Solve the following inequality.
-8 < 3x+1 <7

Value of composite functions (g-f)(x)  and (f/g)(x) are x² - 2x - 8 and

(x+1)/(2x - 3) respectively.both of these functions don't have the same

domain and range.

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given functions,

f(x) = x² - 3x - 4

g(x) = 2x² - 5x - 12

1. (g - f)(x)

= g(x) - f(x)

= 2x² - 5x - 12 - (x² - 3x - 4)

= 2x² - 5x - 12 - x² + 3x + 4)

= x² - 2x - 8

x is defined for all real numbers

Domain = (-∞, ∞)

let y = x² - 2x - 8

x = √y + 2(x) - 8

Function is defined for y ≥ 9

Range is {y∈R , y ≥ 9}

2. (f/g)(x)

= f(x)/g(x)

= (x² - 3x - 4)/(2x² - 5x - 12)

= (x² - 4x + x - 4)/(2x² - 8x + 3x - 12)

= (x(x - 4) + 1(x - 4))/(2x(x - 4) + 3 (x - 4))

= (x+1)(x-4)/(2x+3)(x-4)

= (x+1)/(2x - 3)

function is defined for x ≠ 3/2, Domain is {x ∈ R : x ≠ 3/2}

Let y = (x+1)/(2x - 3)

y.2x - 3y = x + 1

-3y - 1 = x - 2xy

x = (-1 - 3y)/(1 - 2y)

function is defined for y ≠ 1/2, Range is {y ∈ R : y ≠ 1/2}

Domain and range are not same for both functions.

Hence,  Value of composite functions (g-f)(x) = x² - 2x - 8 and

(f/g)(x) = (x+1)/(2x - 3), Domain and range is not same for both functions.

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The number of possible outcomes are 8 if we have 4 spinners labeled Red, Blue, Yellow and green by using permutations.

The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.

There are 4 spinners: Red, Blue, green  and yellow.

Here Number of possible outcomes will be calculated by using permutation.

So, we get that:

Number of possible outcomes = 4 × 2

Number of possible outcomes = 8 ways.

Therefore, the number of possible outcomes are 8 if we have 3 spinners.

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The factorization of the given polynomial is 10x²(x+1).

The factors are the polynomials which are multiplied to produce the original polynomial.

The given polynomial is 10x³+10x².

Here, factors of the terms 10x³ and 10x² are

10x³= 2×5×x×x×x

10x²= 2×5×x×x

GCF of the terms is 2×5×x×x=10x²

10x²(x+1)

Therefore, the factorization is 10x²(x+1).

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The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The volume of each packet is given as,

v = 16 x 9 x 4

v = 576 cubic cm

The volume of the cubical box is given as,

V = (1.2 x 100) x (1.2 x 100) x (1.2 x 100)

V = 120 x 120 x 120

V = 1,728,000 cubic cm

Then the number of packets is given as,

n = V / v

n = 1,728,000 / 576

n = 3,000

The number of packets of dimensions 16 cm by 9 cm by 4 cm in a cubical box will be 3,000.

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Answer:

1:8

Step-by-step explanation:

since the base and sides are equal, I'll use 2 as a value for them. since all square sides are equal, we can find the area of the square. 2(2)=4. this means that in the situation the area of the triangle is 16.

16=1/2(2)h

32=2h

16=h

the height of the triangle is 16, while the side of the square is 2. the ratio is 2:16, or 1:8

Answer:

4/49

Step-by-step explanation:

1 week : 5 working days

5*$4= $20

20/245= 4/49

To create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Yaseen can produce 15 kits, the cost per kit she should charge is

p = 10 + 0.5q

p = 10 + 0.5(15) (15)

p = $17.50

She can produce 15 kits, the cost per kit she should charge is:

p = 30 - 0.5(15) (15)

p = $22.50

She can provide 60 kits, the cost per kit should be as follows:

p = 10 + 0.5q

Here, q=60

p = 10 + 0.5(60)

p = $40

She can produce 60 kits, the cost per kit should be set at:

p = 30 - 0.5(60) (60)

p = $15

Therefore, to create 15 kits, Yaseen charge for each of these kits based on her supply function is $17.50.

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Answer:

To add different quantities of liquids with different units of measurements, we need to convert them all to the same unit of measurement. In this case, let's convert everything to quarts since that is what we want the final answer to be in.

