What are the domain and range of the function the quantity of x squared minus 4x minus 12, all over x plus 2?.

The Total Surface area of cardboard in the box is 992 cm².

The region that includes the base(s) and the curved portion is referred to as the total surface area. It is the overall area that the object's surface occupies. The total area of a shape with a curved base and surface is equal to the sum of the two areas.

Given:

length= 20 cm

width = 12 cm

height= 8 cm

So, the TSA of Cuboid

= 2(lw + wh + lh)

=2( 20 x 12 + 12 x 8 + 8 x 20)

=2( 240 + 96 + 160)

= 2(496)

= 992 cm²

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The values are :

What is trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships and properties of angles and the trigonometric functions such as sine, cosine, and tangent. It is based on the study of the geometric properties of triangles and is used extensively in fields such as physics, engineering, architecture, and astronomy.

In trigonometry, the relationships between the sides and angles of a triangle are expressed using the six trigonometric functions: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). These functions describe the ratios between the sides of a right triangle, where one angle is 90 degrees. Trigonometric functions can also be defined for any angle, not just those in a right triangle, using the unit circle or other methods.

Trigonometry has many practical applications, such as in navigation, surveying, and the design of structures such as bridges and buildings. It is also used extensively in science and engineering, particularly in fields such as physics, mechanics, and electromagnetics.

If tan x = 0, then tan(-x) = 0.

The tangent function is an odd function, which means that tan(-x) = -tan(x). However, since tan x = 0, this means that -tan(x) = 0 as well. Therefore, tan(-x) = 0.

If sin x = 0.3, then sin(-x) = -0.3.

The sine function is an odd function, which means that sin(-x) = -sin(x). Since sin x = 0.3, this means that -sin(x) = -0.3. Therefore, sin(-x) = -0.3.

If cos x = 0.3, then cos(-x) = 0.3.

The cosine function is an even function, which means that cos(-x) = cos(x). Since cos x = 0.3, this means that cos(-x) = 0.3 as well.

If tan x = -2, then tan(pi+x) = tan(pi + atan(-2)) = tan(2.0344 + pi) = -2.

To find tan(pi + x), we need to use the identity tan(a + pi) = -tan(a). In this case, a = atan(-2), which is the inverse tangent of -2. Using a calculator or a table, we can find that a is approximately 2.0344 radians. Therefore, tan(pi + x) = -tan(2.0344) = -(-2) = 2.

Hence, values are

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Step-by-step explanation:

classic Christian from x x + 4 + 8 is equal to 21 what is the answer

The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

What is the placebo effect is an experimental study refers to the?

The placebo effect is a phenomenon where people report real improvement after taking a fake or nonexistent treatment, called a placebo. Because the placebo can't actually cure any condition, any beneficial effects reported are due to a person's belief or expectation that their condition is being treated.

Hence , The placebo effect refers to an experiment where neither the participants nor the experimenters know who belongs to the treatment group and who belongs to the control group. As a​ result, it is impossible for the experiments to link certain effects to certain​ patients, which make the results difficult to interpret.

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C. A placebo refers to a situation in which a patient improves simply because they believe they are receiving a useful treatment.

The length of q is approximately is 0.4 cm.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:

a/sin A = b/sin B = c/sin C

where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.

In triangle AOPQ, we know that:

Side p = 6.3 cm (opposite angle P)

Angle O = 149° (opposite side q)

Angle P = 29° (opposite side p)

Let use angle sum property of triangles to find the measure of angle Q:

Angle Q = 180° - Angle O - Angle P

Angle Q = 180° - 149° - 29°

Angle Q = 2°

Now we can use the law of sines to solve for the length of q:

q/sin Q = p/sin P

q/sin(2°) = 6.3/sin(29°)

q = sin(2°) × (6.3/sin(29°))

q=0.034 × (6.3/0.484)

q = 0.442 cm

Therefore, the length of q is approximately is 0.4 cm.

