Suppose that f(4)=2, g(4)=5, f'(4)=6, g'(4)=-3, f'(5)=8, and g'(2)=10.
Find h'(4) where
(a) h(x)=f(x)g(x)
(b) h(x)= g(x)/f(x)+g(x)
(c) h(x)=f(g(x))
please help

For the given graph of the function: Period = π, Domain = [0,π], Range = (-∞, + ∞), Asymptotes at x = 0.

Period:

A function is referred to as periodic if it repeats a pattern, such as sine or cosine. The shortest interval with exactly one instance of the repeating pattern is said to have a period, which is its length.

Period = π

Domain:

The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).

Domain = [0,π]

Range:

A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.

Range = (-∞, + ∞)

Asymptotes:

The graph of the a function approaches an asymptote as either x or y approach positive or negative infinity, respectively.

Asymptotes at x = 0.

As a result, whenever x = 0, the function possesses a vertical asymptote.

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The appropriate choice is for all actual x values of x 1.5, the function is declining.

A linear polynomial is a polynomial of degree one, which means it is a polynomial that has only one variable raised to the power of one and no other variables or exponents.

A function f(x), which is made up of two linear polynomials, is given as follows:

f(x)=(x-4)(x+1)

We now know that when we multiply the two linear polynomials, a quadratic polynomial results.

As a result, the function f(x) will be shown as:

f(x)=x(x+1)-4(x+1)

f(x)=x²+x-4x-4

f(x)=x²-3x-4

In order to determine which claims about the function are accurate, we shall plot the function's graph.

1) The function increases for all real x values greater than zero.

Since we get from the graph that function f(x) is decreasing for x<0.

This statement is false.

2)The function is increasing for all real values of x where x < –1 and where x > 4.

This option is incorrect as the function is decreasing for x<-1

whereas it is increasing for x>4.

3)Where -1 <x<4, the function decrements for all real values of x.

This is the incorrect choice.

Because of the function's dual trend of growing and dropping in the interval (-1,4).

4)For all actual x values of x< 1.5, the function is declining.

This choice is the best one.

since, it is obvious from the graph that the function declines for x<1.5.

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The complete question is;

The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.

Answer:

y = (-3)2^x

Step-by-step explanation:

We can substitute the two points in the equation y = abˣ and we get two equations. By solving the two equations, we can find the values of a and b.

Substitute (0, -3)  in the equation y = abˣ            

-3 = a * b⁰            

-3 = a * 1              

[tex]\boxed{\bf a = -3}[/tex]

Substitute (4, -48) in the equation y =abˣ

-48 = (-3) * b⁴

[tex]\dfrac{-48}{-3}=b^4\\\\ b^4 = 16\\\\b^4 = 2^4\\\\ \boxed{\bf b = 2}[/tex]

Exponential function:

           [tex]y = (-3)2^x[/tex]

Step-by-step explanation:

the area of a rectangle is

length × width

the perimeter of a rectangle is

2×length + 2×width

so,

length×width = 48 cm²

2×length + 2×width = 28 cm

length + width = 14 cm

length = 14 - width

we use this in the first equation :

(14 - width) × width = 48

14×width - width² = 48

-width² + 14×width - 48 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = width

a = -1

b = 14

c = -48

width = (-14 ± sqrt(14² - 4×-1×-48))/(2×-1) =

= (-14 ± sqrt(196 - 192))/-2 =

= (-14 ± sqrt(4))/-2 =

= (-14 ± 2)/-2 =

= 7 ± 1

width1 = 7 + 1 = 8 cm

width2 = 7 - 1 = 6 cm

length1 = 14 - width1 = 14 - 8 = 6 cm

length2 = 14 - width2 = 14 - 6 = 8 cm

so, we see, one of them must be 8 cm, and the other 6 cm.

let's length be the longer side, so

length = 8 cm

width = 6 cm

The relations that are functions are the ones in options 12 and 13

A relation is a function only if each one of the inputs is mapped to a single one output, so if you see a relation where the same input is mapped into different outputs, this is not a function.

Then the relations that are functions are options 12 and 13, in the other two we can see that there are multiple outputs for the same inputs.

