x^2 + 12x + 32 and g(x) = x + 4, find (f/g)(x) and express the result as a polynomial in simplest form.

The cost of a folder is: $20

The cost of a package of sheets is $50.

The system of equations with variables:

Juan paid 120 pesos for a folder and 2 packages of sheets:

C + 2P = 120

Clearing C:

C = 120 - 2P

Manuel paid 190 pesos for 3 packages of sheets and 2 folders:

2C + 3P = 190

Substituting the "C":

2 * (120 - 2P) + 3P = 190

240 - 4P + 3P = 190

-P = 190 - 240

-P = -50

P = $50

The price for a folder is:

C = 120 - 2 * 50

C = $20

Translated question "Juan paid 120 pesos for a folder and 2 packages of sheets while Manuel paid 190 pesos for 3 packages of sheets and 2 folders.Calculate the cost of a folder and a package of sheets."

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Option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.

An expression is combination of variables, numbers and operators.

The given expression is 3x³. 2x²y. 4x²y.

We need to find the equivalent expression of the given expression.

Equivalent expressions are expressions that work the same even though they look different.

(3×2×4)x³. x²y. x²y.

24x³. x²y. x²y.

When bases are same then the powers will be added.

24x⁷y²

Hence, option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.

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The bearing are as follows:

(a) W from O = 70 degree south by east

(b) O from CA = 17 degree south by west

(c) CA from W = 21 degree west by north

What is angle ?

In geometry, an angle is the measure of the amount of rotation between two intersecting lines or surfaces, typically measured in degrees or radians.

An angle is formed when two lines or surfaces intersect at a point, which is called the vertex of the angle. The two lines or surfaces that form the angle are called the arms or sides of the angle. Angles are usually denoted using the vertex point, with a small angle symbol (such as ∠ABC).

Corresponding angles are a pair of angles that are in the same relative position at two different intersections of a line and a pair of parallel lines. In other words, if two parallel lines are intersected by a third line (called a transversal), then any pair of angles that are in the same position relative to the parallel lines are corresponding angles.

a. 70 degree south by east

b. 17 degree south by west

c. 21 degree west by north

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AThe bearing are as follows:

(a) W from O = 70 degree south by east

(b) O from CA = 17 degree south by west

(c) CA from W = 21 degree west by north

What is angle ?

In geometry, an angle is the measure of the amount of rotation between two intersecting lines or surfaces, typically measured in degrees or radians.

An angle is formed when two lines or surfaces intersect at a point, which is called the vertex of the angle. The two lines or surfaces that form the angle are called the arms or sides of the angle. Angles are usually denoted using the vertex point, with a small angle symbol (such as ∠ABC).

What is corresponding angle ?

Corresponding angles are a pair of angles that are in the same relative position at two different intersections of a line and a pair of parallel lines. In other words, if two parallel lines are intersected by a third line (called a transversal), then any pair of angles that are in the same position relative to the parallel lines are corresponding angles.

According to given conditions :

a. 70 degree south by east

b. 17 degree south by west

c. 21 degree west by north

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Answer:

1/4

Step-by-step explanation:

0.25 * 4 = 1

so, 1/4 = 0.25

Answer: j/11 = 367

Step-by-step explanation:

Keywords: QUOTIENT. Quotient indicates a division answer. The quotient, in this case, is 367.

It also makes sense that j is the dividend and 11 is the divisor.

---
For the SOLVED version: j = 4037.
Multiply 11 on both sides, canceling the 11 on one side and getting 4037 when you multiply 11 by 367.

Answer:

J/11 = 367; this is the equation as When J is divided by 11 it answers to 367

Step-by-step explanation:

total answer;

J = 367(11)

J= 4037

-2 is to be multiplied in the second equation to make the y-values additive inverses.

Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.

Given are two equations,

3x-4y = -5.....(i)

5x-2y = -6.....(ii)

We need to find the additive inverse of y variable,

The coefficients of y variables in the both equations are ;-

-4 and -2

The additive inverse of -4 is 4,

If we multiply -2 by -2 it becomes 4,

Hence, -2 is to be multiplied in the second equation to make the y-values additive inverses.

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The simplification of the expression gives 40x + 4y

Simplification is a way of determining an answer for a complex calculation that may involve numbers on division, multiplication, square roots, cube roots, plus and minus, etc.

The expression 2y + 3x +42x+5y-3y - 5x can be simplified by adding or subtracting like terms. That is:

2y + 3x +42x+5y-3y - 5x = 3x +42x- 5x + 5y-3y + 2y

                                         = 40x + 4y

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-8a + 32b using the distributive property as 8(-a + 4b).

An expression is combination of variables, numbers and operators.

To express -8a + 32b using the distributive property, we need to factor out the greatest common factor that the terms share.

The greatest common factor of -8a and 32b is 8.

-8a + 32b

= 8(-a + 4b)

Using the distributive property, we can check that this expression is equivalent to the original:

8(-a + 4b) = 8(-a) + 8(4b) = -8a + 32b

Therefore, we can express -8a + 32b using the distributive property as 8(-a + 4b).

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Answer:

B. 2/3

Step-by-step explanation:

If y directly varies with x, then y = kx where k is a constant

Given that when y = 20 when x = 30 we get the equation: 20 = k x 30

or

20 = 30k

Dividing by 30 both sides and switching sides gives

k = 20/30 = 2/3

The equation becomes
y = 2/3 x

Therefore if x = 1 we get

y = 2/3 x 1 = 2/3

Choice B

The number of minutes that you watch TV to get a 70% in math will be 77.14 minutes.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The grade you earn in math varies inversely with the number of minutes per night you watch TV.

We know that in inverse proportionality, the product of grade and number of minutes remains constant.

Let 'N' be the number of minutes. Then the equation is given as,

70N = 90 × 60

70N = 5,400

N = 77.14 minutes

The number of minutes that you watch TV to get a 70% in math will be 77.14 minutes.

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The table for the parabola is

x y

-2 24

0 0

2 8

4 0

6     -24

To create a table for a parabola with equation y = -2x^2 + 8x, we can simply plug in values of x and solve for y.

with x-values from -2 to 6,:

For x = -2, y = -2(-2)^2 + 8(-2) = -24

For x = 0, y = -2(0)^2 + 8(0) = 0

For x = 2, y = -2(2)^2 + 8(2) = 8

For x = 4, y = -2(4)^2 + 8(4) = 0

For x = 6, y = -2(6)^2 + 8(6) = -24

To plot the parabola on a graph, we can plot the points from the table and draw a smooth curve through them. The graph of y = -2x^2 + 8x looks like a downward-facing parabola with its vertex at the point (2, 8).

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Camden purchased 4 cans of soup and 3 frozen dinners.

We can solve this problem by using a system of two linear equations.

Let x be the number of cans of soup purchased and y be the number of frozen dinners purchased.

Then, based on the information given, we can set up two equations as follows:

150x + 300y = 1500 (the total amount of sodium consumed is 1500 mg)

x + y = 7 (Camden purchased 7 cans of soup and frozen dinners)

Now, we can use either substitution or elimination to find the values of x and y.

Using substitution:

Solve the second equation for y: y = 7 - x

Substitute the expression for y into the first equation: 150x + 300(7 - x) = 1500

Simplify the expression: 150x + 2100 - 300x = 1500

Combine like terms: -150x + 2100 = 1500

Solve for x: -150x = -600

Divide both sides by -150: x = 4

Use the second equation to find y: y = 7 - x = 7 - 4 = 3

So, Camden purchased 4 cans of soup and 3 frozen dinners.

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The volume of the solid shown can be found to be 105 cm ³ .

The volume of the solid can be found by the formula :

= Length x Width x Height

This is because this is a rectangular prism and their volumes require multiplying the sides of the rectangle in the above manner .

The volume of the solid is therefore:

= 35 x 1 x 3

= 35 x 3

= 105 cm ³

In conclusion, the volume of the solid would be 105 cm ³ .

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The solution to the division 3x³ - 2x² + 4x - 3 divided by x² + 3x + 3 is: 3x - 11  ( 28x  +  30) / (x² + 3x + 3).

