Yes, x +3 is a factor of polynomial X³ +3x² -4x -12
Polynomial:
In mathematics, a polynomial is an expression which includes indeterminates (also called variables) and coefficients, that entails handiest the operations of addition, subtraction, multiplication, and effective-integer powers of variables. An instance of a polynomial of a single indeterminate x is x² − 4x + 7. An example with 3 indeterminates is
x³ + 2xyz² − yz + 1.
Polynomials appear in lots of areas of arithmetic and technological know-how. For example, they're used to form polynomial equations, which encode a wide range of issues, from elementary word troubles to complicated clinical issues; they may be used to outline polynomial functions, which seem in settings ranging from basic chemistry and physics to economics and social science; they're utilized in calculus and numerical analysis to approximate other features. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which can be primary concepts in algebra and algebraic geometry.
Factor out the greatest common factor from each group.
Group the first two terms and the last two terms.
(x³ + 3x²)− 4x− 12
Factor out the greatest common factor (GCF) from each group.
x²(x+3)−4(x+3)
Factor the polynomial by factoring out the greatest common factor,
x+3.(x+3)(x2−4)
Rewrite
4 as 2².
(x+3)(x²−2²)
Since both terms are perfect squares, factor using the difference of squares formula,
a²−b²=(a+ b)(a−b)
where
a = x and b = 2.
(x+3)[(x+2)(x-2)]
Remove unnecessary parentheses.
(x+3)(x+2)(x−2)
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Which theory would be an example of discontinuity?
Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. Examples include Piaget’s stages of cognitive development and Erikson’s psychosocial stages.
Discontinuity function is an explanation of development that emphasizes sudden changes or shifts, rather than gradual progressions, in development. This theory suggests that development does not occur in an orderly, linear fashion, but instead involves abrupt changes in which an individual moves from one distinct stage to the next. Examples of discontinuity theory include Piaget’s stages of cognitive development and Erikson’s psychosocial stages, which are made up of distinct stages of development that an individual must progress through before reaching the next stage. According to discontinuity theory, development is not a gradual, continuous process, but rather is made up of distinct stages with abrupt changes in between. This theory has been useful in helping to explain the development of various aspects of an individual, such as cognitive, social, and emotional development.
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Does △abc appear to be the same size and shape as △xyz? explain.
Yes, △ ABC appears to be the same size and shape as △ XYZ by SAS similarity, and △ ABC can be mapped by translation and rotation, so option A is correct
What is triangle?
Simple polygons with three sides and three internal angles make up triangles. One of the fundamental geometric shapes, it is represented by the symbol and consists of three connected vertices.
Right triangles ABC and XYZ. ABC has a shorter leg equal to 5 and a hypotenuse equal to 13,
The triangles ABC and XYZ are similar by SAS similarity, as,
AC = XZ = 5,
AB = YZ = 13
∠ ACB = ∠ XZY
When you translate and then rotate triangle ABC, you will get triangle XYZ.
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What is the angle opposite to the side lm of LMN?
In the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.
What do we mean by angles?
An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.
The Latin word "angulus," which means "corner," is the source of the English term "angle."
The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.
So, according to the given figure, the angle opposite to side LM in triangle LMN is ∠n.
Therefore, in the triangle LMN, the angle opposite side LM is indicated by the supplied figure as being ∠N.
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Solve for the constant of variation, k. z varies jointly as x and y. x = 3, when y = -8 and z = 6.
Answer:
k = -0.25
Step-by-step explanation:
If z varies jointly, that means z = k * x * y
putting in the numbers it gives us,
6 = k * (3) * (-8)
6 = k * (-24)
k = -(1/4) = -0.25
help me again sorry if I am like.....
Answer:
6. X, Y and Z are different numbers. X is a factor of Y. Z is a multiple of Y. Which of the following is DEFINITELY true?
B. Z is divisible by X7. The following graph shows Vinit's journey as he cycled from his home to a park, 4 kilometers away in 800 seconds. Which of these can be said based on this graph?