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If A 15-foot pole is leaning against a tree and  bottom of the pole is 8 feet away from the bottom of the tree. then the top of the pole  reaches option (C) 12.7 feet

We can use the Pythagorean theorem to solve this problem. Let's call the height we're trying to find "x". Then, we have a right triangle where the pole is the hypotenuse, the distance from the bottom of the pole to the tree is one leg, and the height we're trying to find is the other leg. Using the Pythagorean theorem, we have:

15^2 = 8^2 + x^2

225 = 64 + x^2

Group the like terms

161 = x^2

x ≈ 12.7 feet

Therefore, the correct option is (c) 12.7 feet

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Answer:

The largest possible whole-number length for the third side of a triangle with two sides of length 7 and 10 is 13. This is due to the fact that the two given lengths must be added together, and then subtracted from the third side in order to create a valid triangle. Therefore, the third side must be at least 13 in order to create a triangle.

The solution is, the answer is: The color is blue (D).

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

here, we have,

Our matrix C is the encoder.  Let X be our secret message and let B be our encoded message.  Therefore the relationship between the 3 can be represented as:

CX = B

So we want to solve for X (our secret message). So using matrix algebra:

X = C^-1*B

where C^-1 is the inverse of C.

C^-1 = | 3 -2 |

          |4 -3 |

So we take C^-1 and multiply it by matrix B to get X.  Matrix B is already given to us.  So just multiply those two.  I used a calculator to get:

X = | 20 8 5 3 15 12 15 |

     | 18 9 19 2 12 21 5 |

And since A = 1, B = 2, C = 3, etc....

We decode our message and it says:

X = | T H E C O L O |

     | R I S B L U E |

So the answer is: The color is blue (D)

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Answer: D

Step-by-step explanation:

Therefore , the solution of the given problem of graph comes out to be

option c is correct it shows an association of the distribution of different mode of transportation among the same age of group.

Academics use graphs to visually represent or chart happenings or quantities in a logical manner. The interaction between a number of objects is frequently represented by a graph point. A graph is a non-linear storage structure made up of nodes, also known as vertices, and edges. The vertices, sometimes referred to as nodes, should be joined together with glue. Vertex numbers in this graph are 1, 2, 3, or 5, while edge numbers are 1, 2, 1, 3, 2, 4, etc. (2.5). (3.5). (4.5). (4.5). (4.5).

Here,

Given : A graph having choices of adult , child , teen  and senior mode of transportation ,

In different age the mode of transportation preferred by among the same ages .

Thus ,

it shows an association of the distribution of different mode of transportation among the same age of group.

So , option c is the correct answer.

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Answer:

6 half-liter

Step-by-step explanation:

To get 3 liters of milk, Toby has two options:

Option 1: Buy 6 half-liter containers

The cost of one half-liter container is $2.43, so the cost of six such containers is 6 x $2.43 = $14.58.

Option 2: Buy 12 250-milliliter containers

The cost of one 250-milliliter container is $1.42, which is equivalent to $5.68 per liter (since 1 liter is equal to 4 250-milliliter containers). Therefore, the cost of 3 liters (which is equivalent to 12 250-milliliter containers) is 12 x $1.42 = $17.04.

Therefore, Toby should buy 6 half-liter containers as it is the cheaper option.

Answer:

Step-by-step explanation:

50% of 366 is 183, therefore your answer is 366.

(a) Ann used 4/10 blue beads i.e. 80.

(b) Ann had 160 beads in the end.

The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

According to mathematicians, any real number may be expressed using the four basic operations, also referred to as "arithmetic operations." The four mathematical operations that produce quotient, product, sum, and difference, respectively, are divide, multiply, add, and subtract.

(a) We are given that Ann had a total of 285 red and blue beads, and she used 45 red beads and 40% of the blue bead.

Let the red beads be x and blue beads be y

So, we get

x + y = 285

x = 285 - y

After using the beads, we get another equation as

⇒(x - 45) / (y - 0.4y) = 1/3

⇒(285 - y - 45) / (y - 0.4y) = 1/3

⇒(240 - y) / (0.6y) = 1/3

⇒720 - 3y = 0.6y

⇒720 = 3.6y

⇒y = 200

So, x = 85

Blue beads used = 40% of 200 = 80

(b) Since, Ann has used 80 blue beads and 45 red beads, so

Beads in the end = 285 - 45 - 80 = 160

Hence, Ann had 160 beads in the end.

