if f(x)=x/2-3 and g(x)=3x²+x-6 find (f+g)(x)

Answer:

Every book is 8 dollars but you have to subtract 10, so like this:

Step-by-step explanation:

p(x) = 8x - 10 Lets say you sell 2 books

p(2) = 8(2) - 10

p(2) = 16 - 10

p(2) = 6  You would make 6 dollars.

The value of x from the expression is 2.083

Given the equation expressed as:

Subtract 14,8 from both sides

32.3 - 14.8 = 14.8 - 14.8 + 8.4x

17.5 = 8.4x

x = 17.5/8.4

x = 2.083

Hence the value of x from the expression is 2.083

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Answer:

Solve.

32.3 = 14.8 + 8.4x

Enter your answer as a mixed number in simplest form in the box.

x = 2 1/12

Correct answers:

Step-by-step explanation:

Answer:

Graphing Polynomial Functions

Find the intercepts, if possible.

Check for symmetry. ...

Use the multiplicities of the zeros to determine the behavior of the polynomial at the x-intercepts.

Determine the end behavior by examining the leading term.

Use the end behavior and the behavior at the intercepts to sketch a graph.

The inequality is used to find the domain of the given function is

5x-5 ≥ 0

A function is a relation from a set of inputs to a set of possible outputs, where each input is related to exactly one output.

Given is function y = √(5x-5)+1, we have to find which inequality can be used to find the domain.

Since, the function is a square root function.

We know that,

The square root function is defined only for the positive values, including 0. i.e. the expression inside the square root must be greater than or equal to 0.

The expression inside the square root is (5x-5) so that must be greater than or equal to 0 which can be written as :

5x-5 ≥ 0

Hence, the inequality is used to find the domain of the given function is 5x-5 ≥ 0

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Answer: 3

Distribute

Subtract the numbers

Simplify

Answer:

8.05 cups per loaf

Step-by-step explanation:

divide 64.4 and 8

equation

64.4÷8=8.05

The different coordinates after respective rotation are:

1) A'(2, 0)

2) A'(0, -2)

3) A'(-2, 0)

There are different methods of transformation such as:

Translation

Rotation

Dilation

Reflection

Now, the coordinate of the given point A is: A(0, 2)

1) The rule for rotation of 90 degrees clockwise is:

(x, y) →(y,-x)

Thus, we have:

A'(2, 0)

2) The rule for rotation of 180 degrees is:

(x, y) → (-x,-y)

Thus, we have:

A'(0, -2)

3) The rule for rotation of 180 degrees is:

(x, y) → (-y,x)

Thus, we have:

A'(-2, 0)

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(a) The production cost per item can be calculated by dividing the total cost of producing 25 items ($8,750) by the number of items (25). Therefore, the production cost per item is $350 ($8,750 / 25).

(b) The company's linear profit function, p(x), can be expressed in the slope-intercept form, y = mx + b. In this case, the slope (m) is the change in profit (9,000 - 10,250 = -1,250) divided by the change in the number of items (75 - 55 = 20). Therefore, m = -62.5. The y-intercept (b) is the total revenue from selling 75 items ($9,000). Therefore, the linear profit function is: p(x) = -62.5x + 9,000.

The linear profit function suggests that the company's profit decreases by $62.50 for every additional item produced and sold. In other words, the company makes a profit of $9,000 when they produce and sell 75 items, but if they produce and sell 76 items, their profit reduces by $62.50. The equation also suggests that the company will not make any profit (in fact, they will make a loss) when they produce and sell more than 158 items.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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The required proportion for the given case is 36/100 = x/150.

A percentage is a value that indicates 100th part of any quantity.

A percentage can be converted into a fraction or a decimal by dividing it by 100.

The given statement is as below,

36% of 150

Suppose the required number is x.

Then, the equivalent form of the given statement is,

36% of 150 = x

=> 36% × 150 = x

=> 36/100 × 150 = x

=> 36/100 = x/150

Hence, the required proportion to to be used to solve the problem is 36/100 = x/150.