B. He stopped at a place in between for 50 seconds,8. How many TENS must be added to 7 000 to make it 70 000.
(70 000 - 7 000) / 10 = 6 300C. 6 300Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-solve the logarithmic equation. log 10 (x raise to power 2 - 4x )=2
Answer:
[tex]x=2+2\sqrt{ 26}[/tex]
[tex]x=2-2\sqrt{ 26}[/tex]
Step-by-step explanation:
Given logarithmic equation:
[tex]\log_{10}(x^{2}-4x)=2[/tex]
[tex]\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b[/tex]
[tex]\implies 10^2=x^2-4x[/tex]
[tex]\implies 100=x^2-4x[/tex]
[tex]\implies x^2-4x=100[/tex]
Add the square of half the coefficient of the term in x to both sides of the equation:
[tex]\implies x^2-4x+\left(\dfrac{-4}{2}\right)^2=100+\left(\dfrac{-4}{2}\right)^2[/tex]
[tex]\implies x^2-4x+\left(-2\right)^2=100+\left(-2}\right)^2[/tex]
[tex]\implies x^2-4x+4=100+4[/tex]
[tex]\implies x^2-4x+4=104[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex]\implies (x-2)^2=104[/tex]
Square root both sides:
[tex]\implies x-2=\pm \sqrt{104}[/tex]
[tex]\implies x-2=\pm \sqrt{4 \cdot 26}[/tex]
[tex]\implies x-2=\pm \sqrt{4} \sqrt{ 26}[/tex]
[tex]\implies x-2=\pm 2\sqrt{ 26}[/tex]
Add 2 to both sides:
[tex]\implies x=2\pm 2\sqrt{ 26}[/tex]
Therefore, the solutions are:
[tex]x=2+2\sqrt{ 26}[/tex][tex]x=2-2\sqrt{ 26}[/tex]What is the factor of x³ 13x² 32x 20?
The factors are (x + 1)(x + 2)(x + 10)
What is Factorization?The process of breaking down an entity—for instance, a number, a matrix, or a polynomial—into a product of another entity—or factors—that, when multiplied together, yield the original number, matrix, or other entity is referred to as factorization or factoring.
Given Equation x³ + 13x² + 32x + 20
so The value of x³ + 13x² + 32x + 20 is
x³ + x² + 12x² + 12x + 20x + 20
=x² (x+1) + 12x (x+1) + 20(x+1)
=(x + 1)(x² + 12x + 20)
=(x + 1)(x² + 10x + 2x + 20)
=(x + 1)[x(x + 10) + 2(x + 10)]
=(x + 1)(x + 2)(x + 10)
Hence the factors are (x + 1)(x + 2)(x + 10).
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The correct question is
Factorize x³ + 13x² + 32x + 20
3 more, please answer question
The required value of the C in the algebraic measure of the angles is 61.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
here,
The property of the triangle states that the sum of the remote interior angles is equal to the exterior angle,
So, adding c - 18 and c -15 will be equal to c +28
c - 18 + c - 15 = c + 28
c = 28 + 33
c = 61
Thus, the required value of the C in the algebraic measure of the angles is 61.
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Write the equation of the line of fit.
y = 5x+20 Carlos plays the game for 25 minutes. Use the
equation of the line of fit to predict his score.
Answer:
145
Step-by-step explanation:
y = 5(25) + 20
y = 125 + 20
y = 145
Find the distance between the two points rounding to the nearest tenth (if necessary). (-7, 0) and (-3, 8)
Answer: 8.9 units
Step-by-step explanation:
We can use the distance formula for a 2d plane:
distance = √[tex](x_2 - x_1)^2 + (y_2 - y_1)^2[/tex]
Plugging in our values for x1, y1, x2, and y2:
x1 = -7
y1 = 0
x2 = -3
y2 = 8
√[tex](-3 - -7)^2 + (8 - 0)^2[/tex]
= √[tex](4)^2 + (8)^2[/tex]
= √[tex]16 + 64[/tex]
= √[tex]80[/tex]
= [tex]8.944271921[/tex]
= 8.9 rounded to the 10th
I need help at math
Answer:
The answer for the problem on the left is 70
The answer to the problem on the right is 120
Step-by-step explanation:
Left Problem:
The sum of the interior angles is 360
(n -2)180 is one formula to find the sum of the interior angles of a polygon. n stands for the number of sides
(4-2)180
2(180
360
We know three of the angles we subtract them from 360 to find the missing angle
360-60-110-120 = 70
Right Problem:
We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180. A straight line has an angle measurement of 180.
180-60 = 120
180 - 50 = 130
Now we just need to find x.
The sum of the interior angles is
(n-2) 180
(5-2)180
3(180) = 540 Subtract what we know
540 -50 - 130 - 120 = 240
The x's have the same value so 2402 is 120 .
Each x is 120
The answer to the problem on the left is 70 and the answer to the problem on the right is 120.
What is geometry?Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, angles and relative position.
Left Problem:
The sum of the interior angles is 360.