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Answer:   3

Step-by-step exp lanation:

divided

Answer:

Step-by-step explanation:

To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:

f(x) = A(x + 1/4)^2(x - 2/3)

where A is a constant that we need to determine to satisfy the condition f(0) = 2.

To find A, we substitute x = 0 into f(x) and set the result equal to 2:

f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2

Solving for A, we find that A = -54.

Therefore, the polynomial f(x) is:

f(x) = -54(x + 1/4)^2(x - 2/3)

Answer:

The ordered pair that is a solution is (2, 10)

Step-by-step explanation:

2x + 6 = 4x + 2  Subtract 2x from both sides

2x - 2x + 6 = 4x - 2x + 2

6 = 2x + 2  Subtract 2 from both sides

6 - 2 = 2x + 2 -2

4 = 2x  Divide both sides by 2

2 = x

Substitute 2 for x in either of the two original equations.

y = 2x + 6

y = 2(2) + 6

y = 4 + 6

y = 10

The ordered pair that is a solution is (2, 10)

The domain are the possible input while the range are the possible output of a function.

(a) The domain = [-√2, √2], the range = [0, 2]

(b) The domain = [-1, 1], the range = [0, 1]

(c) The domain = [-1, 1], the range = [0, -1]

(d) The domain = [0, 2], the range = [0, 1]

(e) The domain = [-(2 + √2), (√2 - 2)], the range = [0, 2]

Reasons:

The given functions can be expressed by the equation; (-x + 1)·(x + 1) = -x² + 1

Therefore, we have;

(a) y = f(x) + 1 = -x² + 1 + 1 = -x² + 2

The x-intercept of the above function are, x = √2, and x = -√2

Which gives;

The domain = [-√2, √2]

The range = [0, 2]

(b) y = 3·f(x) = 3 × (-x² + 1) = -3·x² + 3

At the x–intercepts, we have;

-3·x² + 3 = 0

x = ±1

The domain = [-1, 1]

The maximum value of y is given at x = 0, therefore;

= -3 × 0² + 3 = 3

The range = [0, 1]

(c) y = -f(x) = -(-x² + 1) = x² - 1

At the x–intercepts, x² - 1 = 0

x = ± 1

The domain = [-1, 1]

The minimum value of y is given at x = 0, which is y = -1

The range = [0, -1]

(d) y = f(x - 1) = -(x - 1)² + 1 = -x² + 2·x

At the x–intercepts, we have;  -x² + 2·x = 0, which gives;

(-x + 2)·x = 0

Which gives, x = 0, or x = 2

The domain = [0, 2]

The maximum value of y is given when x = -b/(2·a) = -2/(2×(-1)) = 1

y = f(1) =  -1² + 2×1 = 1

Therefore;

The range = [0, 1]

(e) y = f(x + 2) + 1 = (-(x + 2)² + 1) + 1 = -x² - 4·x - 2

At the x–intercepts, we have;  -x² - 4·x - 2 = 0, which gives;

x = -(2 + √2) or x = x = √2 - 2

The domain = [-(2 + √2), (√2 - 2)]

The maximum value of y is given when x = -4/(2)) = -2

Which gives;

-(-2)² - 4·(-2) - 2 = 2

The range = [0, 2]

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Answer: $2,850

Step-by-step explanation:

Hope this helped you. Brainliest if possible! :D

I also answered first! (Please don't copy my answer for anyone that answer this question!) :D

The equation of the ellipse in standard form is 16x² + 25y² = 400.

The standard form of the equation of an ellipse centered at the origin is:

x²/a² + y²/b² = 1

where a is the distance from the center to a vertex along the x-axis, and b is the distance from the center to a co-vertex along the y-axis.

In this case, we know that the center of the ellipse is at (0,0), a vertex is at (-5,0), and a co-vertex is at (0,4).

The distance from the center to a vertex along the x-axis is the absolute value of the x-coordinate of the vertex, which is 5. So, a = 5.

The distance from the center to a co-vertex along the y-axis is the absolute value of the y-coordinate of the co-vertex, which is also 4.

So, b = 4.

Substituting these values into the standard form equation, we get:

(x²/5²) + (y²/4²) = 1

Simplifying and multiplying by 5² and 4², we get the standard form equation of the ellipse:

16x² + 25y² = 400

Therefore, the equation of the ellipse in standard form is 16x² + 25y² = 400.