2 gallons = 8 quarts (since 1 gallon = 4 quarts)

5 quarts of pineapple juice = 5 quarts (no conversion needed)

4 pints of cranberry juice = 8 cups = 2 quarts (since 1 pint = 2 cups and 1 quart = 4 cups)

6 cups of apple juice = 1.5 quarts (since 1 cup = 0.25 quarts)

Now we can add up all the quantities:

2 + 5 + 2 + 1.5 = 10.5

Maya made 10.5 quarts of fruit punch in all

thus, a = -39 is the solution to the equation -a = 4b-7 when (a, -8) is a solution

An equation is a fine statement that asserts the equivalency of two expressions. It generally consists of two sides, with an equal sign between them. Equations are used to describe connections between variables, and to break problems in colorful fields, including mathematics, wisdom, engineering, and economics.

Given by the question.

the equation given is -a = 4b - 7.

We are also told that (a, -8) is a solution to this equation. This means that if we substitute a for x and -8 for y, the equation will be true.

Substituting the given values, we get:

a = 4b - 7 (Given equation)

a = 4(-8) - 7 (Substituting b = -8, since (a, -8) is a solution)

a = -32 - 7 (Simplifying)

a = -39 (Final answer)

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So, if you only have $125 to spend, you may go around 90.91 miles in the van.

An equation in mathematics is a statement that two mathematical expressions are equal. Equations are used to represent mathematical relationships and to describe the behavior of systems or processes. An equation typically consists of two sides, separated by an equal sign (=). On one side of the equal sign is the expression representing what is known or given, and on the other side is the expression representing what is being found or sought. Equations can be used to model real-world situations, to describe the behavior of mathematical functions, to solve problems, and to make predictions. They are an important tool in many areas of mathematics and science, including algebra, calculus, physics, and engineering.

Here,

Let's call the number of miles you want to travel "m". The total cost of the rental is given by the expression 75 + 0.55m. We know that this total cost must be less than or equal to $125, so we can write the inequality:

75 + 0.55m ≤ 125

We can isolate the variable m by subtracting 75 from both sides of the inequality:

0.55m ≤ 125 - 75

0.55m ≤ 50

Finally, we can solve for m by dividing both sides of the inequality by 0.55:

m ≤ 50 / 0.55

m ≤ 90.91

So, if you have a maximum of $125 to spend, you can travel a maximum of approximately 90.91 miles in the van.

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In the given diagram, the measure of arc DE, mDE, is 90°

From the question, we are to find the measure of the given arc.

The angle measure of an arc is the angle subtended by the arc at the center of the circle.  

From the given diagram, we are to determine the measure of arc DE.

In the given diagram, we can observe that the angle subtended by arc DE is a right angle. That is, the measure of arc DE is a right angle.

The measure of a right angle is 90°.

Hence, the measure of arc DE is 90°

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The accepted method for representing both integer and non-integer numbers is the decimal numeral system.

It is the expansion of the Hindu-Arabic numeral system to non-integer values. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A decimal between decimals is a decimal number that lies between two other decimal numbers.

For example, if you have two decimal numbers 0.2 and 0.3, a decimal between them would be any number that is greater than 0.2 and less than 0.3.

Some examples of decimals between 0.2 and 0.3 include 0.25, 0.26, 0.27, and so on.

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The question when translated in English is, "What is a decimal between decimals?"

Answer: x = -7

explanation:

2(x+4)= -6

2x+8= -6

-8 -8

2x -14

Divide both sides by 2

X = -7

Answer:x=-7 I hope this helps

Step-by-step explanation:

2(x+4)=-6

Divide both sides of the equation by 2

X+4=-3

Move the constant to the right-hand side and change its sign

X=-3-4

Calculate the difference which means subtract-3 minus 4 which give you -7

X=-7

And that how you solve for X

We can use the Pythagorean theorem to find the length of the short cut up the flight of stairs. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's call the length of the short cut "x". Then, we can set up the following equation:

x^2 = 60^2 + 80^2

Expanding the squares:

x^2 = 3600 + 6400

x^2 = 10000

Taking the square root of both sides:

x = sqrt(10000)

x = 100

So, the length of the short cut up the flight of stairs is 100 meters.