(n -2)180 is one formula to find the sum of the interior angles of a polygon. n stands for the number of sides
(4-2)180
2(180
360
We know three of the angles we subtract them from 360 to find the missing angle
360-60-110-120 = 70
Right Problem:
We can find the bottom left and the bottom right angles by subtracting the exterior angle from 180. A straight line has an angle measurement of 180.
180-60 = 120
180 - 50 = 130
The sum of the interior angles is
(n-2) 180
(5-2)180
3(180) = 540 Subtract what we know
2x = 540 -50 - 130 - 120 = 240
x = 240 / 2 = 120
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How do you solve and graph inequalities in algebra?
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality.
What are the steps to graphing an inequality?The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
Step 1: Always begin by separating the variable y from the inequality's left side.
Step 2: Replace the symbol for inequality with that for equality.
Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.
Step 4: Shading one side or area of the boundary line is the final step.
Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.
Here show an example for better understanding:
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
This side of the inequality is shaded below (instead of above) because y is lower than (or equal to) the other side.Because working with a "or equal to" inequality, draw a solid line rather than a dashed one. Points on the solid line denote locations where the inequality has been solved.To know more about inequality refer to:
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camilla and megan hung out at the mall on saturday. they spent 1 hour and 25 minutes shopping for clothes and 55 minutes at the food court. then they spent 2 hours and 35 minutes at the video arcade before heading home. if it was 12:55 p.m. when camilla and megan started shopping for clothes, what time was it when they left the mall?
It was 5:50 p.m. when Camilla and Megan left the mall.
Add 1 hour and 25 minutes to 12:55 p.m. to determine the time when Camilla and Megan finished shopping for clothes:
12:55 p.m. + 1 hour and 25 minutes = 2:20 p.m.
Add 55 minutes to 2:20 p.m. to determine the time when Camilla and Megan finished eating at the food court:
2:20 p.m. + 55 minutes = 3:15 p.m.
Add 2 hours and 35 minutes to 3:15 p.m. to determine the time when Camilla and Megan left the mall:
3:15 p.m. + 2 hours and 35 minutes = 5:50 p.m.
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3. Write < or > for each pair of numbers.
-6.48 -6.5
5.983 5.99
3.09. 3.01
-6.48 > -6.5
5.983 < 5.99
3.09 > 3.01
Hope it helps
2 1/2 divided by 4
please help asap
Answer:0.625
Step-by-step explanation:
What is the distance between the points 3 7 and 15 16 on a coordinate plane?
The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.
How to calculate distance between two points in coordinate plane?In coordinate geometry, every point is denoted by definite coordinates since every point is situated at a fixed distance from the origin point (0,0). Any two points on a coordinate space are situated at a constant distance since their coordinates are fixed with respect to the origin. A line segment has two endpoints, and the coordinates of the endpoints help to determine the length of the line segment. Let us suppose (x1,y1) and (x2,y2) are the two points on a coordinate space then the distance between these two points is given by the distance formula as per the below:
[tex]d = \sqrt{(x1 - x2)^2 + (y1 -y2)^2}[/tex]
Calculation:given points are (3 ,7) and (15 ,16).
(x1,y1) = (3,7) and (x2,y2) = (15,16)
We know that two points on a plane have a constant distance in between them, and the distance formula gives the distance between these two points.
d =[tex]\sqrt{(x1 - x2)^2 + (y1 - y2)^2}[/tex]
∴ d = √(3 - 15)^2 + (7 - 16)^2
∴ d = 15 unit.
The distance between the points (3 ,7) and (15 ,16) on a coordinate plane is 15 units.
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Which congruence criterion do you use in the following if ∆ Abe ≅ ∆ CDB *?
The ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent.
To use a congruence criterion in the given situation, you will need to determine which criterion is most appropriate based on the information provided. There are several congruence criteria that can be used to determine whether two triangles are congruent, including the Side-Side-Side (SSS) criterion, the Side-Angle-Side (SAS) criterion, the Angle-Side-Angle (ASA) criterion, and the Angle-Angle-Side (AAS) criterion.
In this case, the ASA criterion might be the most appropriate, as it states that two triangles are congruent if two angles and the included side are congruent. Given that ∠A=∠C=90∘ and AE=CB, you can use the ASA criterion to conclude that triangles AEB and CED are congruent.
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The question is -
Which congruence criterion do you use in the following? Given: EB = BD, AE = CB, ∠ A = ∠ C = 90°.
Mathematic,Englih and Life Skill book were ditributed to 50 tudent in a cla. 22 had Mathematic book,21 Englih book and 25Life Skill book,7 had Mathematic and Englih book. Find the number of tudent who had :(a) all three book ,(b)exactly two of the book,(c)only Life Skill book
One had all three, had exactly two and 21 had life skill book according to given situation.
