If f(x) =x - 5 and g(x) = 2x + 3, find values for each of the following.
a. f(g(1)) =
b. g(f (2)) =
c. g(g(0)) =
d. (f 0 9) (-2) =
e. (g o f) (3) =
f. (f o f) (-1) =

The 4 quadrants are called as Quadrant I, Quadrant II, Quadrant III and Quadrant IV.

The term quadrant in math is also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, are basically constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis and it creates a grid with four quadrants.

According to the cartesian system, here the coordinate plane is divided into four equal parts by the intersection of the x-axis and the y-axis such as the vertical number line.

Here the four quadrants are written as,

Quadrant I that is placed upon the upper right quadrant is the first quadrant, denoted as Quadrant I and the value on the x-axis and the y-axis both have positive numbers.

Next one is Quadrant II which is placed on the upper left quadrant is the second quadrant, denoted as Quadrant II and the value of the x-axis has negative numbers and the y-axis has positive numbers.

Third one is Quadrant III placed on the bottom left quadrant is the third quadrant, denoted as Quadrant III and the value of both the x-axis and the y-axis have negative numbers.

Final one is Quadrant IV which is placed on the bottom right quadrant is the fourth quadrant, denoted as Quadrant IV and here the value of the x-axis has positive numbers and the y-axis has negative numbers.

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A function A = 3000 e^(-0. 05t) is an exponential decay function.

And the landfill after 9 years =  1912.8 acres

From given information, the number of acres in a landfill is given by the function A = 3000 e^(-0. 05t), where t is measured in years.

To find:  the landfill after 9 years

Substitute t = 9 years in above function.

A = 3000 × e^(-0. 05t)

A = 3000 × e^(-0.05 × 9)

A = 3000 × e^(-0.45)

A = 3000 × 0.6376

A = 1912.8                 .............(1)

Substitute t = 9 years in given function.

A = 3000 e^(-0. 05t)

A = 3000 × e^(-0.05 × 0)

A = 3000 × e^(0)

A = 3000 × 1

A = 3000

This means, initially a landfill was 3000 acres.

From (1) we can observe that after 9 years, the landfill is  1912.8    acres.

A landfill has been reduced.

So, a function is exponential decay function.

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The least possible unit of the perimeter of the triangle will be 85 units.

In order for the three sides of a triangle to fit together, any two sides' differences must be bigger than the length of the third side.

Draw some triangles on a piece of paper and try to accept that this is the case.

So, by properties of triangle = 42 - 33 = 9

The third side must be greater than 9 units.

Given that it is an integer, 10 must be the minimum possible value.

The perimeter is the sum of all sides.

So our least possible perimeter will be 42 + 33 + 10 = 85 units.

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The value of x in the triangle WXY is 19 degrees

An equation shows how two or more numbers and variables are related to each other.

From the question, we have the following parameters that can be used in our computation:

The triangle XYZ and the line YZ such that lie YZ and XW are parallel lines

Using the above as a guide, we have the following:

∠ZYW = ∠XWY (alternate angles are equal)

∠XWY = 2x (Given)

So, we have

∠XWY + ∠XYW + ∠YXW = 180° (the sum of angles in a triangle)

Substitute the known values in the above equation, so, we have the following representation

2x + (3x - 5) + 90 = 180

Open the brackets and solve

5x - 5 = 90

Evaluate the like terms

5x = 95

Divide both sides by 5

x = 19°

Hence, the value of x is 19°

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The Sutton family's condo's worth in 8 years will be $216000.

An exponential function is a mathematical function in the form f(x) = aˣ, where {x} is a variable and {a} is a constant which is called the base.

Given is that Condos in Georgetown go up in value by 10% each year. Sutton family's condo's current worth is $120,000.

We can write the function to calculate the worth after {T} years as follows.