The sum of all the angles of triangle is 180°

We have the following angles:

The sum of all these angles will be equal to 180°

[tex] \sf \: 70 + 90 + 2x + 6 = 180[/tex]

[tex] \sf166 + 2x = 180[/tex]

[tex] \sf2x = 180 - 166[/tex]

[tex] \sf2x = 14[/tex]

[tex] \sf2x \div 2 = 14 \div 2[/tex]

[tex] \boxed{ \tt \: x = 7}[/tex]

The given angle is 2x+6, So put the value of x in this and find the value of angle

Answer:

m∠6 = 142°

m∠7 = 38°

Step-by-step explanation:

You will be using postulates and theorems to solve this question.

Two parallel lines are cut by a transversal          (Given)

- m∠1 = 38°                         (Given)

- m∠1 ≅ m∠3                      (Vertical Angles Theorem)

  ∴ m∠3 = 38° (Definition of Vertical Angles Theorem)

- m∠3 ≅ m∠5                     (Alternate Angles Theorem)

 m∠3 = 38° ∴ m∠5 = 38° (Definition of Alternate Angles Theorem)

- m∠5 ≅ m∠7                     (Vertical Angles Theorem)

 m∠5 = 38° ∴ m∠7 = 38° (Definition of Alternate Angles Theorem)

m∠7 + m∠6 = 180°            (Corresponding Angles Postulate)

m∠7 = 38°                          (Given above)

Plug in 38 for m∠7 and solve for m∠6:

(38) + m∠6 = 180

Isolate m∠6. Note the equal sign, what you do to one side, you do to the other. Subtract 38 from both sides of the equation:

m∠6 + 38 = 180

m∠6 + 38 (-38) = 180 (-38)

m∠6 = 180 - 38

m∠6 = 142°

-

Answers:

m∠6 = 142°

m∠7 = 38°

~

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Answer: PLEASE GIVE BRAINLIEST

B) 55h + 65

Step-by-step explanation:

The correct expression is B) 55h + 65, which models the situation as $55 per hour of work (h) plus a $65 service call fee.

Answer: la response est 1,235 je pense

Step-by-step explanation: trois decimal veux dire trois chiffre après la virgule donc on decale la virgule de 3 vers la gauche

The balance amount when compounded daily at a rate of 4.075% after 6 months is  $269,320.60.

What is meant by compound interest?

The interest you earn on interest is known as compound interest. Compound interest, also known as interest on principal & interest, is the practice of adding interest to the principal amount of a loan or deposit. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this. If we examine our bank statements, we will typically see that our account is credited with interest on a yearly basis. Even while the principal remains the same, the interest changes annually. We can observe that interest rises over time. Thus, we can infer that the interest the bank charges is compound interest rather than simple interest.

Given,

Principal amount P = $263,000

Rate of interest r = 4.075%

Time period t = 6 months = 0.5 years

Final amount =  [tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

where n = 365

A = [tex]P(1 + \frac{r}{n})^{nt} =263000(1 + \frac{0.04075}{365})^{365*0.5}[/tex]  = $269,320.60

Therefore the balance amount when compounded daily at a rate of 4.075% is  $269,320.60.

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It will take Thoriso 30 minutes to walk to school.

what is speed ?

Speed is a measure of how quickly an object is moving. It is defined as the distance traveled by an object in a given amount of time. The formula for speed is:

Speed = distance / time

The unit of speed depends on the units of distance and time used. Common units of speed include meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph).

Given by the question:
We can use the formula:

time = distance / speed

to calculate the time it will take Thoriso to walk to school.

Let d be the distance from Thoriso's home to school. Since the distance is the same whether she walks or rides her bicycle, we have:

distance walked = distance biked = d

Let's first calculate how long it takes Thoriso to bike to school:

time biked = distance biked / biking speed

time biked = d / 15 km/h

We are given that it takes her 10 minutes (0.167 hours) to bike to school, so we can set up the following equation:

0.167 hours = d / 15 km/h

Solving for d, we get:

d = 2.5 km

Now, we can calculate how long it will take Thoriso to walk to school:

time walked = distance walked / walking speed

time walked = d / 5 km/h

time walked = 2.5 km / 5 km/h

time walked = 0.5 hours or 30 minutes

Therefore, it will take Thoriso 30 minutes to walk to school.

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4v + (9 x 7)= 4v +56

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

ii

350x + 200y - 4200 = 0

Therefore, the equation in standard form that models the number of funnel cakes, x, and the number of deep-fried Oreos, y, Francis can buy if he spends $42.00 is:

350x + 200y - 4200 = 0

To find the x-intercept, we set y to zero and solve for x:

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

Therefore, the x-intercept is 12. This means that if Francis only buys deep-fried Oreos (y = 0), he can buy 12 funnel cakes with $42.00.