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Path z is the longest path that leads to the lake.

An algebraic expression is a combination of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division. It is a mathematical phrase that can contain one or more terms separated by mathematical operators.

For example, 3x + 4y - 2z is an algebraic expression that contains three terms: 3x, 4y, and -2z. Each term is made up of a coefficient and a variable, where the coefficient is the numerical value that multiplies the variable.

In algebraic expressions, variables are used to represent unknown values, and the expression can be evaluated by substituting known values for the variables. For instance, if x = 2, y = 3, and z = 1, then the expression 3x + 4y - 2z can be evaluated as 3(2) + 4(3) - 2(1) = 12.

Algebraic expressions can also include exponentiation, roots, and other advanced mathematical operations. They are widely used in mathematics and other fields, such as physics and engineering, to represent relationships between variables and to model real-world situations.

Let's start by assigning variables to each path:

Let x be the length of path x (in meters).

Then path y is 116 meters longer than path x, so its length is x + 116.

Path w is 51 meters shorter than path y, so its length is x + 116 - 51 = x + 65.

Path z is 85 meters longer than path w, so its length is x + 65 + 85 = x + 150.

To find the longest path, we need to compare the lengths of all four paths. We can do this by looking at the expressions we just derived:

Path x has length x.

Path y has length x + 116.

Path w has length x + 65.

Path z has length x + 150.

Since all four paths have a common component of x, the lengths of the paths can be compared by comparing the values of the expressions that add to x. We can see that x + 150 is the largest expression, which means that path z is the longest.

Therefore, path z is the longest path that leads to the lake.

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The answers to the probability problem have been stated below

The mean of the distribution would be 29

The standard deviation would be  8.7/√40 = 1.38

If the sample was larger, the mean would stay the same, the standard error would decrease.

3. The corresponding z score with

43.8 - 29 / 8.7

= 1.70

b. z = (43.8-29)/(8.7/√40) = 8.94

14.8 /1.38

= 10.7

c) the fisherman is more likely to catch one fish

d) z = (30.8-29)/(8.7/√40) = 1.26

= 1.8 / 1.38

= 1.304

e) He is more likely to catch 40 fishes.

4.a) Proportion in the middle = 0.95

Proportion on left and right side of normal curve = (1-0.95)/2

= 0.025

Z score at p = 0.025 using excel = NORM.S.INV(0.025) = 1.96

X1 = µ - z*σ = 29 - (1.96)*8.7

= 11.948

X2 = µ + z*σ = 29 + (1.96)*8.7

= 46.052

between 11.948 and 46.052

b)

Proportion in the middle = 0.95

Proportion on left and right side of normal curve = (1-0.95)/2 = 0.025

NORM.S.INV(0.025) = 1.96

x1 =  29 - (1.96)*8.7/√40

= 29 - 2.698

= 26.30

x2 = 29 + 2.698

= 31.698

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Answer:

the wholesale discount is 28%.

Step-by-step explanation:

To find the wholesale discount, we need to calculate the difference between the retail price and the wholesale price as a percentage of the retail price. We can use the following formula:

Wholesale discount = ((Retail price - Wholesale price) / Retail price) x 100%

Substituting the given values into the formula, we get:

Wholesale discount = ((1320 - 950.40) / 1320) x 100%

Wholesale discount = (369.60 / 1320) x 100%

Wholesale discount = 0.28 x 100%

Therefore, the wholesale discount is 28%.

To write the answer as a whole number or an exact decimal, we can multiply 0.28 by 100 to get:

Wholesale discount = 28%

So the wholesale discount is 28%.

Answer:

7:11

28:44

Step-by-step explanation:

Multiply both sides by 4.

The correct statement regarding the association of the time the player spent practicing and the number of points he scored in the game is given as follows:

As the time a basketball player practices increases, the number of points scored in a game increases with a strong nonlinear association.

The more the player practices, the better he/she performs, that is, the more points are scored, hence the number of points increases as the number of hours practiced increase.

However, there reaches a certain threshold where the player is as good as possible, hence the points tend to stabilize, meaning that there is a nonlinear association between the variables.