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The revised Doubtful Debts Provision should be, $4,555.

Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):

Net Debts x Provision Rate equals Adjusted PDD.

The computation would then be:

= $91,100 x 0.05

= $4,555 is the adjusted PDD.

Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,

= $4,555 - $3,500

= $1,055

Hence, The revised Doubtful Debts Provision should be $4,555.

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9514 1404 393

Answer:

  22/21

Step-by-step explanation:

Taking the derivative, we have ...

  2x·dx +2y²·dx +4xy·dy +3·dy = 0

  dx(2x +2y²) +dy(4xy+3) = 0

At the given point, this is ...

  dx(2·2 +2·(-3)²) +dy(4·2·(-3) +3) = 0

  22dx -21dy = 0

  dy/dx = 22/21

The slope of the tangent at the point of interest is 22/21.

The value of dy/dx is -cotθ, d^2y/dx^2 is -6cosec³θ, slope is -cotθ, concavity is -6cosec³θ.

Parametric Equations Point x = 6cosθ, y = 6sinθ and θ = π/4

We have to determine the value of dy/dx.

We can define dy/dx as;

dy/dx = (dy/dθ)/(dx/dθ)

We first define dy/dθ and dx/dθ.

x = 6cosθ                             y = 6sinθ

dx/dθ = -6sinθ                     dy/dθ = 6cosθ

Now put the value

dy/dx = 6cosθ/(-6sinθ)

dy/dx = -cotθ

Now we have to determine the value of d²y/dx².

d²y/dx² = d/dx(dy/dx)

We can write it as

d²y/dx² = \(\frac{\frac{d}{d\theta}(\frac{dy}{dx})}{dx/d\theta}\)

We first determine the value of d/dθ(dy/dx)

d/dθ(dy/dx) = d/dθ(-cotθ)

d/dθ(dy/dx) = cosec²θ

Now put the value

d²y/dx² = cosec²θ/(-6sinθ)

d²y/dx² = -6cosec³θ

Now we have to determine the slope.

Slope = dy/dx

Slope = -cotθ

Now we have to determine the concavity.

Concavity = d²y/dx²

Concavity = -6cosec³θ

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The composite mapping (f o g)(x) ≥ 3 for the functions f(x) = 2x + 1 and g(x) = x² + 1. And (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

A mapping is composite when the co- domain of the first mapping is the domain of the second mapping.

For the functions f(x) = 2x + 1 and g(x) = x² + 1

If x > 0, say x = 1 then;

g(x) = 1² + 1

g(x) = 2

(f o g)(x) = 2(2) + 1

(f o g)(x) = 4 + 1

(f o g)(x) = 5

If x = 0, then;

g(x) = 0² + 1

g(x) = 1

(f o g)(x) = 2(1) + 1

(f o g)(x) = 2 + 1

(f o g)(x) = 3

For the functions f(x) = x² and g(x) = x

If x < 0, say x = -0.5, then;

g(x) = -0.5

(f o g)(x) = (-0.5)²

(f o g)(x) = 0.25

In conclusion, the composite mapping (f o g)(x) ≥ 3 for functions f(x) = 2x + 1 and g(x) = x² + 1 and (f o g)(x) > 0 for the functions f(x) = x² and g(x) = x.

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Option (b) is the correct answer: Perpendicular segments.

Perpendicular rays, perpendicular segments, perpendicular lines, and parallel lines are important concepts in geometry that describe the relationship between lines and line segments.

1. Perpendicular Rays: Perpendicular rays are two rays that intersect at point and form a right angle (90 degrees) at the point of intersection. The rays extend indefinitely in opposite directions from the point of intersection.

2. Perpendicular Segments: Perpendicular segments are line segments that intersect at a right angle. They share a common endpoint but do not extend indefinitely like rays. The right angle is formed at the point of intersection.

3. Perpendicular Lines: Perpendicular lines are lines that intersect at a right angle. They continue indefinitely in opposite directions and form four right angles at the point of intersection. Perpendicular lines are often denoted by a symbol ⊥.