A{T, R} = A{i} {1 + RT}

A{T, R} = {120000} {1 + (10/100) x 8}

A{T, R} = {120000} {1 + 0.1 x 8}

A{T, R} = {120000} {1 + 0.8}

A{T, R} = {120000 x 1.8}

A{T, R} = 216000

Therefore, the Sutton family's condo's worth in 8 years will be $216000.

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The algebraic expression for the sequence 1, 10, 19, is given as a(n) = 1 + (n-1) 9.

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.

For the given sequence the common difference between two consecutive terms is 19 - 10 = 9.

The general form of the nth term of an arithmetic sequence is given as:

a(n) = a + (n-1) d

Since, the value of a = 1 and the common difference d =9, the resulting expression is:

a(n) = 1 + (n - 1) 9

Hence, the algebraic expression for the given sequence is a(n) = 1 + (n - 1) 9.

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Answer:

Using doubles plus one fact the sum of 7 + 7 is equal to 15 it is done by simply adding 1 to the given number.

Given :

Expression - 7 + 7

Doubles plus one fact is used to add numbers that are next to each other. for example, if a number given is 8 + 8 we have to evaluate it by using doubles one fact so 8 + 8 = 8 + 8 + 1 = 17.

The sum of 7 + 7 can be determined by using doubles plus one fact as:

Simply add 1 in 7 + 7 to get the result required.

Therefore by using doubles plus one fact the sum of 7 + 7 is equal to 15.

Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4

The perimeter, or total length, of a shape is referred to as its perimeter in geometry. A shape's perimeter is calculated by summing the lengths of all of its sides and edges. By adding together the lengths of all a shape's sides, one may determine its perimeter.  The circumference of a field, for instance, will be 78 yards for a rectangle with dimensions of 24 yards long by 15 yards wide.

Here,

Given :

Perimeter of rectangle = 84 feet

Thus,

Length is 6 times more than its 2 time width

=> 6L = 2W

=> W = 3L

In the perimeter formula:

=> 3L + 2L =84

=> 5L = 84

=>L = 84/5

=>16.8

and

W = 3L

=> W = 3*16.8

=> W = 50.4

Therefore , the solution of the given problem of perimeter comes out to be length = 16.8 and width = 50.4

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On solving the provided question, we can say that the spherical balloon's initial radius is 7 cm.; the final radius is 14 cm. ratio =  (7/14) ^2 = 1:4

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

The spherical balloon's initial radius is 7 cm.

The final radius is 14 cm.

ratio =

(7/14) ^2 = 1:4

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∠EFH and ∠ACD are angles of alternate exterior angles in the figure as  alternate external angles are those that are generated on the outer side of the parallel lines .

When two straight lines connect at a 90° angle or are perpendicular to one another, an angle is formed. The symbol denotes a right angle. In the picture up above, many right angle formations are visible. Shapes include the correct angles. Triangles classified as right triangles have one of their internal angles at a 90 degree right angle. The three interior angles of a triangle add up to 180 degrees, so the three interior angles of a right triangle must always add up to 90 degrees because one of them is always 90 degrees.

given

The pair of angles known as alternate external angles are those that are generated on the outer side of the parallel lines but on the transverse side.

sum up to 180 degrees, you can calculate the size of the inner angle adjacent to it if you know the size of the outer angle (since together they are the angle on a straight line). The internal angles at the other two vertices are added to create the outer angle of a triangle.

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Answer:

5x-7-5+X=5-x-5+X

or,6x-12=0

or,6x=12

or,X=12/6

:.X=2

Answer:

1)  23x + 6y

2) 8x  - 4y

3)  4x - x² + 7

Step-by-step explanation:

Simplify:

Multiply each term of (3x + 6y) by 5 and multiply each term of (2x - 6y) by 4.

5(3x + 6y) + 4 (2x - 6y)  = 5*3x + 5*6y + 4*2x - 4*6y

                                       = 15x + 30y + 8x - 24y

Now, combine like terms. Like terms have same variable with same power.

