To add the two expressions (2x^2+6x−3) and (2x^3 −3x+2), we need to combine like terms. Like terms are terms that have the same variable and exponent.
The two expressions have no like terms, so we can simply add them as follows:
(2x^2+6x−3) + (2x^3 −3x+2) = 2x^2 + 6x − 3 + 2x^3 − 3x + 2
= 2x^2 + 2x^3 + 6x − 3x − 3 + 2
= 2x^2 + 2x^3 + 3x − 3 + 2
= 2x^2 + 2x^3 + 3x − 1
The resulting expression is (2x^2 + 2x^3 + 3x − 1).
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Given equations: 2x^2+6x-3+2x^3-3x+2
= 2x^2+2x^3+6x-3x-3+2
=2x^3+2x^2+3x-1
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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
What is the formula of line segment?
Answer:
The length of the line segment is
d = √(x₂ - x₁)² + (y₂ - y₁)²
Solve for Z.
X= 2/3(Y+Z)
Answer: Z=[tex]\frac{3}{2}[/tex]x-y
Step-by-step explanation: first multiply both by the reciprocal of 2/3 to cancel it. the reciprocal of 2/3 is 3/2
x(3/2)=y+z
then to solve for x, move the to the left side by -y on both sides
you're then left with z=x(3/2)-y
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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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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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
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°.
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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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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Thank you so much to whoever answers :)
They are two separate questions btw
How do you find the missing length of a triangle on a calculator?
By using a² + b² = c² this formula we can find the missing length of a triangle.
A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.
If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:
a² + b² = c²
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:a = √(c² - b²)
If leg b is unknown, then:b = √(c² - a²)
For hypotenuse c missing, the formula is:c = √(a² + b²)
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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
What does ∆ mean in calculus?
In lambda expressions and lambda (λ) phrases, the Greek letter lambda () is used to signify binding a variable in a function. You can have typed or untyped lambda calculus.
Functions can only be used in typed lambda calculus if they are able to accept the "type" of data that the input is. The Greek symbol lambda () is commonly used to represent wavelength, which is equal to the speed (v) of a wave train in a medium divided by its frequency (f): wavelength = v/f. The majority of the time, students struggle to understand calculus because they don't practice after class, can't concentrate in class, have gaps in their math knowledge, and believe it's a waste of time.
The actions you can do to make calculus simple are listed below. Calculus is the most difficult math topic, and very few students, whether in high school or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract and easier to understand because it is more concrete. The mean number of events within a particular period of time or space is denoted by the Greek letter lambda () in the Poisson distribution formula. For instance, = 0.748 floods annually.
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Correct Question:
What does λ mean in calculus?
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 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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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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What are the possible rational zeros of f X X 4 6x 3 3x 2 17x 15?
The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
What is mean of rational zero ?
A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.
A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.
Have given ,
f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex]
This is a fourth degree polynomial.
Using the rational root theorem, the possible zeros of the polynomial are the factors of 15.
We know that
Factors of 15 = ± 1, ±3, ±5, ±15
Therefore , The possible rational zeros of f(x) = [tex]x^{4} + 6x^{3} - 3x^{2} +17x-15[/tex] are ± 1, ±3, ±5, ±15.
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How would you describe a rigid transformation?
A transformation that leaves a geometric figure's size or shape unaltered is known as a rigid transformation (also known as isometry). is a unique type of metamorphosis in which a figure's size or shape are left unaltered.
What is rigid transformations?During a rigorous alteration of the geometric object, the distance between each pair of its points is maintained. In other words, an object's size and shape are maintained through a hard transformation. For example, the rigid transformation of a triangle preserves the triangle's angles and lengths. Consider a rigid form distortion that resembles a cardboard shape.
There are translations, reflections, and isometric rotations. As a result, none of these changes have an impact on the figure's size. If neither the size nor the shape of the figures are changed, the figures are constant.
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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
If triangle LMB is dilated by a scale factor of 0.5, which of the following statements is not true?
A. Triangle LMN is similar to triangle L’M’N’.
B. Triangle L’M’N’is smaller than triangle LMN
C. The sides of triangle LMN are congruent to the sides of triangle L’M’N’.
D. The angles of triangle LMN are congruent to the angles of triangle L’M’N’.
According to the properties of geometry the correct option is C.
What is geometry?
The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.
Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.
If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.
Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.
It is given that LMN is dilated by a scale factor of 0.5.
Since scale factor is lies between 0 to 1, therefore it shows the compression.
Therefore sides of L'M'N' is smaller than LMN.
Since corresponding angles of similar figure are congruent.
So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.
Therefore option C is correct.
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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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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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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]
2 1/2 divided by 4
please help asap
Answer:0.625
Step-by-step explanation:
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
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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What is the mean deviation of 8 9 12 15 16 20?
8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
What is the mean deviation?The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection.
It is a statistical summary of statistical variability or dispersion.
So, the sum of all the values:
8 + 9 + 12 + 15 + 16 + 20 + 24 + 30 + 32 + 34 = 200
A number of observations:
= 10
Formula: Mean = (sum of all observations)/(Total number of observations)
Now, calculate using the formula as follows:
Mean = (sum of all observations)/(Total number of observations)
Mean = (200 / 10)
Mean = 20
Now, we must determine how far the provided values are from the mean.
20 - 8 = 12
20 - 9 = 11
20 - 12 = 8
20 - 15 = 5
20 - 16 = 4
20 - 20 = 0
24 - 20 = 4
30 - 20 = 10
32 - 20 = 12
34 - 20 = 14
Formula:
Mean deviation = (sum of the distance of each value from mean) / (Total number of observations.)
Sum of each value's deviation from the mean = 12 + 11 + 8 + 5 + 4 + 0 + 4 + 10 + 12 + 14 = 80
Mean deviation = 80 / 10 = 8
Therefore, 8 is the required mean deviation of the given data set 8, 9, 12, 15, 16, 20, 24, 30, 32, 34.
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Complete question:
What is the mean deviation of the data:8,9,12,15,16,20,24,30,32,34?
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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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 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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