ √10307.251

  b ≈ 101.52

Answer:

7

Step-by-step explanation:

Let's say our sum is s.

s = 10 right angles

a right angle is 90 degrees

s = 10 (90)

s= 900

Given the amount of sides in a polygon (n), the sum of the interior angles is equal to

(n-2) * 180

Therefore, the sum of the interior angles is equal to

(n-2) * 180 = 900

divide both sides by 180 to help isolate n

n-2 = 5

add 2 to both sides to isolate n

n = 7

Answer:

3,952 ft

Step-by-step explanation:

Use the sine function since you need to find the hypotenuse but know the opposite side of the angle, since sine is equal to opposite/hypotenuse.

sin8°=\(\frac{550}{c}\)

csin8°=550

c=550/sin8°

c= 3,952

Answer:

43

Step-by-step explanation:

just trust me

Answer:

13ft a second it's just a an average it the feet divided by the time by 2

The result of adding -4 (row 1) to row 3 is determined as (0  - 9   2)|12.

The resultant of the row multiplication in the Matrice is calculated by applying the following method;

row 1 in the given matrices = [1  2  1] | -5

To multiply row by -4, we will multiply each entity by 4 as shown below;

= -4(1 2  1) | -5

= (-4  -8  - 4) |20

To add the result to 3;

(-4  -8  - 4)|20 + (4  - 1   6) | -8

= (0  - 9   2)|12

Thus, the result of the row multiplication is determined by multiplying each entry in row 1, by - 4.

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The first and last expressions are identified as a limit that exists.

'In Mathematics, a limit is defined as a value that a function approaches the output for the given input values.'

According to the given problem,

For expression 1,

     \(\lim_{n \to4}\frac{x^{2}-x-12 }{2-x}\)

⇒ \(\lim_{n \to4} \frac{x^{2}-4x+3x-12 }{4-x}\)

⇒ \(\lim_{n \to4}\frac{-x(4-x)-3(4-x)}{4-x}\)

⇒ \(\lim_{n \to4}\frac{(4-x)(-x-3)}{4-x}\)

⇒ \(\lim_{n \to4 }(-x-3)\)

Now, we put the value of x as 4

⇒ - 4 - 3

= -7

Therefore, the limit exists.

For the last expression,

    \(\lim_{x \to 2} \frac{x^{2}+3x-10 }{x^{2} -4}\)

⇒ \(\lim_{x \to 2} \frac{x^{2}+5x - 2x-10 }{(x+4)(x-4)}\)

⇒ \(\lim_{x \to2} \frac{x(x+5) -2(x+5)}{(x+4)(x-4)}\)

⇒ \(\lim_{n \to 2} \frac{(x+5)(x-2)}{(x+4)(x-4)}\)

Now, putting the value of x = 2 in the expression,

⇒ (2+5)(2-2) / (2+4)(2-4)

⇒ 7*0 / 6*(-2)

= 0

Therefore, the limit exists.

For the other expressions, we cannot factorize the numerator or the denominator to cancel out the denominator because of which if we put the values of x directly into the denominator without cancelling it out, the denominator would be zero, which means infinity because zero in the denominator of a fraction means infinity or undefined or does not exist.

Hence, we can conclude that expressions 1 and 6 are limits that exist.

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The measure of m<JMO is 20 degrees

The triangle JOK is a 60 degrees equilateral triangle. Hence the measure of m<O at the center is 60 degrees.

Since the base angles of triangle KOL and OLM are equal hence;

Substitute the base angles and the equilateral angles to get angle JOM

80 + 80 + m<JOM + 60 = 360

m<JOM = 360 - 360 - 220

m<JOM = 140 degrees

Since the sum of angle in the triangle JOM is 180 degrees, hence;

2m<JMO + m<JOM = 180

2m<JMO = 180 - 140

2m<JMO = 40

m<JMO = 20 degrees

Hence the measure of m<JMO is 20 degrees

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Answer:

8.64

Step-by-step explanation:

8.64

\(12\;percent\;of\;72=8.64\)

Answer:The answer is the 2 one

Step-by-step explanation:

Answer:

4 over 9

Step-by-step explanation:

4 over 7 = 0.571428571

2 over 5 = 0.4

7 over 8 = 0.875

4 over 9 = 0.444444444444444

Answer:

4/7 and 4/9

Step-by-step explanation:

14)The sum of the tangent and the sine of the angle is obtained as 1.21.