                                         = 15x + 8x + 30y - 24y

                                           = 23x + 6y

2) 3(4x - 2y) - 2*(2x -y) = 3*4x + 3*(-2y) + (-2)* 2x + (-2)*(-y)

                                     = 12x - 6y - 4x + 2y

                                     = 12x - 4x - 6y + 2y

                                    =  8x - 4y

3) f(x) = 3x + 2

To find f(x +1),  replace x with (x +1)

f(x +1) = 3*(x + 1) + 2

          = 3*x + 3*1 + 2

          = 3x + 3 + 2

          =3x + 5

f(2x) = 3*(2x) + 2

        = 6x + 2

f(2x) + h(x) = 6x + 2 - x² - 2x + 5

                 = 6x - 2x - x² +2 + 5

                 = 4x - x² + 7

Answer:

2b - 1

Step-by-step explanation:

To solve this problem, we will need to open the parentheses. To do this, we will put an imaginary 1 in front of both sets of parentheses to open them using the distributive property, this gives us:

1(6b + 2) - 1(4b + 3)

We will open the first set of parentheses with no problem, but in the second set, we have -1, so we need to make every positive number negative and every negative number positive, giving us:

6b + 2 - 4b - 3

Then, we group our like terms:

6b - 4b + 2 - 3

Then, we subtract, giving us:

2b - 1

So the most simplified version is 2b - 1.

Hope this helped!

Answer:

Step-by-step explanation:

You begin by distributing the negative so -4b -3

then you will multiply (6b+2) by (-4b -3)

24b^2 - 18b - 8b - 6

answer = 24b^2 - 26b - 6

It looks like there may be a typo in the function you provided. It appears that you meant to write "f(x) = 80(0.5)^x", which would represent the distance after a pendulum begins swinging, where x is the number of swings.

This function indicates that the distance traveled by the pendulum decreases by half with each swing. For example, after the first swing, the distance traveled would be 80(0.5)^1 = 40 units. After the second swing, the distance traveled would be 80(0.5)^2 = 20 units. And so on.

The exponent x in the function represents the number of swings, so the distance traveled by the pendulum can be calculated by plugging in the desired value of x into the function. For example, to calculate the distance traveled after 10 swings, we can plug in x = 10:

f(10) = 80(0.5)^10 = 0.390625 units

This indicates that the pendulum has traveled a distance of approximately 0.39 units after 10 swings.

Answer:

11

Step-by-step explanation:

remember that the absolute value function always gives a positive value, that is

| - a | = | a | = a

substitute the given values into the expression

- a² - 2bc - | c |

= - (- 2)² - 2(3)(- 3) - | - 3 |

= - (4) - 2(- 9) - | 3 |

= - 4 + 18 - 3

= 14 - 3

= 11

No, 1 gram is not equal to 1 mole. The numerical values of mole and gram are different for an object.

What is 1 gram?

Avogadro number of atoms makes up one mole. It is possible to convert a mole into grams if you know the mole quantity.

Mole: The International System of Units uses the mole (symbol: mol) as the unit of material quantity. How many elementary entities of a particular substance are present in an object or sample is determined by the quantity of that material. It is specified that the mole contains exactly 6.02214076×10²³ elementary entities.

The relation between  gram  and mole is

1 gram = Mole × atomic weight.

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Answer:

48 units.

Step-by-step explanation:

Since the triangles are similar (proportional), their dimensions are increased at the same ratio at any point, which means their perimeter too. So the base of the larger triangle is twice as long as the base of the smaller triangle.

The perimeter of the smaller triangle is 10 + 6 + 8 = 24 units.

24 * 2 = 48. Because the ratio of increase is 2:1 from the bigger triangle to the smaller triangle.

Hope you could understand this,

Answer:

Yes

Step-by-step explanation:

there are 16 cups in a gallon. if he uses 1/2 a cup to make 1 pitcher, there would be 32 pitchers made. 19+9 is 28 so the answer is yes.