Answer:

350x + 200y - 4200 = 0

x intercept is (12,0)

y intercept (0,21)

steps:

3.50x + 2.00y = 42.00

3.50x + 2.00y - 42.00 = 0

Multiplying both sides by 100 to eliminate the decimals, we get:

350x + 200y - 4200 = 0

x-intercept means what is x when y is 0

350x + 200(0) - 4200 = 0

350x = 4200

x = 12

y-intercept means what is y when x is 0

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

To find the y-intercept, we set x to zero and solve for y:

350(0) + 200y - 4200 = 0

200y = 4200

y = 21

Therefore, the y-intercept is 21. This means that if Francis only buys funnel cakes (x = 0), he can buy 21 deep-fried Oreos with $42.00.

So the x-intercept is (12, 0) and the y-intercept is (0, 21).

ChatGPT

The system of equations are y = ( 5/4 )x and y = 6 - 3x where the value of x and y are 1.4117 and 1.765 respectively

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first equation be P

y = ( 5/4 )x   be equation (1)

Let the second equation be Q

y = 6 - 3x   be equation (2)

Substituting the values in the equation , we get

( 5/4 )x = 6 - 3x

Adding 3x on both sides of the equation , we get

6 = ( 5/4 + 3 ) x

( 17/4 )x = 6

Multiply by 4 on both sides of the equation , we get

17x = 24

Divide by 17 on both sides of the equation , we get

x = 24/17 = 1.4117

Substitute the value of x in equation (1) , we get

y = ( 5/4 ) ( 24/17 )

y = ( 30/17 )

y = 1.765

Hence , the equations are solved and the value of x and y are 24/17 and 30/17 respectively

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The number of cubes that has 1 face in red will be 54 which is placed at the center of all faces.

Samples are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

Meg paints the whole outside of a 5 x 5 x 5 cube red and then cuts it up into 1 x 1 x 1 cube.

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The actual train is 957 inches long.

A ratio indicates the number of times one number contains another. The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given that, the ratio of the model train to the actual train is 1 : 87.

The model train is 11 inches long, therefore,

1=11

Then, the value of 87 is:

87 = 87×11

   = 957

Hence, the actual train is 957 inches long.

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The main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

Both exponential equations are in the form y = ab^x - c, where a is the vertical scaling factor, b is the horizontal scaling factor (also known as the growth factor), and c is the vertical translation. The difference between the two equations lies in the values of the parameters a, b, and c.

The first equation, 2 (1/5)x-5, has a vertical scaling factor of 2, a horizontal scaling factor of 1/5, and a vertical translation of -5. The graph of this equation will increase at a slower rate than the graph of the second equation.

The second equation, 3 (1/2)x-3, has a vertical scaling factor of 3, a horizontal scaling factor of 1/2, and a vertical translation of -3. The graph of this equation will increase at a faster rate than the graph of the first equation.

In summary, the main difference between the two equations is the rate at which the graphs increase (determined by the horizontal scaling factor) and the vertical position of the graph (determined by the vertical scaling factor and translation).

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Answer: Θ = [tex]45[/tex]

Step-by-step explanation:

tan x=sinx/cosx

and tan x is negative in the first and third quadrants.

tan x=1 for 45 degrees so tan x=-1 in the first quadrant 135 degrees and the third quadrant= 315 degrees

Answer:

Below

Step-by-step explanation:

I will assume they are all there on day 1

 then the LCM of  4  6  2  and 3   is 12 days

    every 12 days they are there together

       12 weeks = 12 x 7 = 84 days

                 84 / 12 = 7 times

day   1    13     25    37    49    62    74

The solution is, the remainder is 9.

Division is the process of splitting a number or an amount into equal parts.

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.

here, we have,

find the remainder in the synthetic division

1         4       6        -1

Take down the first number 4 as it is. then multiply it with divisor 1 and put it below 6. then add it and do the same till we get remainder

1         4       6        -1

        0        4        10

       --------------------------------

        4        10       9 -> Remainder

So the remainder is 9.

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The relationship between the number of hours past noon and the temperature outside is y = -5x + 12

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

Initial = 12 degrees

Rate = -5 degrees

To represent the relationship between the number of hours past noon and the temperature outside, we can use the equation:

y = Rate * x + Initial

So, we have

y = -5x + 12

where y represents the temperature in degrees Fahrenheit and x represents the number of hours past noon.

The graph of the equation is a linear equation

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