The functions f(x) = x^2 – 3 and g(x) = –x^2 + 2 are shown on the graph.


Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the solution set be identified?

y ≤ x^2 – 3
y > –x^2 + 2

Step-by-step explanation:

I know that both sides of the cats, males and females, receive the same # of new cats.

I write an equation, (not an inequality though):

3((34+2x)/5)=2((13+2x)/5)

From here on, I solve for x. I get x = -38. I know we can't have negative pairs and we're only bringing in more cats, and not taking any away. I add 38, and try to see what percentage of cats are male, and I get fairly close, getting to about 62.5% I think. Then, I divide 38 by 2, getting 19, and see what else I can get. I try to find a value between the 38 and lesser 19 so as to find a value which will give me a male cat percentage of 60%. I get about 57.5% with 19 plugged in, which is when I see that hey, the differences are the same. What I then do is find the average of 19 + 38, which is 57.5. I round that to 58, and I get the right answer.

I see that perhaps my solution wasn't really orthodox or anything, but with a little bit of trial and error and a bit of my creative thinking, I guess I managed to solve the problem. What worries me though is this is the first problem in the "questions" section of the inequalities section of AoPS, so I'm definitely struggling to deal with the concepts.

The domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

Given is a graph of the function.

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that function takes. So, we can write the domain as -

Domain → [-5, 10)

Range → [-3, 3)

Therefore, the domain and range of the the function are given below -

Domain → [-5, 10)

Range → [-3, 3)

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Answer:

The graph of g(x) = 3x−5 is obtained from the graph of g(x) = 3x by applying the transformation (f(x) = f(x) + b) where b = -5. This transformation is a vertical shift of the graph of g(x) = 3x downward by 5 units.

The graph of g(x) = 3x is a line with a slope of 3 and y-intercept of 0. By subtracting 5 from each y-coordinate, the y-intercept of the graph is shifted downward by 5 units, resulting in a y-intercept of -5. The slope of the graph remains the same as the original function, 3. So the graph of g(x)=3x−5 is the same line as g(x)=3x, but shifted downward 5 units.

Step-by-step explanation:

Using it's definition, it is found that the function f(x) has a point of inflection at:

A. x = 8 only.

Inflection points are points where the function changes concavity.

The critical points of a function are the values of x for which:

f" (x) =0

Additionally, there has to be a change in the sign of f" (x)

Researching the problem on the internet, it is found that:

For 0 < x < 5, f"(X) > 0

For x = 5, f" (x)  is undefined.

For 5 < x < 8, f (x) < 0

For x = 8, f"(x) = 0

For 8 < x < 12,f" (x) > 0

For x = 12, f (x) = 0

For 12 < x < 16, f"(x) > 0

The two conditions,  f"(x) = 0 and a change in the signal of  f" (x) are only respected at x = 8, which is the lone inflection point.

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Complete option

of f for values of x in the interval (0,16) is given in the table above. At what values of x in the interval (0,16) does the graph of f have a point of inflection?.

Answer: abrimos

Step-by-step explanation: That's what it is on my quiz.

In the sentence "Nosotros _____ la ventana", the correct verb form is "abrimos". The best answer is option D.

The verb "abrir" is a Spanish verb that means "to open", and the first person plural form of this verb is "abrimos". So the sentence "Nosotros abrimos la ventana" translates to "We open the window".

The other verb forms in the options ("compartimos", "abro", and "escribimos") do not fit the context of opening the window. "Compartimos" means "we share", "abro" means "I open" (first person singular), and "escribimos" means "we write". So these forms are not the correct form to complete the sentence.

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If the expression be −2/5h+7h+6 then the value of h be -10/11.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one arithmetic operation, and the expression itself. Any one of the following mathematical operations can be used.

An expression in mathematics is made up of a number of variables, functions, and other elements (such as addition, subtraction, multiplication or division etc.) In some ways, phrases and expressions are comparable.

Using mathematical operations like addition, subtraction, multiplication, and division, a combination of numbers and integers can be expressed numerically in mathematics.

Let the equation be -2/5h + 7h + 6 = 0

Move 6 to the right side

-2/5h + 7h = -6

Multiply both sides by 5

-2/5h × 5 + 7h × 5 = -6 × 5

Simplifying the above equation, we get

33h = -30

Divide both sides by 33

33h/33 = -30/33

Therefore, the value of h = -10/11.

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Dilation is a transformation that can be used to resize an item. Dilation can cause the items to grow or shrink.

Resizing an object is accomplished through a change called dilation. The objects can be enlarged or shrunk via dilation. A shape identical to the source image is created by this transformation. The size of the form does, however, differ.

You have most likely started labour when your cervix is 3 cm dilated. Your cervix slowly widens to around 6 cm during this phase. It can take anywhere from a few hours to a few days to complete this stage of labour, however it typically takes between 8 and 12 hours. An average woman can dilate between 0.5 and 0.7 cm per hour during the active stage of labour. Whether this is your first child or not will also influence how quickly your cervix dilates. Experienced mothers typically progress through labour more quickly.

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This means that C-Town flour is more expensive because it is only $1.88 per pound compared to Food Bazaar's $2.25 per pound.

Cost is the amount of money or resources needed to acquire, maintain, or produce something. It can refer to either the expense of buying a good or service, the expense of labor, or the expense of resources such as time and materials. In a business context, cost is often used to refer to the total amount of money a company has spent on a particular activity or product.

C-Town's smaller bag size may make it a more convenient purchase, but it is not a good price compared to Food Bazaar.

In order to get the best deal, the shopper needs to compare prices and consider all of the factors. The size and quantity of the bags, the number of servings in each bag, the cost per serving, and the store's location are all important considerations. For example, C-Town may be closer geographically, but if the shopper needs more servings for their recipe, the extra cost to buy multiple bags at C-Town may be more expensive than buying a larger bag of flour at Food Bazaar.

In addition to the cost of the flour, other costs such as the cost of transportation to the store, the cost of any necessary packaging, the cost of any other ingredients needed for the recipe, and the cost of any other items purchased should also be taken into account.

Finally, shoppers should take the quality of the product into consideration. The type of flour, the freshness and shelf life of the product, and any special features of the product should also be taken into account. A low-cost bag of flour may be far less desirable than a more expensive bag of flour with higher quality ingredients.

Overall, to get the best deal on flour, shoppers need to consider all of these factors and compare prices between stores.

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The system of inequality the satisfies the given credit conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.

One or more linear inequalities in each of the same two variables make up a system of linear inequalities in two variables. A linear inequality's solution is an ordered pair that resolves all of the system's inequalities, and the inequality's graph is a representation of all of the system's solutions.

Given that to graduate the core credit must be at least 13 credits. This is represented as follows:

C ≥ 13.

The credit of the electives should be at least 6, this is represented as follows:

E ≥ 6

The total credits should be no more than 27, this is represented as:

C + E ≤ 27

Hence, the system of inequality the satisfies the given conditions is option a, C ≥ 13, E ≥ 6 and C+E ≤ 27.

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The next three terms of the alternating series are - 1 / 16, 1 / 32 and 1 / 64, respectively.

Herein we find an alternating series of the form:

sₙ = (- 1)ⁿ · rⁿ⁻¹, for n = {1, 2, 3, ..., n}

Where:

By direct inspection, we find that r = 1 / 2 and the next three terms are: n = {5, 6, 7}

n = 5

s₅ = (- 1)⁵ · (1 / 2)⁵⁻¹

s₅ = - 1 · (1 / 16)

s₅ = - 1 / 16

n = 6

s₆ = (- 1)⁶ · (1 / 2)⁶⁻¹

s₆ = 1 · (1 / 32)

s₆ = 1 / 32

n = 7

s₇ = (- 1)⁷ · (1 / 2)⁷⁻¹

s₇ = 1 · (1 / 64)

s₇ = 1 / 64

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If each of the aforementioned limits (or both) is a real integer, then y = 1/e, where k is the limit's value.

The study of mathematics comprises the study of quantities and their fluctuations, formulae and associated structures, objects and their positions, and locations where they may found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outcomes where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on procedures, each functions, many-to-one functions, within functions, and on functions.

given

f(x) = e^( x-2)

f(x) = 1/e

Step 1: Locate lim x f (x). apply the function's limit as x, etc.

Step 2: Determine lim x - f(x).

Step 3: Write the horizontally asymptote as y = k, where k is the value of the limit, if each (or both) of the aforementioned limits are real integers.

If each of the aforementioned limits (or both) is a real integer, then y = 1/e, where k is the limit's value.

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An equation, containing variable m that represents the situation described is 2,700 = 6,200 - 350m.

An equation is a mathematical statement showing the equality or equivalence of two or more mathematical or algebraic expressions.

Equations go with the equal symbol (=) unlike mathematical expressions, which combine variables, numbers, constants, and values with the mathematical operands.

The initial balance in the checking account = $6,200

Monthly withdrawal = $350

The final account balance = $2,700

Let the number of months of withdrawal = m

2,700 = 6,200 - 350m

Check:

2,700 = 6,200 - 350m

350m = 3,500

m = 10 months

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The angular speed of the fan  138π radians/minute or 433.54  radians/minute.

The linear speed of the tip of a blade is 8237.26 inches/minute

a) The angular speed of a fan is the number of revolutions per minute (RPM) multiplied by 2π radians per revolution.

So the angular speed of the fan in radians per minute is:

69 RPM × 2π radians/revolution = 138π radians/minute

b) The linear speed of the tip of a blade is found by multiplying the angular speed in radians per minute by the radius of the fan.

So the linear speed of the tip of a blade in inches per minute is:

138π radians/minute × 19 inches = 8237.26 inches/minute

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Answer:

I have solved it and attached in the explanation.

Step-by-step explanation:

The amount of Cashew nuts is 0.205

The amoun of Peanuts is 0.295

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

Amount of Cashew nuts = x

Amoun of Peanuts = y

Now,

We can make two equations.

x + y = 1/2 ____(1)

x = 1/2 - y  _____(20

Substituting (2) in (3)

6.25x + 2.10y = 1.90 _____(3)

6.25 (1/2 - y) + 2.10y = 1.90

3.125 - 6.25y + 2.10y = 1.90

3.125 - 4.15y = 1.90

3.125 - 1.90 = 4.15y

y = 1.225/4.15

y = 0.295

And,

x = 1/2 - y

x = 1/2 - 0.295

x = 0.205

Thus,

Amount of Cashew nuts = 0.205

Amoun of Peanuts = 0.295

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The point on the graph that shows the price of 2 ounces of medicine, given the formula, is 4 currency units.

The graph shows the relationship between the ounces of medicine and the price of those ounces in the formula y = 2 x. The value of x in this instance, is the number of ounces of medicine to be sold.

The value of y would be the price of those two ounces to be sold. The formula, y = 2 x means that the price of a single ounce of medicine, is 2 currency units.

For 2 ounces therefore, the price is:

y = 2 x

y = 2 x 2

y = $ 4

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Answer:

$83.75

$220.40 x 38% =$83.75

Answer:

40.5=40 1/2

Step-by-step explanation:

Answer: 40.5 as a fraction is 81/2. ✅

Step-by-step explanation:

Sure, here's a step-by-step explanation of how I got the fraction 81/2 for the decimal number 40.5:

Identify the number of decimal places in the decimal representation of 40.5, in this case, it's 1.

Write the decimal number as a fraction by placing the decimal number over a power of 10 that has the same number of zeroes as there are decimal places in the decimal representation. In this case, it's 40.5 / 10^1 (or 40.5/10).

Simplify the fraction if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction is already in its simplest form.

The fraction representation of 40.5 is 405/10

Simplify the fraction again if possible by dividing both the numerator and denominator by a common factor if one exists. In this case, the fraction can be simplified further by dividing both the numerator and denominator by 5.

So, the fraction representation of 40.5 is 81/2

Hence, the fraction representation of 40.5 is 81/2.

A non-function inverse would be a mathematical operation that does not produce a new function.

A function inverse is a new function that can be used to "undo" the effects of an original function. An example of a function inverse would be the inverse sine function of sin(x).

A non-function inverse would be a mathematical operation that does not produce a new function. Examples of non-function inverses include division, subtraction, and multiplication. These operations can be used to undo the effects of an original function, but they do not create a new function. Division can be used to “undo” multiplication, for example. However, the end result is not a new function, but rather a number or set of numbers. Subtraction and multiplication can be used to “undo” addition and division, respectively, but again, the end result is a number or set of numbers, not a new function. Therefore, these operations are not function inverses.

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22.22 was spent on a pass and lunch for each student.

Now, According to the question:

Total money spend on passes = 674.73

Total no. of people = 47 + 2

                                = 49

Money spend on pass for each person  = 674.73/49

                                                                  = 13.77

Total money spend on lunch = 414.07

Total no. of students = 49

Money spend on lunch for each student = 414.07/49

                                                                  = 8.45

Total = 13.77 + 8.45

       = 22.22

Hence, 22.22 was spent on a pass and lunch for each student.

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The solution to both function f(x) and g(x) is (0.02, 1.29)

An equation is an expression relating two or more numbers and variables.

The standard form of an equation is:

Ax + By = C

A, B, and C are constants

The slope intercept of an equation is:

y = mx + b

Where m is the rate of change(slope) and b is the y intercept.

The first function:

f(x) = -34x + 2

while, The second function:

g(x) = 14x + 1

The solution of -34x + 2 = 14x + 1 is the point of intersection of both functions in the graph.

The solution is (0.02, 1.29)

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Note that the area of Triangle CDE will be 4 square units.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

The area of a ΔCDE is derived as follows:

Given that:

C = (4,1)

D = (4, -5) and

E = (2, -3)

A = 1/2 [x1 (y2 - y3_ + x2(y3-y1) + x3 (y1-y2)]

Inputting the given values, we have:

A = 1/2 [ 4(-5+3) + 4(-3+1) + 2(-1+5)]

A = 1/2 [4(-2) + 4 (-2) + 2(4) ]

A = 1/2 [-8-8+8]

A = 1/2(-8)

A = -4

| A | = 4

Thus, the area of ΔCDE is 4 units.