^^mark brainliest pls:D

If Punit had 12 tomatoes. He cut each into 6 lice. He used 4 lice of the 16 sandwiches he made then 68 slices were remaining.

There were 12 tomatoes and each was cut into 6 slices, giving a total of 72 slices. Here we have to multiply 6 with 12

12×6=72

Of these, 4 slices were used to make sandwiches, leaving 68 slices remaining. Here we have to subtract 4 from 72

72-4=68

Therefore, Punit had 68 slices left, or 11.33 tomatoes, after making the sandwiches. This means that Punit had 68 lice of tomato remaining after making the sandwiches.

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C). The highest amount their liability coverage will provide is  $400,000

This is because most standard liability policies will provide up to $300,000 for bodily injury and $100,000 for property damage, but the policyholder may be able to purchase additional coverage for higher limits if they need it. The exact amount of coverage will depend on the policy the policyholder purchased.

Liability insurance is a component of the general insurance system of risk financing that protects the purchaser from the risks of liabilities imposed by lawsuits and similar claims, as well as the insured if the purchaser is sued for claims covered by the insurance policy.

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Answer: In this exercise we have to calculate the values ​​of the people who voted to expand the parking lot, so we have to:

Yes: parents will be 150 and not parents 40

No; parents will be 40 and not parents 30

As it is about sets, we have to use the data that were:

   total: 250 adults

   180 of whom were parents a park should be expanded.

   40 of the adults who were not parents thought the park should be expanded.

then calculate that:

Step-by-step explanation:

The surveyed parents favor park extension, and two way table is a way or representation of data. and The two-way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

The two-way table shown in the table is attached below.

What is two way table?

Two-way table is a way of representing of data to better understand it.

Given information-

The total number of adults took the survey is 250.

Total number of parents took the survey is 180.

150 of the adults with children and 40 of those without thought the park should be expanded.

Suppose the number of adults who are not the parents and took the survey is .

As the total number of adults took the survey is 250 in which the number of parents took the survey is 180. Thus the number of adults who are not the parents and took the survey is,

Suppose the parents who does not thing that the park should be expanded is .

There is total 180 parents. As 150 of the adults with children thought the park should be expanded. Thus, the parents who does not thing that the park should be expanded is,

Form the 70 adults who are not parents things that park should be expanded is 40, hence the adults who are not parents does not thing the park should be expanded is (70-40) which is 30.

Hence the two way table is completed as,

                        yes      no

parents              150  |    30

                                 |

not parents        40   |      30

the two way

YES                    NO

                          30  

                          30

(parents 150

not parents_40

The total number of coins Piper has in her collection is 100 coins.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Piper has a coin collection. She keeps 12 of the coins in her box, which is 2% of the collection.

Let, The total number f coins in the box be 'x'.

Therefore, 2% of 'x' is 12 which can be numerically expressed as,

(2/100)×x = 12.

0.02x = 12.

x = 2/0.02.

x = 100.

So, She has 100 coins in her box.

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$164.86 more is needed to reach the goal of $1,200.00.

First, we need to find out how much money Mrs LeBlanc's class has raised since they have raised 50% of the total needed. We can do this by multiplying the total needed by 50%:

$1,200.00 * 50% = $600.00

Next, we need to find out how much money Ms Warner's class has raised since they have raised one-third as much as Mrs LeBlanc's class. We can do this by multiplying the amount raised by Mrs LeBlanc's class by one-third:

$600.00 * 1/3 = $200.00

Now we can add up the amount raised by all three classes to see how much has been raised in total:

$600.00 (Mrs. LeBlanc's class) + $235.14 (Mr. Patel's class) + $200.00 (Ms. Warner's class) = $1035.14

Finally, we can subtract the total amount raised from the goal amount to find out how much more is needed:

$1,200.00 - $1,035.14 = $164.86

So $164.86 more is needed to reach the goal of $1,200.00.