4. Parallel Lines: Parallel lines are lines that never intersect. They remain equidistant from each other at all points. Parallel lines have the same slope and do not converge or diverge. In Euclidean geometry, parallel lines are denoted by a double vertical line symbol (||).

Understanding these concepts is fundamental in geometry as they help define angles, shapes, and spatial relationships. The properties of perpendicular and parallel lines play a crucial role in various geometric theorems and applications.

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The area of the complex figure is 132 square units

From the information given, we have that the composite shape is a combination of a:

The formula for area of a square is given as:

Area = a ²

Where 'a' is the length of it side

Area = 6²

Area of square = 36 square units

The formula for area of a rectangle is given as:

Area = width × length

Area = 8 × 12

Area of rectangle = 96 square units

Area of the complex figure = Area of square + area of rectangle

= 36 + 96

= 132 square units

Thus, the area of the complex figure is 132 square units

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The graph of option B is the graph of y=sin(0.5x).

The formula to find the period of the graph of sin(bx) is \(P=\dfrac{2\pi}{b}\)

Use the formula \(P=\dfrac{2\pi}{b}\) in order to find the graph of y=sin(0.5x) where we will substitute b=0.5.

We will get,

\(P=\dfrac{2\pi}{0.5}\\P=\dfrac{20\pi}{5}\\\\P=4\pi\)

Here the period of the graph y=sin(0.5x) is \(4\pi\\\).

So, the graph of option B is the graph of y=sin(0.5x) as it has the period of \(4\pi\\\).

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Answer:

D on edge 2023

Step-by-step explanation:

The domain and range for the function shown in the graph above include the following:

D. D: [-∞, ∞]

    R: [-10, ∞]

In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.

In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = [-∞, ∞] or all real numbers.

Range = [-10, ∞] or y ≥ -10

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Answer:

12 3/4, 12.7, 12 3/5

Step-by-step explanation:

12 3/5 = 12.60

12 3/4 = 12.75

Denis's and Dasha's methods use different operations to simplify the expressions in different orders.

Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.

Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.

Denis's Assignment

2* 6+2w-54

12+2w = 54

12-12+2w= 54-12

2w=42

w= 21  

Dasha's Assignment

54-2* 6

54-12= 42

The two widths add to 42 cm

42/ 2-21

We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.

She subtracts the product of 2 and 6 from 54.

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Answer:

49 prizes each, with 5 left

Step-by-step explanation:

985/20 is 49 with 5 left over.

The producer's surplus is 258.84.

Producer's surplus is a measure of the profit earned by a producer in a market. It is calculated as the difference between the price at which a producer is willing to supply a good and the actual market price. The formula for producer's surplus is PS = (P_e - MC) × Q_e, where P_e is the equilibrium price, MC is the marginal cost, and Q_e is the equilibrium quantity.

In this problem, the supply function is given by S(x) = √x+5, where x is the quantity of the item produced. The equilibrium point (x_e, P_e) is given as (40, 6.71). To find the producer's surplus, we need to first find the marginal cost.

The marginal cost is the additional cost incurred by producing one more unit of the good. In this case, it is the derivative of the supply function with respect to x, which is MC = S'(x) = 1/(2√x+5). Substituting x = 40, we get MC = 0.0905.

Now, substituting the values of P_e, Q_e, and MC in the formula for producer's surplus, we get PS = (6.71 - 0.0905 × 40) × 40 = 258.84. Therefore, the producer's surplus is 258.84.

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After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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Answer:

y=2x+6

Step-by-step explanation:

Answer:

1/5x

Step-by-step explanation:

1/5x

Answer: 3/20

Step-by-step explanation:

p(A)=the day selected in Monday =1/5

p(B)=student is absent

P(A∩B)=it is Monday AND a student is absent =3/100

Events A and B are independent so

P(A∩B) = P(A) · P(B)

3/100=1/5*p(B)

p(B)=3/20

Answer:

the opposite of the fraction is 3/8

Answer:

y

a= ——

(r + 1 )t

Step-by-step explanation:

divide both sides