Define problem in mathematics.A mathematical problem is one that can be represented, examined, and potentially resolved using mathematical techniques.
Write an example of mathematical problem.Jack has two dogs and eight cats. Jill owns 4 dogs and 7 cats. In total, how many dogs are there? How many more cats does Jane have than I do if she has 23 and I have 2, and then Jane gives me 5 cats?
Let X people have all three books then
three books=X
Math and Eng=7-X
Math and Life= 6-X
Eng and Life= 9-X
Then:
X+(7-X)+(6-X)+(9-X)+[22-(7-X)-(6-X)]+[21-(7-X)-(9-X)]+[25-(16-X)-(9-X)]=50
After simplification
X=1
(i). One had all three books
(ii) 6 had two
(iii). 21 had life skill book.
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edward received a gift card for $85 to a movie theater. he may use the gift card for either admission tickets or snacks. tickets cost $7.50 and his favorite snack costs $3.75. if he wants to use his gift card for at least 15 individual purchases, which is a combination of tickets and snacks edward may purchase? (5 points) 7 tickets and 8 snacks 10 tickets and 6 snacks 8 tickets and 6 snacks 11 tickets and 3 snacks
The answer choice which represents a combination of ticket and snacks Edward may purchase is; 7 tickets and 8 snacks.
Which combination of tickets and snacks can he purchase?The given word problem can be expressed as a system of equations as follows;
Let x = number of tickets and
Let y = number of snacks;
Therefore; the system of equations is;
x + y = 15.............(I)
7.50x + 3.75y = 85
The second equation can be expressed as follows;
2x + y = 68 / 3.........(II)
Therefore, by subtracting equation 1 from we have that;
x = 68/3 - 15
x = 7.667 tickets.
And y = 15 - 7.667
y = 7.333 snacks.
On this note, the best combination of tickets and snacks he can get is; 7 tickets and 8 snacks.
By checking; 7 tickets cost; $52.5 and 8 snacks cost; $30. Total = $52.5 + $30 = $82.5.
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Thank you so much to whoever answers :)
They are two separate questions btw
How many numbers in 1000 are divisible by 3?
333 integers, there are 333 integers between 1 and 1,000 which are divisible by 3.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here
add all the numbers,
1 + 2+ 3 + 4+ 5 = 15
and 15/3 = 5
so it is divisible by 3
not by 9
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What are types of expressions?
Types of expressions in math:
1. Algebraic Expressions: An expression that consists of numbers, symbols and operators (like +, -, ×, ÷) put together to represent a mathematical equation. 2. Trigonometric Expressions: An expression that consists of trigonometric functions (like sine, cosine, tangent, etc.) and constants.3. Logarithmic Expressions: An expression that consists of logarithmic functions (like log, ln, etc.) and constants.4. Exponential Expressions: An expression that consists of exponential functions (like e, a^x, etc.) and constants.5. Factorial Expressions: An expression that consists of factorial functions (like n!, etc.) and constants.6. Polynomial Expressions: An expression that consists of polynomial functions (like x^2, x^3, etc.) and constants.7. Rational Expressions: An expression that consists of rational functions (like 1/x, 1/x^2, etc.) and constants.Math expressions:The types of expressions in math listed above are all valid and commonly used expressions in mathematics. Algebraic expressions are used to represent equations, while trigonometric, logarithmic, exponential, factorial, polynomial and rational expressions are used to represent different types of functions.
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Which of the following is a step in copying a line segment?
Copying of line segment involves 6 steps.
How to copy a line segment?Steps to copy line segment are:
1) Draw a point that will serve as the new line segment's endpoint.
2) Open the compass width from the original line segment's beginning with the compass pin in that position.
3)Place the compass pin at the new line segment's plotted point using the above-mentioned step's adjusted compass width, and then draw an arc in the area where the new line segment is to be situated.
4) Decide where the other end of the new line will be on the arc.
5) Draw a line from the location chosen in the previous step to the point designated as the start of the new line segment.
6) The original line segment's length and the length of the line depicted above are equal.
Copying of line segment involves 6 steps.
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Q Which of the following is the first step when copying a line segment to construct a new line segment?
a. draw a line segment
b. use a straight edge to connect the point not on the line segment to a point in the arc
c. plot a point not on the original line segment
d. draw an arc
Let f be the continuous function defined on [-4, 3] whose graph, consisting of three line segments and a semicircle centered at the origin, is given above.
