The result is (x + 8).
What is a polynomial?Polynomial is an equation written with terms of the form kx^n.
where k and n are positive integers.
There are quadratic polynomials and cubic polynomials.
Example:
2x³ + 4x² + 4x + 9 is a cubic polynomial.
4x² + 7x + 8 is a quadratic polynomial.
We have,
x² + 12x + 32 and g(x) = x + 4.
Now,
(f/g)(x)
= (x² + 12x + 32) / (x + 4) _____(1)
Now,
We can factorize x² + 12x + 32.
x² + 12x + 32
= x² + (8 + 4)x + 32
= x² + 8x + 4x + 32
= x(x + 8) + 4(x + 8)
= (x + 4) (x + 8) ______(2)
From (1) and (2),
(f/g)(x)
= (x² + 12x + 32) / (x + 4)
= (x + 4) (x + 8) / (x + 4)
= x + 8
Thus,
The result is (x + 8).
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2x _ 2 +9x _−5 . factor trinomials (a>1) level 2
The factored form of the given trinomial as required in the task content is; (2x - 1) (x + 5).
What is the factored form of the given trinomial?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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HURRY PLEASE LIKE TODAY
What could you multiply the second (purple) equation by to make the y-values additive inverses?
-2 is to be multiplied in the second equation to make the y-values additive inverses.
What are 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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Tony has a rectangular piece of cardboard that will have congruent squares removed from its corners with a length of 3 inches. The length of the piece of cardboard is four times larger than its width. Tony also know that the volume of the box he is able to create from this piece of cardboard is 336 cubic inches. What are the dimension of this box?
The dimensions of the box are given as follows:
Length of 3 inches.Width of 0.75 inches.Height of 149.3 inches.How to obtain the volume of the rectangular prism?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:
Length of 3 inches.Width of 1/4 x 3 = 0.75 inches.Volume of 336 cubic inches.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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For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0.75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0.75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.For your birthday, you received a $15 gift card to your favorite arcade. All of the games at the arcade cost $0.75. Complete the equation to represent the total amount of money, m, remaining on the gift card after playing g arcade games.
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.
What are equation models?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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Camden went to the grocery store and purchased cans of soup and frozen
dinners. Each can of soup has 150 mg of sodium and each frozen dinner has
300 mg of sodium. Camden purchased a total of 7 cans of soup and frozen
dinners which collectively contain 1500 mg of sodium. Graphically solve a
system of equations in order to determine the number of cans of soup
purchased, x, and the number of frozen dinners purchased, y.
Camden purchased 4 cans of soup and 3 frozen dinners.
How to solve for thisWe 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 grade you earn in math varies inversely with the number of minutes per night you watch TV. If you watch 90 minutes of TV per night, you get a 60% in math. How much TV can you watch to get a 70% in math?
The number of minutes that you watch TV to get a 70% in math will be 77.14 minutes.
What are ratio and proportion?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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-8a+32b in distributive property
-8a + 32b using the distributive property as 8(-a + 4b).
What is Expression?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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what's the domain and range of the function f(x) = 5(4)^x + 2
The required domain and range of the function are (-∞, ∞) and (2, ∞).
How to find the domain and range of the function?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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Write the sentence as an equation.
the quotient of j and 11 is equal to 367
Type a slash (/) if you want to use a division sign.
Submit
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
What is the area of a square with side lengths of 3/5
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
comment savoir si un graphique est proportionnelle ?
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:
The diagram shows the relative positions of three MRT stations.
Find the bearing of
(a) W from O
(b) O from CA
(c) CA from W
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).
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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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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25 points! write the radical ³√32m³ using rational exponents
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.
I need to find the table for a parabola and the equation is
y=-2x^2+8x
The table for the parabola is
x y
-2 24
0 0
2 8
4 0
6 -24
How to create the table for the parabolaTo 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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y=3.8x10 [tex]x^{5}[/tex]
What is 0.25 as an improper fraction?