15)The area of the segment is 95.6 m^2 while the perimeter of the segment is 11.047 m.

16)The angle opposite the largest side is  130°.

The trigonometric ratios are the ratios that are designated as cos, tan and sine. It is important to note that the  trigonometric ratios are particular to the right angled triangle. The meaning of the right angle triangle is that one of the angles in the triangle is about 90 degrees.

14)) We can find the hypotenuse by the use of the Pythagoras theorem that is used to find the parts of the right angle triangle.;

a = √2^2 + 3^2

a = √ 4 + 9

a = 3.6

We know that;

tan θ = 2/3 = 0.66

sin θ = 2/3.6 = 0.55

Then;

tan θ + sin θ

0.66 + 0.55

= 1.21

We can see by the use of the trigonometric ratios that we would obtain the sum of the sine and the tangent as 1.21.

15)

The area of the segment is obtained as;

Area of the triangle;

1/2r^2 sinθ

r= radius of the circle

θ = angle of inclination

1/2 * (10)^2 * sin 60

= 43.3

Area of the sector;

60/360 * 3.142 * (10)^2

= 52.3

Therefore the area of the triangle is;

43.3 +  52.3 = 95.6 m

b)The perimeter of the segment;

(2πr * θ/360) + 2rsin(θ/2)

(2 * 3.142 * 60/360) + (2 * 10 * sin (60/2))

1.047 + 10

= 11.047 m

16)

Using;

c^2 = a^2 + b^2 - 2abcos C

20^2 = 13^2 + 9^2 - 2(13 * 9) cos C

400 = 250 - 234cosC

400 - 250 = - 234cosC

150 =  - 234cosC

Cos C = -(150/234)

C = Cos-1-(150/234)

C = 130°

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Answer:

ang hirap naman plss answee

Answer:

37.5

Step-by-step explanation

your answer is 37.5

Answer:

She probably wants attention from you maybe compliment her outfit or something like that.

The probability of more than 3 successes in 6 trials with a probability of success of 0.6 is 0.4558.

To calculate the probability of more than 3 successes in 6 independent trials with a binomial distribution where the probability of success is 0.6, we can use the cumulative distribution function (CDF) of the binomial distribution:

Pr(x > 3) = 1 - Pr(x ≤ 3)

To find Pr(x ≤ 3), we can use the binomial probability mass function (PMF) for each possible value of x and add them up:

Pr(x = 0) = (6 choose 0) × 0.6^0 × 0.4^6 = 0.0041

Pr(x = 1) = (6 choose 1) × 0.6^1 × 0.4^5 = 0.0409

Pr(x = 2) = (6 choose 2) × 0.6^2 × 0.4^4 = 0.1536

Pr(x = 3) = (6 choose 3) × 0.6^3 × 0.4^3 = 0.3456

Therefore, Pr(x ≤ 3) = 0.0041 + 0.0409 + 0.1536 + 0.3456 = 0.5442

Finally, we can calculate Pr(x > 3) as follows:

Pr(x > 3) = 1 - Pr(x ≤ 3) = 1 - 0.5442 = 0.4558

Therefore, the probability is 0.4558

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Answer:

Step-by-step explanation:

15 - 5(4c - 7) = 50

Multiply the terms in the bracket

That's

15 - 20c + 35 = 50

50 - 20c = 50

Subtract 50 from both sides

That's

50 - 50 - 20c = 50 - 50

- 20c = 0

Divide both sides by - 20

c = 0

Hope this helps you

The required frequencies are 3, 2, 4, 1.

The quantity of times a specific data value happens is known as its frequency. For instance, the score of 80 is said to have a frequency of four if four pupils receive an overall math score of 80.

Number between 79 to 83 are 3.So, frequency is 3.

Number between 84 to 88 are 2.So, frequency is 2.

Number between 89 to 93 are 4.So, frequency is 4.

Number between 94 to 98 are 1.So, frequency is 1.

Thus, required frequencies are 3, 2, 4, 1.

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Answer:

y=6x

Step-by-step explanation:

The slope-intercept form is y=mx+b. m in the equation represents the slope, which is 6 and b in the equation represents the y-intercept, 0. Everytime there's an equation with 0 as y-intercept, you don't have to write the equation like this: y=6x+0 but like this is better: y=6x.

Answer:

92%

Step-by-step explanation: