What is one solution to the trigonometric equation sinx − cos^2 x - 1 = 0 in the interval [0, 2π]?​

Answers

Answer 1

The solution to the trigonometric equation given in the task content is; π / 2.

What is a solution to the given trigonometric equation?

Given; sin x − cos² x - 1 = 0 in the interval [0, 2π].

Recall; cos² x = 1 - sin² x

Therefore; sin x − 1 + sin² x - 1 = 0

sin² x + sin x - 2 = 0

Let, y = sin x;

y² + y - 2 = 0

y = -2 or y = 1

Therefore, the valid value of y is; y = 1.

Therefore; 1 = sin x

x = sin-¹ (1)

x = 90° = π/2.

Consequently, the one solution which represents the solution as required is; π / 2.

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Related Questions

Suppose that E and F are two events and that P(E and F)=0.1 and P(E)=0.2. What is P(F/E)

Answers

From the given information provided, the probability of event F given that event E has occurred is 0.5.

Conditional probability is probability of an event A occurring with given that event B has occurred. It is denoted as P(A|B) and is calculated as follows:

P(A|B) = P(A and B) / P(B)

To find P(F/E), we use the conditional probability formula:

P(F/E) = P(E and F) / P(E)

We are given that P(E and F) = 0.1 and P(E) = 0.2. Substituting the given values in the formula, we get:

P(F/E) = 0.1 / 0.2

Simplifying this expression, we get:

P(F/E) = 0.5

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Car and $0. 10 for every mile driven. Salma wants to rent a car, knowing that:
She plans to drive 275 miles. She has at most $140 to spend. Write and solve an inequality which can be used to determine d, the number of days Salma can afford to rent while staying within her budget

Answers

The inequality for solving the problem is d * cost per day + 275 * $0.10 ≤ $140

To solve this problem, we need to write an inequality that represents the total cost of renting the car and driving the planned miles. The total cost is the sum of the daily rental fee (d times the cost per day) and the cost of driving the planned miles (275 times $0.10 per mile). We can write the inequality as follows:

d * cost per day + 275 * $0.10 ≤ $140

Next, we need to solve for d, the number of days Salma can afford to rent the car. To do this, we can rearrange the inequality to isolate d on one side:

d * cost per day ≤ $140 - 275 * $0.10

d ≤ ($140 - 275 * $0.10) / cost per day

Now we can plug in the given cost per day for the car rental and solve for d. For example, if the cost per day is $30, we would have:

d ≤ ($140 - 275 * $0.10) / $30

d ≤ ($140 - $27.50) / $30

d ≤ $112.50 / $30

d ≤ 3.75

Since Salma cannot rent the car for a fraction of a day, we need to round down to the nearest whole number. Therefore, Salma can afford to rent the car for at most 3 days while staying within her budget.

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evaluate the expression 5 ⋅ � 3 � 2 x 2 5⋅x 3 ​ start fraction, 5, dot, x, cubed, divided by, x, squared, end fraction for � = 2 x=2x, equals, 2.

Answers

The value of the expression is found to be 1 0 when the value of x is equal to 2.

The expression provided to us is 5.x³/x² for x = 2.

Now, in order to evaluate this expression, we will follow the simple,

5.x³/x² = 5x.

First as we can see, x³ can be divided by x²and then we will get x as the outcome of the simple division operation,

So, we will get,

5x

Now, we have to put the value of x equal to 2 so that we get to know about the exact value of the expression,

x = 2,

= 5(2)

= 10

So, the value of the expression is found to be 10 when the value of x was 2.

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Complete question - Evaluate the expression 5.x³/x² for x equals to 2.

What is the length of Line segment A B? Round to the nearest tenth.

Triangle A B C is shown. Angle A C B is a right angle and angle C A B is 75 degrees. The length of C A is 10 meters and the length of hypotenuse A B is x.

9.7 m
10.4 m
37.3 m
38.6 m.

Answers

The length of the line segment AB is 38.6 m. The solution has been obtained by using trigonometry.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle falls under the umbrella of the branch of mathematics known as trigonometry.

We are given a right angled triangle, with angle ACB = 90° and angle CAB = 75°.

We know that cos theta = adjacent side/hypotenuse

So,

⇒cos θ = 10/x

Here, θ = 75°

So,

⇒cos 75° = 10/x

⇒x = 10/cos 75°

x = 38.6

Hence, the length of the line segment AB is 38.6 m.

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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Answers

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x + 15 < 10 – 5x, which can be simplified to x < 5

and

-6x – 5 < 10 – x, which can be simplified to -5x < 15, and then x > -3

Therefore, the correct options are:

x < 5

A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

Linda plans to sign up for three field events. She wants to run a total of more than a kilometer but less than 1.5 kilometers which three events should she sign up for?

Answers

Linda can choose any combination of three events that adds up to more than a kilometer but less than 1.5 kilometers

In order to find the best combination of events for Linda to sign up for to run a total of more than a kilometer but less than 1.5 kilometers, we must first determine the total distances of the individual events.

Depending on the events offered, Linda can choose three events that add up to more than a kilometer but less than 1.5 kilometers.

If Linda has the option of running the 100m, 200m, and 800m, she can satisfy her requirement of running more than a kilometer but less than 1.5 kilometers by choosing the 100m, 200m, and 800m.

This would add up to 1100m, which is slightly over a kilometer but below 1.5 kilometers.

Another option for Linda is to run the 100m, 400m, and 600m, which would add up to 1100m, once again satisfying her requirement.

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The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 24 feet and a width of 26 feet. The length of the new space is 36 feet. Find the perimeter of the space used for the new playground.

Answers

Answer:

The perimeter of the new space used for the playground is 108 feet.

The perimeter of the space used for the new playground is 150 feet.

What is Scale factor?

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

The current space is rectangular and has a length of 24 feet and a width of 26 feet.

and, the new space is 36 feet long.

let the width of new space is x.

Since, the two space are similar then the scale factor will be

= 36/24 = 1.5

So, the width of new space = 1.5 x 26 = 39 feet

Thus, the Perimeter of new space

= 2(l +w)

= 2 (36+ 39)

= 150 feet

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A statistical technique that would allow a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is called...A case studyMeta-analysisStatistical significanceFactor analysisZ score

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We know that a statistical technique that allows a researcher to cluster such traits as being talkative, social, and adventurous with extroversion is known as the Factor analysis.

Factor analysis is most likely a statistical procedure that identifies clusters of related items also known as factors which are on a test; used to identify different dimensions of performance that underlie one's total score.

We can say that factor analysis is more like a technique which is used in mathematics for reducing a larger number into a smaller number.

In other words, its a method for reducing a large variable into a smaller variable factor also this technique takes out the maximum ordinary variance from all of the variables and then puts them in the common score.

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help me please i will give brainliest

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On 1 slice of pizza there will be 1/24th of the cheese and the constant of proportionality is 1/3.

Define Proportion.

The word "proportion" generally denotes a portion, share, or sum when contrasted to a total. When two ratios are equal, they are in proportion, as stated by the definition of proportion. Two ratios or fractions are equal when an equation is applied, or when a statement to that effect is made.

Two sets of supplied numbers are said to grow or fall in the same ratio in terms of proportion if they are directly proportionate to one another. For proportionality, use the symbols ":" or "=".

Given, 50lbs of cheese is used for 150 large pizzas.

For 1 pizza cheese used will be= 50/150

=1/3

So, the constant of proportionality here is 1/3.

Now, in 1 pizza there are 8 slices.

Cheese for each slice= 1/3 × 1/8

= 1/24.

Therefore, on 1 slice of pizza there will be 1/24th of the cheese.

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a. Find the length of EF.

Type the answer in the box below.

Answers

The length of EF= 15 cm.

How to solve for EF?

As, the question states that the triangles are similar; their ratios are also equal.

AC/DF = AB/DE - CB/EF

Plug in the values

12/10 = AB/DE = 18/EF

If we isolate EF,

EF = 180/12

EF= 15cm

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Will give Brainly please

Answers

The value of the mean excluding the outlier is 130. 5

What is an outlier?

An outlier can be defined as a data point that differs significantly or greatly from other observations.