Answer:
1/4
Step-by-step explanation:
0.25 * 4 = 1
so, 1/4 = 0.25
Agustín pagó $ 120 por una carpeta y dos paquetes de hojas; mientras que Mauricio pagó $ 190 por
costo de una carpeta y de un paquete de hojas. Después resuelve dicho sistema.
tres paquetes de hojas y dos carpetas. Plantea un sistema de ecuaciones que permita calcular el costo de una carpeta y de un paquete de hojas
Ayúdenme por favor
The cost of a folder is: $20
The cost of a package of sheets is $50.
How do we calculate cost of each folder and pack of sheets?The system of equations with variables:
C: number of foldersQ: number of packs of sheets
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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In AVWX, the measure of ZX=90°, XW = 3, WV = 5, and VX = 4. What is the value of
the tangent of ZW to the nearest hundredth?
(x + 3)^2 Write your answer as a list of values separated by commas.
The values are written in commas as x², 6x and 9
How to determine the valuesIt 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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what is the definition of opposite rays in geometry
Answer:
Opposite rays point in opposite directions and therefore make a 180-degree angle with each other.
Step-by-step explanation:
1. 3x3 2x2 y 4x2 y is equivalent to:
a. 9x7 y 2 b. 9x12 y 2 c. 24x7 y 2 d. 24x12 y e. 24x12 y
Option C is correct, the expression 24x⁷y² is equivalent to 3x³. 2x²y. 4x²y.
What is Expression?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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5.) 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. Today she
white tint to 3 gallons of base paint. Explain the error in her reasoning. says that she should add 9 parts red tint and 2 parts
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.
What is error?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.
Divide 3x³ - 2x² + 4x - 3 by x² + 3x + 3.
The solution to the division 3x³ - 2x² + 4x - 3 divided by x² + 3x + 3 is: 3x - 11 ( 28x + 30) / (x² + 3x + 3).
What is the quotient of the long polynomial division?
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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Consider the equation
2x + 3y - 6 - 3z + 4y - 6x = 4x + 2y = 4z + 10
a. How many terms are there in this equation?
b.
What are the variables in this equation?
c.
What are the constants in this equation? (hint: constants are the numbers that
are "unattached" to variables)
d. Combine the like terms on the left side of the equation. What are the coefficients
of the variables? (hint: the coefficients are the numbers that multiply the
variable-for example, in 6x, 6 is the coefficient)
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
How many terms are there in this equation?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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2. Simplify the expression below by multiplying and then grouping like terms. Please look at CW # 4.11 or
# 4.12 if you need help!
2y + 3x +42x+5y-3y - 5x
The simplification of the expression gives 40x + 4y
How to simplify an expressions?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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35 cm
What is the volume of the solid shown above?
1 cm
3 cm
The volume of the solid shown can be found to be 105 cm ³ .
How to find the volume ?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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What are the basic means of differentiation?
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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C is the circumcenter of isosceles triangle ABD with vertex angle ∠ABD. Does the following proof correctly justify that triangles ABE and DBE are congruent?
It is given that triangle ABD is an isosceles triangle, so segments AB and DB are congruent by the definition of isosceles triangle.
It is given that C is the circumcenter of triangle ABD, making segment BE a median.
By the definition of perpendicular, angles AEB and DEB are 90°, so triangles ABE and DEB are right triangles.
Triangles ABE and DEB share side BE making it congruent to itself by the reflexive property.
Triangles ABE and DBE are congruent by HL.
Triangle ABD with segments BC, DC, and AC drawn from each vertex and meeting at point C inside triangle ABD, segment BC is extended past C with dashed lines so that it intersects with side AD at point E.
There is an error in line 1; segments AB and BD are given to be congruent.
There is an error in line 2; segment BE should be a perpendicular bisector.
There is an error in line 4; segment BE is not a shared side.
The proof is correct.
The proof is not correct.
How did we arrive at this assertion?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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If aΔb=a² + ab + b², then what is the value of -3Δ5?
A. 4
B. -14
C. -7
D. 1
E. 19
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 value of y varies directly with x. if y = 20 and x = 30, what is the value of y if x = 1?
A. 200
B. 2/3
C. 110/3
D. 9/2
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