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The width of the frame is 8 inches.

Now, According to the question:

The length of a rectangular frame is 15 inches

The diagonal length of the frame is 17 inches.

To find the width of the frame in inches.

Let's take the width of the frame is = w

Based on the information given, it should be noted that the diagonal will be the longest side. Therefore, we'll use the Pythagoras theorem to solve the question.

This will be:

17² = 15² + w²

289 = 225 + w²

289 - 225 =  w²

64 =  w²

w = [tex]\sqrt{64}[/tex]

w = 8

Hence, The width of the frame is 8 inches.

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The independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

In this scenario, the amount of Neil's bonus (B) is dependent on the number of hours he works (h). The number of hours he works is the input or independent variable, while the amount of bonus he receives is the output or dependent variable. It can be said that the number of hours he works is the cause and the amount of bonus is the effect.

The equation is B = f(h) where f is the function that relates the two variables.

Thus, the independent variable is h (the number of hours Neil works) and the dependent variable is B (the amount of Neil's bonus).

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Complete Question is-

Neil works as a consultant at a software company and the amount of his annual bonus is based on the number of hours he works, which variable is independent and which is dependent? With B as the amount of Neil's bonus, and h as the number of hours Neil works.

This is a symbol in mathematics that represents "to the power of" or "exponent".

It is used to indicate that a number or expression is being multiplied by itself a certain number of times. For example, if the expression 2aˆ3 is written, it means that 2 is being multiplied by itself 3 times, or 2x2x2. In other words, 2aˆ3 = 2x2x2 = 8.

The number to the right of the aˆ symbol is called the "exponent". The number or expression to the left of the aˆ symbol is called the "base". When a number is raised to the power of one, it is equal to itself. Any number to the power of zero is equal to one. The exponent can be a positive, negative, or fractional number.

Exponents are used to simplifying calculations and can be used to represent large numbers in a more concise form.

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The initial amount of the investment is $800, the investment grows at the rate of 10% each year, and the value of the investment after 12 years is $1760.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates from the graph.

(0, 800), (1, 880), (2, 968)

x-coordinate is the number of years and the y-coordinate denotes the Value.

Now,

The initial amount of the investment is when x = 0.

= 800

Now,

Rate of change of the value each year.

=(880 - 800) / (1 - 0)

= $80

Rate of percentage.

= 80/800 x 100

= 10%

Now,

The value of the investment after 12 years.

= 800 + 12 x 80

= 800 + 960

= $1760

Thus,

The initial amount of the investment is $800.

The investment grows at the rate of 10% each year.

The value of the investment after 12 years is $1760.

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A statement which best describes the solution set of the given inequality 5n + 1.5 ≥ 4 is: C. all rational number values of n that are at least 0.5.

In Mathematics, a rational number can be defined a type of number which comprises fractions, integers, terminating or repeating decimals such as the 12, 0.5, √16, etc.

Next, we would translate the word problem into algebraic inequality and then solve for the value of n as follows;

5n + 1.5 ≥ 4

Subtracting 1.5 from both sides of the algebraic inequality, we have:

5n + 1.5 - 1.5 ≥ 4 - 1.5

5n ≥ 2.5

Dividing both sides of the algebraic inequality y 5, we have:

n ≥ 2.5/5

n ≥ 0.5

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Complete Question:

Grant reads as part of his homework each week. he must read for at least 4 hours each week as part of his homework. This past weekend, he reads for 1.5 hours. Grant makes a graph of the inequality 5n +1.5 greater than or equal to 4 to determine all the numbers, n, of hours he could read on each of the 5 weekdays this week. The graph is shown.

Which describes the solution set of the inequality?

A. all whole number values of n that are at least 1

B. all whole number values of n that are greater than 1

C. all rational number values of n that are at least 0.5

D. all rational number values of n that are greater than 0.5