It occurs as a result of;

variability in the measurement indication of novel dataexperimental error

From the information given, we have that;

121, 89, 410, 203, 55, 230, 182, 148, 135, 233, 11, 219, 108, 192

Since, the outlier is 410

The mean is given as;

= 121 + 89+ 203+ 55 + 230+182 + 148 + 135 + 233+ 11+ 219 + 108 + 192/13

Add the values

= 1696/13

= 130. 5

Hence, the value is 130. 5

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A square lawn with a side length of 15 yards has a square shed built near the back, which has a side length of x yards. What are the factors that represent the
area of the yard that can be mowed?
xn

Answers

The factor that represents the area of the yard that can be mowed is (225 - x²).

What is area?

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The total area of the lawn is given by the formula -

Area of square lawn = (side length of square lawn)²

= (15 yards)²

= 225 square yards

The shed is also a square, with side length x yards.

So, the area of the shed is -

Area of square shed = (side length of square shed)²

= x²

To find the area of the yard that can be mowed, we need to subtract the area of the shed from the total area of the lawn -

Area of yard that can be mowed = Area of square lawn - Area of square shed

= 225 - x²

Therefore, the value is obtained as (225 - x²).

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3x + 8 = 3x+

Find one value of x

Answers

3x + 8 = 3x + x, which has one solution at x = 8 for the equation..

What is the solution to the equation?

In arithmetic, a solution to the equation expresses can be substituted for the variable to provide a piece of real number information.

The equation is given as 3x+8=3x+ ____.

If 3x + 8 = 3x + 9 has no solution for the equation.

If 3x + 8 = 3x + 8 has infinite solutions for the equation.

If 3x + 8 = 3x + x is equal to 3x + 8 = 4x, which has one solution at x=8 for the equation.

Therefore, 3x + 8 = 3x + x, which has one solution at x = 8 for the equation.

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The question seems incomplete, the complete question would be as:

3x+8=3x+ ____

What value could you write in after 3x that would make the equation true for:

Group of answer choices

no values of x

[ Choose ]

all values of x

[ Choose ]

just one value of x

[ Choose ]

The price of chicken breast rises from $3.00 to $3.60 per pound. In response to the price change, the demand for chicken breast falls by 25%. The absolute value of the price elasticity of demand for chicken breast is _____, and the price elasticity of demand is _____.a. 0.8; inelasticb. 1.25; inelasticc. 0.8; elasticd. 1.25; elastic

Answers

Answer: We can use the formula for the price elasticity of demand to solve this problem:

Price elasticity of demand = percent change in quantity demanded / percent change in price

We are given that the price of chicken breast rises from $3.00 to $3.60 per pound, which is a 20% increase:

percent change in price = (3.60 - 3.00) / 3.00 = 0.20 = 20%

We are also given that the demand for chicken breast falls by 25%, which is a 25% decrease:

percent change in quantity demanded = -25%

Using these values in the formula, we get:

Price elasticity of demand = (-25%) / (20%) = -1.25

Since we are interested in the absolute value of the price elasticity of demand, we have:

|Price elasticity of demand| = |-1.25| = 1.25

A price elasticity of demand greater than 1 is considered elastic, and a price elasticity of demand less than 1 is considered inelastic. Therefore, the answer is (d) 1.25; elastic.

Step-by-step explanation:

Please help me I am very confused

Answers

The solutions are x=3.69 and x=-4.2

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

2x²+x-31=0

Solve this with the quadratic formula

x=-b±√b²-4ac/2a

a=2,b=1,c=-31

x=-1±√1+248/4

x=-1±√249/4

x=-1+√249/4

x=-1 + 15.77/4 =14.77/4

x=3.6925

and x=-1-√249/4

x=-1 -15.77/4 =-4.1925

Hence, the solutions are x=3.69 and x=-4.2

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Write the radical expression [tex]\frac{8}{\sqrt[7]{x^1^5} }[/tex] in exponential form.

Answers

The value of the exponential equation is A = ( 8 ) x ^ -105/2

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

A = 8 / ( 7√x¹⁵ )   be equation (1)

On simplifying the equation , we get

The value of √x¹⁵ = x ^ 15/2

Now , the 7th root of √x¹⁵ is = x ^ 105/2

Now , the equation will be

A = ( 8 ) x ^ -105/2

Hence , the exponential equation is A = ( 8 ) x ^ -105/2

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what can be concluded from the fact that the correlation coefficient between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation is -0.32?

Answers

The correlation coefficient -0.32 which is negative and close to zero, we conclude that there is an inverse and weak correlation between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation

What Is the Correlation Coefficient?

The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1.

Properties of correlation coefficientA positive correlation coefficient indicates a direct relationship between two variablesA negaitive correlation coefficient indicates an inverse relationship between two variablesA correlation coefficient close to 1 indicates a strong relationship between two variablesA correlation coefficient close to zero indicates a weak or no relationship between two variables

Now, since the correlation coefficient between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation is -0.32.

Since the correlation coefficient is negative and close to zero, we conclude that there is an inverse and weak correlation between the acceptance rate at the top 100 u.s. mba programs and the percent of students in those programs who are employed upon graduation

So, there is an inverse and weak correlation between them.

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how many pattern blocks trapezoids would create 1 hexagon

Answers

Answer: 2 trapezoids

Step-by-step explanation: so 1 trapezoid has the same angles and edges as a hexagon, you get 2 and put them together 1 upside one one forward side up, it makes a hexagon

SAVINGS If $10,000 is deposited into a savings account that pays 2.3% annual interest, how much more would the account be worth if interest were compounded monthly rather than annually over a period of 30 years? Round to the nearest dollar.

Answers

The extra income earned in monthly compounding is $142.04.

What is compound effect?

Compounding is defined as calculating interest on both the amount borrowed plus previous interest.

Given is that $10,000 is deposited into a savings account which is compounded monthly followed by compounded annually.

Annual compounding for 30 years -

Total money after annual compounding for 30 years -

T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)

T{A} = $19,781.95

Monthly compounding for 30 years -

Total money after annual compounding for 30 years -

T{A} = 10000 + (10000 x 0.023/1)^(30 x 1)

T{A} = $19,923.99

Extra interest earned -

E = 19,923.99 - 19,781.95 = $142.04

Therefore, the extra income earned in monthly compounding is $142.04.

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Is it possible to form a triangle with side lengths 8, 9, and 17? If not, explain why not.

Answers

This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

What does a triangle actually mean?

Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons.

Here,

No, it is not possible to form a triangle with side lengths 8, 9, and 17.

To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Symbolically, for sides a, b, and c, this can be written as:

a + b > c

a + c > b

b + c > a

Let's check if these inequalities are satisfied for the sides of 8, 9, and 17:

8 + 9 > 17 (true)

8 + 17 > 9 (true)

9 + 17 > 8 (true)

All three inequalities are true, which means that the given side lengths satisfy the triangle inequality and a triangle can be formed.

In this case, we see that 8 + 9 = 17, which is exactly the length of the third side.

This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.

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A desk is on sale for $224 which is 65% less than the regular price ,what is the regular price 

Answers

Answer: $640

Step-by-step explanation:

100%-65%=35%

$224/35%=6.4

6.4*100%=$640

To check the solution

$640*65%=$416

$224+$416=$640

Help pls, I’m giving 20 points

Answers

The area of the shaded part in the circle will be 10840.99 ft².

How to calculate the area

The circumference = 2 * pi * r = 221.056

Use this fact to find r

2*pi*r =  221.056

Divide by pi

2*r =  221.056 / 3.141

2*r =  70.378      

Divide by 2

r = 35.19

Now that you have the radius of the inner circle, use it to find the area.

Area = pi * r^2

Area = 3888.37

Now we need the radius of the outer circle

r = 35.19 + 33.3

r = 68.49

Find the area of the other circle

Area = pi * 68.49^2

Area = 14729.36

Finally the area of the shaded region is the area of the large circle - the area of the small circle

Area of the shaded area = 14729.36- 3888.37

Area of the shaded area = 10840.99 to the nearest hundredth.

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Evaluate the expression for j = –2.
10lj| − 12 =

Answers

Answer:

8

Step-by-step explanation:

To evaluate the expression for j = -2, we simply substitute -2 for j and simplify:

10l(-2)l - 12 = 10 * |-2| - 12 (Note that the absolute value of -2 is 2)

= 10 * 2 - 12

= 20 - 12

= 8

Therefore, the value of the expression 10lj| − 12 when j = -2 is 8.

The binomial probability distribution is a ​ __________ probability distribution that describes probabilities for experiments in which there are two​ __________ outcomes.
discrete
mutually exclusive

Answers

The binomial probability distribution is a discrete ​probability distribution that describes probabilities for experiments in which there are two mutually exclusive​ outcomes.

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either success or failure.

In binomial probability distribution, the number of ‘Success’ in a sequence of n experiments, where each time a question is asked for yes-no, then the boolean-valued outcome is represented either with success/yes/true/one (probability p) or failure/no/false/zero (probability q = 1 − p). A single success/failure test is also called a Bernoulli trial or Bernoulli experiment, and a series of outcomes is called a Bernoulli process.

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two tickets are drawn without replacement from the following box of tickets: 1, 1, 1, 2, 2, 3, 4, 5. find the probability that the second ticket is 2, given that the first ticket is 5. express your answer as a fraction.

Answers

The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

What is probability tree?

The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.

Let A be an event: the first ticket extracted was the 5.

Let B be an event: the second ticket is 2.

The probability for the following is given as:

P (B/ A) = 2/7

Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.

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Simplify, Rationalize the denominator.

[tex]\frac{9}{7+\sqrt{2} }[/tex]

Answers

Answer:

[tex]\frac{9(7-\sqrt{2}) }{47}[/tex]

Step-by-step explanation:

How Many Cups In A Pounds ?

Answers

Answer:

There are 1.91 cups in a pound

5 is what percent smaller than 10?

Answers

Answer:

50% smaller

Step-by-step explanation:

Which equation represents the graph?
a graph of a line that passes through the points 0 commas negative 3 and 4 commas negative 1

y equals negative one-half times x plus 6
y equals one-half times x minus 3
y = 2x − 3
y = −2x + 6

Answers

The equation of line passes through the points (0, -3) and (4, -1) will be;

⇒ y = 1/2x - 3

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, -3) and (4, -1)

Now,

Since, The equation of line passes through the points (0, -3) and (4, -1).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 1 - (-3)) / (4 - 0)

m = 2 / 4

m = 1/2

Thus, The equation of line with slope 1/2 is,

⇒ y - (-3) = 1/2 (x - 0)

⇒ y + 3 = 1/2x

⇒ y = 1/2x - 3

Therefore, The equation of line passes through the points ((0, -3) and

(4, -1) will be;

⇒ y = 1/2x - 3

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Which could be the function?

f(x) = (x + 4)2
f(x) = x2 + 4
f(x) = (x – 4)2
f(x) = x2 – 4

Answers

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

What is the function?

A function is a mathematical relationship between two variables, where each input value (independent variable) corresponds to exactly one output value (dependent variable). It is often represented using a formula or equation.

All of the given expressions are functions, but the first three are quadratic functions, while the last one is a quadratic function with a negative constant term.

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How to convert 7km in miles? What are the 13 parts of an animal cell? which organ absorbs most of the nutrients from your food? what is 5pm military time What portion of the process (obtaining, refining, manufacturing ortransporting) do you think used the most energy for the cell phones?Justify your answer. Which equation is true when x=3?A. 8x=28B. x-19=16C. 28+x=25D. X/3=1 when large organizations face multiple environments and interact with each environment at different organizational levels is called? write the phase as an algebraic expression k less than 24 how to convert 1ml to cc? what is 88 6/12 rounded to the nearest whole number by the 1910s, the conditions described in the excerpt were most addressed by Please help I am going to get expelled if I cant get my grades up ahahahahaha Which of the following legal duties of board members suggests that a director does not need to be an expert or actually run the company?a. Duty of careb. Duty of good faithc. Duty of candord. Duty of loyalty Translate Jacques found a cat into French by filling in the missing letters:Jac_ues_t_ _v_un_hat best assessment of fluid resuscitation in the adult burn patient? primary and secondary waves are _____ waves and kove waves are_____waves slow fast slow, slow body, surface body, body surface what event would cause the end of the use of the santa fe trail? What happens when the recurrent laryngeal nerve is damaged? The nurse is preparing to care for a patient who has myasthenia gravis. The nurse will be alert to symptoms affecting which body system in this patient?a. Cardiovascular system and postural musclesb. Central nervous system (CNS), memory, and cognitionc. Gastrointestinal system (GI) and lower extremity musclesd. Respiratory system and facial muscles Who believe that many forms of abnormal and normal psychological functioning ore psychogenics. believe that unconscious psychological process are at the root of such functioning?