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Answer:

Step-by-step explanation:

Pour trouver la forme standard de l'équation d'une ellipse à partir des extrémités des grands axes et des petits axes, nous pouvons utiliser les formules suivantes:

Le centre de l'ellipse est le point (h, k), où h est la moyenne des coordonnées x des extrémités des grands axes et k est la moyenne des coordonnées y des extrémités des petits axes. Donc,

h = (2 + 8) / 2 = 5

k = (3 + 1) / 2 = 2

Donc, le centre de l'ellipse est (5, 2).

La distance a est la moitié de la longueur du grand axe, donc

a = (8 - 2) / 2 = 3

La distance b est la moitié de la longueur du petit axe, donc

b = (3 - 1) / 2 = 1

Maintenant, nous pouvons utiliser ces valeurs pour écrire l'équation de l'ellipse en forme standard:

(x - h)^2 / a^2 + (y - k)^2 / b^2 = 1

En substituant les valeurs trouvées précédemment, nous avons:

(x - 5)^2 / 3^2 + (y - 2)^2 / 1^2 = 1

Ce qui est la forme standard de l'équation de l'ellipse.

The simplified expression for this problem is given as follows:

-3(x + y) = -3x - 3y.

With the application of the distributive property, the outer term multiplies each of the inner terms of the expression. If possible, these inner terms than can be added or subtracted combining the like terms.

For this problem, the outer term -3 multiplies both of the inner terms, x and y, hence:

Hence the simplified expression is defined as follows:

-3(x + y) = -3x - 3y.

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Answer:

the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.

Step-by-step explanation:

The total number of ways to choose 5 cards from a deck of 52 cards is given by the combination formula:

C(52, 5) = 52! / (5! (52 - 5)!) = 2,598,960

Now, we need to count the number of ways of choosing 5 cards from the same suit. There are 4 suits in a deck of cards (hearts, diamonds, clubs, and spades), so we need to count the number of ways to choose 5 cards from each of these suits and add them up.

For each suit, the number of ways of choosing 5 cards from that suit is given by the combination formula:

C(13, 5) = 13! / (5! (13 - 5)!) = 1,287

So the total number of ways of choosing 5 cards from the same suit is:

4 * 1,287 = 5,148

Therefore, the probability of getting 5 cards from the same suit is:

5,148 / 2,598,960 ≈ 0.00198

So the probability of being dealt 5 cards from the same suit is approximately 0.00198, or about 0.198%.

The equations that determine the cost of each hamburger and each fries is 4x + 5y = 20 and 10x + 7y = 41.20

An equation is an expression that shows the relationship between two numbers and variables using mathematical operations like addition, subtraction, multiplication, exponents

Let x represent the cost of each hamburger and y represent the cost of each fries.

She purchased 4 hamburgers and 5 fries for $20.00, hence:

4x + 5y = 20    (1)

She purchased 10 hamburgers and 7 fries for $41.20, hence:

10x + 7y = 41.20   (2)

From both equations, solving simultaneously:

x = 3; y = 1.6

The cost of each hamburger is $3 while the cost of each fries is $1.6

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The values of m for the given inequality should be in the interval

(-∞, -18/19).

What is meant by inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. Typically, we use the "not equal" sign to indicate that two values are not equal. However several inequalities are utilised to compare the numbers, whether it is less than or higher than.

Given the inequality,

8m + 95 < -87m +5

We are asked to solve the inequality.

this means we have to find the value of m.

8m + 95 < -87m +5

8m + 87m < 5 - 95

95m < -90

m < -90/95

m< -18/19

Therefore the values of m for the given inequality should be in the interval (-∞, -18/19).

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Answer:

Step-by-step explanation:

line a is 5ft

The regression equation is y = 1.56 + 0.69⋅x².

Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

x: 4 5 6 6 9

y: 3 6 5 7 7

Σx=28, ΣΥ=27, Σxy = 163, Σx' = 174

a = ΣΥ ΣΑΣΑ Σ ΑΥ = 27-174-28-163 = 1.558

b= 5.163 28 27 /5-174-(28)2 = 0.686

y = 1.558 + 0.686x²

Hence, The regression equation is y = 1.56 + 0.69⋅x².

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