The value of g(2) = -1/4 and the value of g(-2) = π/2 - 3/2
The graph of function g is having a point of inflection at x=-2 and x=0 and x = 1 because g''(x) = f'(x) changes at each of these values.
A function is basically a relation between two sets having a domain , range and a co-domain.
We can represent functions graphically by plotting their equations and putting the value of co- ordinates.
A graph consists of four quadrants two positive and two negative. It helps to visualize data in a clear manner and helps to present data more efficiently.
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which of these is an example of a literal equation:
A: AX-BY=K
B: 5X+9Y
C: 4+12= 4²
D: 8-2X=14
Among the given equation, AX - BY = K is the example of a literal equation.
What is literal equation?
A literal equation is one that is mostly made up of letters. Examples of literal equations include formulas. Every variable in the equation "literally" represents a crucial aspect of the overall relationship that the equation expresses. The letter "L" stands for the rectangle's one side's length.
Given equations are:
A. AX - BY = K: is a literal equation as per definition.
B. 5X + 9Y: is not an equation.
C. 4 + 12= 4^2: it is not an equation.
D.8 - 2x = 14: it is not an equation. It is a linear equation with variable 'x'.
Hence, among the given equation, AX - BY = K is the example of a literal equation.
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Maria has ridden 44 miles of a bike course. The course is 80 miles long. What percentage of the course has Maria ridden so far?
Answer:
55percent
Step-by-step explanation:
[tex]\frac{44}{80} =0.55\\0.55x100\\55[/tex]
What shape has 7 sides called?
Having seven sides, a heptagon is a polygon.It is also occasionally referred to as a septagon.
What is the name of the 7-sided shape? Having seven sides, a heptagon is a polygon.It is also occasionally referred to as a septagon, though this usage is not advised because it combines the Greek suffix -gon (from the Greek root gonia, which means "angle") with the Latin word sept- (derived from septua-, meaning "seven").Having seven sides, a heptagon is a polygon.It is also occasionally referred to as a septagon, though this usage is not advised because it combines the Greek suffix -gon (from the Greek root gonia, which means "angle") with the Latin word sept- (derived from septua-, meaning "seven").A two-dimensional shape called a heptagon has seven sides and seven angles.In two-dimensional geometry, it is a member of the polygon class.Polygons are closed geometric figures composed entirely of straight lines.
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How do you expand a 3 term binomial?
The expanded form of a 3-term binomial is typically written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial is given by ax^2 + bx + c = a(x^2 + bx/a + c/a).
1. Take the coefficients of the binomial (which are the constants a, b and c)
2. Multiply the coefficient a with the remaining terms in the binomial (x^2 + bx + c).
3. Simplify the expression by multiplying the coefficient a with the terms (x^2 + bx/a + c/a).
4. The result is the expanded form of the 3-term binomial ax^2 + bx + c.
The expanded form of a 3-term binomial can be written as ax^2 + bx + c, where a, b and c are constants. The expanded form of the binomial can be obtained by multiplying the coefficient a with the remaining terms in the binomial (x^2 + bx + c) and simplifying the expression.
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What are the 3 ways we can prove triangle congruence?
In geometry, there are several ways to prove that two triangles are congruent, which means that they have the same size and shape. Here are three common methods for proving triangle congruence SSS congruence, ASA congruence, and SAS congruence.
Side-Side-Side Congruence: If all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent. This can be written as:
If AB = DE, AC = DF, and BC = EF, then ∆ABC ≅ ∆DEF
Angle-Side-Angle (ASA) Congruence: If two angles and the side between them in one triangle are congruent to two angles and the side between them in another triangle, then the triangles are congruent. This can be written as:
If ∠A = ∠E, ∠B = ∠F, and AC = EF, then ∆ABC ≅ ∆DEF
Side-Angle-Side (SAS) Congruence: If two sides and the angle between them in one triangle are congruent to two sides and the angle between them in another triangle, then the triangles are congruent. This can be written as:
If AB = DE, ∠A = ∠E, and BC = EF, then ∆ABC ≅ ∆DEF
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What is the y-intercept of the line whose equation is y =- 5x 6?
y = -(5/3)x + 4 is slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
rewrite the equation of the given line in to slope-intercept form by solving for y
3y + 5x = 6
3y = -5x + 6 (subtract 5x from both sides)
y = -(5/3)x + 2 (divide both sides by 3)
Our line is parallel to this line, so it has the same slope, and a
y-intercept of 4, so we have...
y = -(5/3)x + 4
the equation ofa line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
here m = 1 and c = 3, hence
y = x + 3 ← is the equation of the line
*slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept
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