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Answer: the right one is d

Step-by-step explanation:

A possible value of a is a > 0 , b = 0 , c < 0

A linear equation is an algebraic equation of the form y=mx+b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

From this diagram we can observe the following:

The diagram opens upwards, which means that the coefficient 'a' is positive. The vertex of the parabola is on the y-axis, which means that the x-coordinate of the vertex is 0. This gives us evidence that the equation of the parabola is f(x) = a(x-0 )²c , which simplifies to f(x) = ax² c. It can also be observed that the y-intercept of the graph is c, which means that the constant term is c. Based on the above observations, we can derive the possible values ​​of a, b and c as follows:

A possible value of a is a > 0 because the graph opens up. A possible value of b is b = 0 because there is no horizontal displacement in the parabola. The possible value of C is c < 0; 0 because the y-intercept is negative. Note that c can be 0, but it cannot be positive because the graph does not intersect the x-axis.

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By first method, he volume of the rectangular prism is (9/32) cubic feet.

By second method, the volume of the rectangular prism is (27/64) cubic feet, which agrees with the volume calculated using the first method.

Volume is a measurement of the amount of space that an object occupies. It is the three-dimensional space occupied by an object. Volume is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, and so on.

We can determine the volume of the rectangular prism in two different ways using the formula:

Volume = Length x Width x Height

First Method:

In the first method, we simply substitute the given dimensions of the rectangular prism into the formula and calculate the volume:

Volume = (3/4) ft x (3/8) ft x (3/4) ft

Volume = (9/32) ft³

Second Method:

In the second method, we can use the fact that the rectangular prism can be divided into 4 smaller rectangular prisms, each with dimensions (3/4) ft x (3/8) ft x (3/16) ft. We can calculate the volume of one of these smaller prisms and then multiply by 4 to get the total volume:

Volume of one smaller prism = (3/4) ft x (3/8) ft x (3/16) ft

Volume of one smaller prism = (27/256) ft³

Total volume = 4 x Volume of one smaller prism

Total volume = 4 x (27/256) ft³

Total volume = (27/64) ft³

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Here is a vector of observations representing the number of defects in 25 1-square-yard specimens of a particular type of woven fabric. This data is provided to facilitate its entry into R.

The data provided is the number of defects in 25 1-square-yard specimens of woven fabric of a particular type. This data can be used to analyze the quality of the fabric and identify any potential issues with the manufacturing process.

It is important to copy this data into R as a vector so that it can be easily analyzed using various statistical techniques. In R, vectors are used to store multiple values of the same type, and they can be used to perform mathematical operations and statistical analyses. Once the data is in R, various descriptive statistics, such as the mean, median, and standard deviation, can be calculated to gain insights into the quality of the fabric and identify any potential trends or patterns in the data.

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Answer:

1,975,906

Step-by-step explanation:

Answer:

The answer is 1975906

Explanation:
If you pick up a Calculator and you input this on it It will give you the answer if u don't have a calculator search on the internet how to multiply numbers

Answer:

see step by step

Step-by-step explanation:

so a laptop starts at 1450 this means the equation is

y=1450(0.75)^x and plug in 4 for x and you get $458.79

solution-

Actual measure= 6m wide ie.600cm wide

her model is =12cm wide

so scale factor =600/12= 50

so length will be =800/50 =16cm

hence gher model will be 16cm long

Answer:

Step-by-step explanation:

350x2x5=3500

Answer:

  40°

Step-by-step explanation:

You want the measure of ∠LNO, marked as y°, given the two vertical angle pairs {100°, (x -y)°} and {y°, 2/7x°}.

Vertical angles have the same measure, so we can write the equations ...

We want the value of y, so it makes sense to solve these equations using a method that eliminates x. Rewriting the second equation to solve for x, we have ...

  x° = 7/2y°

Substituting this into the first equation gives ...

  100° + (7/2y -y)°

  100° = 5/2y°

  2/5(100) = y° = 40°

The measure of ∠LNO is 40°.

The missing variables of the triangle is given as follows:

17.) X=20

18.) X= 32

19) X = 31

20) X= 149

21) X= 125

22.) X= 10

23.) X= 13

To calculate tye variables the formula SOHCAHTOA is used.

For question 17.)

The adjacent of the triangle = 14

The hypotenuse of the triangle = X

The given angle = 45°

Therefore Cos ∅ = 14/X

X = 14/cos∅

X = 14/0.707106781

X = 20( approximately)

For question 18.)

The opposite of the triangle = x

The hypotenuse of the triangle = 45

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin 45° = X/45

X = sin45°×45

X = 0.707106781×45

X = 32 (approximately)

For question 19.)