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Answer:

0

Step-by-step explanation:

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction. Using the direction chart we get the equator is at 0 distance away from the location of kylie.

Given-

Kylie uses the number 400 to represent 400 miles north of the equator.

Kylie uses the number -2000 to show 2000 miles south of the equator.

What is the direction?

Direction is defined as the path that something takes. North, south, east and west all are the direction. Up down, left and right are also used to represent the direction.

As Kylie use the number 400 to represent 400 miles north of the equator. Thus if he need to back at 400 towards the south to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Similarly Kylie uses the number -2000 to show 2000 miles south of the equator. Thus if he need to come back at 2000 towards the north to reach back to the equator. Thus the equator is the point from where he has started and the equator is at 0 distance away from the location of kylie where he had started earlier.

Hence both the statement suggest that the equator is at 0 distance away from the location of kylie where he had started earlier.

Therefore , the solution of the given problem of distance comes out to be D = 11.66.

An object's travels are quantified by distance. Simply explained, distance, or t, is the amount of space an object covers within a specific period of time. Displacement is still the shortest distance a moving object can travel. We frequently take into account the concepts of distance et displacement.

Here,

provided parameters

Dimensions of A = (-4,5)

B's coordinate number is (2,-5)

Unknown:

Size of AB =?

Solution:

Use the formula below to calculate the distance between these two places;

D = √(y2-y1)²+(x2-x1)²

x₁ = -4

x₂ = 2

y₁ = 5

y₂ = -5

enter the parameters, then solve;

=> D = √(2-(-4))  ²+(-5-5)   ²

=>D = √6² + (-10)² = 11.66

Therefore , the solution of the given problem of distance comes out to be D = 11.66.

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If a resident who is 40 or older is chosen at random, the probability that they have completed a bachelor's or master's degree is given as follows:

0.436 = 43.6%.

A probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The desired and total outcomes for the conditional probability in this problem are given as follows:

Hence the number of total outcomes is given as follows:

3827 + 7106 = 10933.

(40-49 + 50 and over).

The number of desired outcomes is given as follows:

726 + 655 + 2160 + 1226 = 4767.

(either master's or bachelor's degree's for both age intervals).

Hence the probability is calculated as follows:

p = 4767/10933

p = 0.436.

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The expression has a product greater than (2 1/6) is 2 [tex]\frac{1}{6}[/tex] x  2 [tex]\frac{1}{6}[/tex] .

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When f(x) = ax + b, where a and b are real values, the function is said to be linear. Here, a denotes the line's gradient and b the y-axis intercept (which is sometimes called the vertical intercept).

The following expression describes a linear function. Y equals f(x) = a + bx. Both the independent and dependent variables of a linear function are one. X is an independent variable, whereas Y is a dependent variable. The y intercept or constant term is called a.

Any function that depicts a straight line on the coordinate plane is said to be linear. For instance, the equation y = 3x – 2 indicates a straight line on a coordinate plane, indicating that it is a linear function. This function can be expressed as f(x) = 3x - 2 since f(x) can take the place of y in the equation.

If the graph of an equation is a straight line, the equation is linear. This will occur when x has a highest power of 1, which is.

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Answer:

The original number is 8.

Step-by-step explanation:

(x + 8) x 3 = 48

x + 8 = 48/3

x = 16 - 8

x = 8

An expression which is equivalent to (m⁶)⁻⁴/m⁻²⁶ for all values of m where the expression is defined include the following: C. m².

In Mathematics, an exponent can be defined as a mathematical operation that is used to raise a quantity to the power of another and it is generally written as bⁿ.

By applying the law of indices for powers, we have the following:

Expression = (m⁶)⁻⁴/m⁻²⁶

Expression = m⁻²⁴/m⁻²⁶

By applying the law of indices for division, we have the following:

Expression = (m⁶)⁻⁴/m⁻²⁶

Expression = m⁽⁻²⁴ - ⁽⁻²⁶⁾⁾

Expression = m⁽⁻²⁴ ⁺ ²⁶⁾

Expression = m²

In conclusion, we can reasonably infer and logically deduce that the given mathematical expression (m⁶)⁻⁴/m⁻²⁶ for all values of m, is defined at m².

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Answer:

impossible

Step-by-step explanation:

If the customers choose to rebook a holiday that is more expensive than the original holiday in Portugal, and the holiday company is offering an incentive worth up to 20% of the value of the holiday, the customers will have to pay the difference between the original holiday and the new holiday, minus the 20% incentive.

Without more information on the cost of the new holiday, it is impossible to determine how much extra it will cost the customers each

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve for x ~

[tex]\qquad \sf  \dashrightarrow \: 3x + 11 = k[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x + 11 - 11 = k - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3x = k - 11[/tex]

[tex]\qquad \sf  \dashrightarrow \: x = \dfrac{k - 11}{3} [/tex]