The division of the polynomial 3x³ - 2x² + 4x - 3 by the polynomial x² + 3x + 3 can be performed using polynomial long division.

Here's the steps for long division:

                     3x - 11    

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

x² + 3x + 3 √ (3x³ - 2x² + 4x - 3 )

                  -  (3x³ + 9x² + 9x )

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

                                -11x² - 5x - 3

                           -  ( -11x² - 33x - 33 )

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

                                          28x  +  30

Thus, the solution to the division 3x³ - 2x² + 4x - 3 divided by x² + 3x + 3 is: 3x - 11  ( 28x  +  30) / (x² + 3x + 3)

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Answer:

Opposite rays point in opposite directions and therefore make a 180-degree angle with each other.

Step-by-step explanation:

There are 10 terms in the equation

The variables are x, y, z

The constants in this equation are -6, 10

The coefficients of the variables of the equation are; 8, 7 and -3

2x + 3y - 6 - 3z + 4y - 6x = 4x + 2y - 4z + 10

The left side of the equation is;

2x + 3y - 6 - 3z + 4y - 6x

= 2x - 6x + 3y + 4y - 3z - 6

= 8x + 7y - 3z - 6

Therefore, the coefficients of the variables on the left side of the equation are; 8, 7 and -3

Variables are unknown numbers usually represented by letters or symbols.

The constant are numbers that cannot change its value

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The proof is not correct.

The given information that segments AB and BD are congruent does not imply that triangles ABE and DBE are congruent. Congruency of triangles requires more information, such as additional side lengths or angle measures.

While it is true that point C is the circumcenter of triangle ABD and that segment BE is a median, it is not necessarily true that BE is also a perpendicular bisector. In fact, this would only be true if triangle ABD were also an equilateral triangle.

The statement that triangles ABE and DEB share side BE is incorrect. Triangles ABE and DEB do not share any sides, but rather have segment BE as a common hypotenuse.

Therefore, the conclusion that triangles ABE and DBE are congruent by HL (hypotenuse-leg) is not valid since the previous steps in the proof are flawed.

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In mathematics, differentiation refers to the process of finding the derivative of a function. The basic means of differentiation include:

Limit definition: The derivative of a function is defined as the limit of the difference quotient as the interval over which the quotient is taken approaches zero.

Power rule: The derivative of a function of the form f(x) = xⁿ is given by f'(x) = nx⁽ⁿ⁻¹⁾

Product rule: The derivative of a product of two functions u(x) and v(x) is given by (u × v)'(x) = u'(x) × v(x) + u(x) × v'(x).

Quotient rule: The derivative of a quotient of two functions u(x) and v(x) is given by (u/v)'(x) = [u'(x) × v(x) - u(x) × v'(x)] / v(x)².

Chain rule: The derivative of a composition of functions f(g(x)) is given by f'(g(x)) × g'(x).

These basic means of differentiation are essential tools for analyzing and modeling functions in calculus and related fields.

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The required domain and range of the function are (-∞, ∞) and  (2, ∞).

The domain of a function is the set of all possible values of the input variable (x) for which the function is defined. In this case, the function is an exponential function with base 4, which means it is defined for all real numbers.

Therefore, the domain of f(x) is all real numbers, or (-∞, ∞).

The range of a function is the set of all possible values of the output variable (f(x)) for all possible values of the input variable (x).

Since 4^x is always positive (for all x), the value of the function f(x) will always be greater than 2 (the constant added to 5(4)^x), no matter what the value of x is.

As x approaches negative infinity, 5(4)^x approaches zero, so the minimum value of f(x) is 2.

As x approaches positive infinity, 5(4)^x increases without bound, so the range of f(x) is (2, ∞).

Thus, required domain and range of the function are (-∞, ∞) and  (2, ∞).

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The dimensions of the box are given as follows:

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

The parameters for this problem are given as follows:

Hence the height of the cardboard is given as follows:

3 x 0.75 x h = 336

h = 336/(3 x 0.75)

h = 149.3 inches.

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Answer:

E) 19

Step-by-step explanation:

To find the value of -3Δ5, we need to substitute -3 and 5 into the equation: aΔb = a² + ab + b².