The opposite of the triangle = 22

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin∅ = opposite/hypotenuse

sin45° = 22/X

X= 22/0.707106781

X= 31

For question 20.)

The opposite of the triangle = x

The hypotenuse of the triangle = 210

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin45° = X/210

X= 0.707106781×210

X= 149 (approximately)

For question 21.)

The opposite of the triangle = 88

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

sin∅ = 88/X

X= 88/0.707106781

X= 125(approximately)

For question 22.)

The opposite of the triangle = 5√2

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

Sin∅= 5√2/X

X= 7.071067811/0.707106781

X= 10

For question 23.)

The opposite of the triangle = 9

The hypotenuse of the triangle = x

The given angle = 45°

Therefore sin ∅ = opposite/hypotenuse

Sin∅ = 9/X

X = 9/0.707106781

X = 13(approximately)

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Assumptions for above case:

1-Equal payments are made monthly.

2-Total amount deposited throughout the year are compounded by end of the year.

3-Annual interest is 6%

4-Total Amount invested plus interest at maturity are reinvested the following year.

Given above, if you create a table in excel for those calculations, you would get $296.330 /month which amounts to $12,000.00 in 3 years approximately.

Year 1 = $3,555.96 Pre-interest =>$3769.32 Post 6% interest

Year 2 = $7,325.28 Pre-interest =>$7,325.28 Post 6% interest

Year 3= $11,320.75 Pre-interest =>$12,000.00 Post 6% interest.

The way to calculate pre interest for each year is just $296.330*12=$3555.96

Afterwards just multiply by the annual interest rate to get the full amount invested + interest (6%) =>$3555.96*(1.06)= $3769.32

Then As per step 1, add another 3555.96 and multiply it all by 1.06, to get 305.06

x = $305.06

Answer:

Table 4

Step-by-step explanation:

The first table is a linear function, with the points of (-240), (-72), (0), (2), and (6).

The second table is also a linear function, with the points of (-768), (-16), (0), (48), and (384)

The third table is a linear function, with the points of (-48), (-6), (0), (6), and (48)

The fourth table is the only one that is a linear function because the first four points are (0) and the last one is (-12)

Answer: you good day

Step-by-step explanation:

Answer:

(x - 4)(x+8)

(Hopefully this helps, and if you can please give me brainliest)

cot θ = 7/4 and θ in degrees = 29.744881 degrees. In this case, the adjacent side is 7 and the opposite side is 4.

Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle.

In this right angle triangle, cot θ can be calculated using the formula

cot θ = adjacent/opposite.

In this case, the adjacent side is 7 and the opposite side is 4.

Therefore, cot θ = 7/4.

Now, to find theta in degrees, we can use the inverse cotangent function, arccot.

arccot (cot θ) = θ.

Therefore, θ = arccot (7/4).

Using a calculator, arccot (7/4) = 29.744881 degrees

Therefore, cot θ = 7/4 and θ in degrees = 29.744881 degrees.

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In this case, 3x plus 12 is 3x plus 12. in this situation, [tex]|3x + 12|[/tex] equals -(3x + 12) for expression.

For the expression:

Two vertical bars serve as the absolute value symbol in mathematics, which is used to represent a number's distance from zero regardless of its sign. In other words, a number's absolute value is never negative.

The number 3x + 12's absolute value is denoted by the expression |3x + 12|. We must take into account two scenarios in order to formulate this expression without the absolute value symbol: the non-negative case for 3x + 12 and the negative situation for 3x + 12.

Example 1: 3x + 12 ≥ 0

Because 3x + 12 is not negative, we may simply remove the absolute value symbols since they are not necessary. In this case, 3x plus 12 is 3x plus 12.

Example 2: 3x + 12 < 0

When 3x + 12 is a negative number, we can multiply it by -1 to get the absolute value. This is so because a negative number's absolute value is the same as its positive equivalent. As a result, in this situation, |3x + 12| equals -(3x + 12).

In light of the aforementioned examples, the phrase |3x + 12| can be expressed as follows:

[tex]|3x + 12| =\\{ 3x + 12 if 3x + 12 ≥ 0\\\\{ -(3x + 12) if 3x + 12 < 0[/tex]

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Answer:

A) 0.5%

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

0.5%

Step-by-step explanation:

7 out of 1400 walk

7/1400 = 1/ 200   divide by 2 equals   0.5/100=0.5%

Step-by-step explanation:

the area of a rectangle is

length × width.

so, the original area is

40 × 21 = 840 cm²

now, we add x to length and width, and we get :

(40 + x) × (21 + x) = 2262 cm²

let's do the multiplication :

40×21 + 40x + 21x + x² = 2262

840 + 61x + x² = 2262

x² + 61x = 1422

x² + 61x - 1422 = 0

a quadratic equation

ax² + bx + c = 0

has the general solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 61

c = -1422

x = (-61 ± sqrt(61² - 4×1×-1422))/(2×1) =

= (-61 ± sqrt(3721 + 5688))/2 =

= (-61 ± sqrt(9409))/2 =

= (-61 ± 97)/2

x1 = (-61 + 97)/2 = 36/2 = 18

x2 = (-61 - 97)/2 = -158/2 = -79

x2 would make the side lengths negative, and that does not make any sense for an actual shape, so

x = 18

is our valid solution.

that means the new length is

40 + 18 = 58 cm

the new width is

21 + 18 = 39 cm

Answer:

the answer is 23 cm

Step-by-step explanation: just a guess

The length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm. In a right triangle, the side opposite the right angle is the hypotenuse, while the other two sides are the legs.

Let's label the sides of the triangle ABC as follows:

BC is the hypotenuse, opposite to the right angle at B.

AB is a leg, adjacent to the angle A.

AC is a leg, opposite to the angle A.

Given that the area of the triangle is 32√3cm^2, we have:

(area) = (1/2) x (base) x (height)

Substituting the values we know, we get:

32√3 = (1/2) x AB x AC

Simplifying, we get:

AB x AC = 64√3

We also know that <A = 30 degrees, which means that <C = 60 degrees (since the angles in a triangle add up to 180 degrees).

Now we can use the trigonometric ratios to find the lengths of the sides. We have:

sin(30) = AC/BC

cos(30) = AB/BC

Solving for AC and AB, we get:

AC = BC x sin(30) = BC/2

AB = BC x cos(30) = BC√3/2

Substituting these values into the equation we got earlier, we get:

(BC/2) x (BC√3/2) = 64√3

Simplifying, we get:

BC^2 = 256

Taking the positive square root, we get:

BC = 16

Substituting this value into the equations we got for AB and AC, we get:

AB = BC√3/2 = 8√3

AC = BC/2 = 8

Therefore, the length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm.

The complete question is:

right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.​

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In conclusion √-36 can be simplified to 6i.

How to simplify and what does a square root mean?

The square root of a negative number is not a real number, as any real number squared gives a non-negative result. Therefore, the expression √-36 cannot be simplified in terms of real numbers.

However, in some mathematical contexts, we define the imaginary unit i as √-1. With this definition, we can write:

√-36 = √(36)√(-1) = 6i

Therefore, in this context, √-36 can be simplified to 6i.

In mathematics, the square root of a non-negative real number is a number that, when multiplied by itself, gives the original number. The square root is denoted by the symbol √.

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If the scooter travels 4.4km with the given radius, the wheel have number of revolutions about 1567 times.

In order to solve this issue, we must first determine the scooter wheel's circumference, which is given by the formula C = 2[tex]\pi[/tex]r, where r is radius of the wheel. Hence, the circumference of a wheel with a 14 cm radius would be:

C = 2[tex]\pi[/tex](14cm) = 28[tex]\pi[/tex] cm

We must translate the distance from kilometres to centimetres in order to determine how many revolutions the wheel completes if the scooter travels 4.4 kilometres. 1 km equals 100,000 cm, so 4.4 km is equal to 440,000 cm.

Now, we can calculate the number of rotations by dividing the distance travelled by the wheel's circumference:

Distance travelled divided by circumference equals the number of revolutions.

440,000 cm / 28 cm divided by the number of revolutions

1566.99 revolutions were made.

Therefore if the scooter travels 4.4km, the wheel will turn about 1567 times.

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Answer:

1

Step-by-step explanation:

5x + 1 / 4y²

5(3) + 1 / 4(2)²

15 + 1 / 4(4)

16 / 16 = 1

Step-by-step explanation:

8 ( 3 + 4 - 2)  =   8 x 3   + 8 x 4    -   8x 2       <  ===== distributive property