So, we have:

-3Δ5 = (-3)² + (-3)(5) + (5)²

= 9 - 15 + 25

= 19

Therefore, the answer is E) 19.

The factored form of the given trinomial as required in the task content is; (2x - 1) (x + 5).

It follows from the task content that the factored form of the trinomial 2x² + 9x - 5 is to be determined.

Therefore, the factorisation is as follows;

2x² + 10x - x - 5

2x (x + 5) -1 (x + 5)

(2x - 1) (x + 5)

Ultimately, the factored form of the trinomial is; (2x - 1) (x + 5).

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Answer:

Pour savoir si un graphique est proportionnel, il faut vérifier si les valeurs de la variable indépendante (l'axe des x) sont proportionnelles aux valeurs de la variable dépendante (l'axe des y). Cela signifie que si on multiplie les valeurs de la variable indépendante par un facteur constant, les valeurs de la variable dépendante seront également multipliées par ce même facteur constant.

Un moyen de vérifier si un graphique est proportionnel est de tracer une ligne droite à travers les points de données. Si tous les points se trouvent sur cette ligne droite, alors le graphique est proportionnel. Si les points ne se trouvent pas sur une ligne droite, alors le graphique n'est pas proportionnel.

Il est également possible de calculer le coefficient de proportionnalité en divisant chaque valeur de la variable dépendante par la valeur correspondante de la variable indépendante. Si le résultat est constant pour toutes les paires de valeurs, alors le graphique est proportionnel.

Enfin, il convient de noter que la proportionnalité n'est qu'un type de relation entre deux variables et que d'autres types de relations peuvent exister, tels que les relations exponentielles, logarithmiques ou quadratiques.

Step-by-step explanation:

Answer: 0.36

Step-by-step explanation:

A=L*W

Since all sides of a square is the same you just do 3/5(3/5) which is 0.36 or 9/25

The required equation model the situation total amount of money, m, remaining on the gift card after playing g arcade games as m = $15 - 0.75g.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's start by representing the total amount of money spent on playing arcade games as 0.75g.

Since the gift card has a value of $15, the total amount of money remaining on the gift card after playing g games can be represented as:

m = $15 - 0.75g

This equation represents the total amount of money remaining on the gift card after playing g games, where m is the remaining amount and g is the number of games played.

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The values are written in commas as x², 6x  and 9

It is important to note that algebraic expressions are expressions that are made of terms, variables, coefficients, factors and constants.

From the information given, we have the quadratic expression as:

(x + 3)^2

Now, take the following steps to determine the values

(x + 3)(x +3)

expand the bracket, we get;

x² + 3x + 3x + 9

Now, collect the like terms and add the values

x² + 6x + 9

Hence, the value is x² + 6x + 9

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Your friend's mistake when wanting to make a new mixture of pink paint is that she is only going to add 2 parts of white paint, the correct formula would be 3.

Error is, the difference between a true value and an estimate, or approximation, of that value.

Given that, yesterday your friend made needs to make 3 more gallons of the same shade. She 1 gallon of dark pink paint using the information in the table, (attached in solution)

The calculation of how much paint you need to make 3 gallons of Pink paint :-

To mix 3 gallons of pink paint we must take into account the following information:

1 gallon of pink paint is equal to 3 parts red paint and 1 part white paint.

To find out how many parts we need to prepare 3 gallons of pink paint we must multiply the mix values for a gallon by 3.

Red paint:

3 x 3 = 9

White paint:

1 x 3 = 3

We need to use 3 parts white paint and 9 parts red paint to make 3 gallons of pink paint.

Hence, She needs to add 3 parts of white paint and 9 parts of red paint. The error is she added 2 parts of white paint.

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The question is incomplete so, I attached the graph.

Answer:

To write the radical ³√32m³ using rational exponents:

1. Rewrite the radical using exponential notation: 32m^3 ≈ 8m^3.

2. Convert the exponent into its equivalent fractional form: 8m^3 ≈ 2^3m^3/2^3.

3. Apply a rational exponent to the numerator: (2^3m^3)^(1/3)/2^3 = 2m.

4. The radical can now be written using rational exponents: (2m)^3/2^3.