What is the factor of 3x² 7x 2?
The factors of the quadratic expression 3x² + 7x + 2 are 3x + 1 and x + 2.
We know for a quadratic expression of the form ax² + bx + c, the sum of the roots is -b/a and product of the root is c/a.
So in the given case
a = 3
b = 7
c = 2
Let the roots be α and β, therefore
α + β = -b/ a = -7/ 3
Also αβ = 2/3
We can find α and β by trial and error method. Else using the identity (a+b)² = a² + 2ab + b² and (a-b)² = a² - 2ab + b², we get
(a - b)² = (a + b)² - 4ab
Therefore
(α - β)² = (α + β)² - 4αβ
(α - β)² = (-7/ 3)² - 4×2/3
(α - β)² = 25/9
Assuming α>β,
α - β = 5/3
So solving α + β = -7/ 3 and α - β = 5/3, α = -1/ 3 and β = -6/3 = -2
Therefore simplifying
3x² + 7x + 2
= 3(x + 1/3)(x + 2)
= (3x + 1)(x + 2)
--The question is incomplete, answering to the question--
"What is the factor of 3x² + 7x + 2?"
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What is the y-intercept of y = 1/2x?
Answer:0
Step-by-step explanation:y=1/2x
straight lines are of the y=mx+c
The c value is where the graph cuts the y axis or the y intercept
as there is no value there c=0
or y intercept =0
How do you simplify complex fraction expressions?
To simplify a complex fraction expression, first identify the numerator and denominator of each fraction.
What is complex fraction?A complex fraction is a fraction that contains one or more fractions in the numerator, denominator, or both. This type of fraction requires additional steps to simplify and can often be reduced to a simpler fraction or a whole number. Complex fractions are also known as compound fractions or nested fractions.
Then, factor each fraction into its simplest form by dividing each numerator and denominator by their greatest common factor. Finally, combine the fractions by multiplying the numerators and denominators. This will result in a simplified expression.
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How do you explain square root to a child?
Therefore , we can explain square roots to the child with the help of following explanation and examples.
How is the square root defined?A number's square root, which is the result of multiplication by itself, yields the original number. Some examples of exponents are squares and square roots. Imagine the number twenty five. Additionally, this can be expressed as expression of 5x5.
Here,
The square root is the same as the square in every way. You could think of it as the square's "root" or the number that was utilized to create the square.
The square root symbol is as follows:√
For example: √9 = √3*3 = 3
√25 = √5*5=5
√4 = √2*2 = 2
are the square roots of the following numbers .
Here we can see it is very easy to calculate the square root
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How long can you stay on sickness benefits?
In one (1) calendar year, a member may receive illness benefits for a maximum of 120 days. The total number of permitted compensable days for the next year cannot be increased by any unused fraction being carried forward.
Sickness benefits are paid for 91 days across two successive benefit periods and are equal to 70% of the average daily salary.
Enhanced Sickness Benefit: For male and female employees, respectively, this benefit is payable to insured people undergoing sterilization for 7 days and 14 days, and it is equal to their entire salary.
The member's daily Sickness Benefit allotment equals ninety percent (90%) of the credit for his or her average daily wage (ADSC). Up to 120 days can be received from the sickness benefit in a single (1) calendar year.
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How do you write 4x 5y 20 in slope intercept form?
4x+5y=20 in slope intercept form would be y= (-4/5)x + 4.
What do you mean by slope?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
4x + 5y = -20
-4x -4x
5y = -4x - 20
divide it all by 5
y = -4/5x - 4
Slope intercept form is y=mx+b. So you would first subtract 4x from both sides. This ends up being 5y= -4x +20. Then divide both sides by 5. This gets you y= (-4/5)x +4.
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What is the relationship between height and base?
A triangle's base and height are perpendicular to one other. In the same manner, if we know the triangle's area and height, we can calculate the triangle's base; conversely, if we know the triangle's area and base, we can calculate the triangle's height.
A triangle's height is always one of the triangle's sides. Drawn at an acute angle to the base must be a height that matches to the base. It is necessary to draw a height at a right angle to the base that matches to the base. Once we select a base, the associated height is represented by just one section.
A=1/2 x b x h
2A/h=b
or 2A/b=h
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Note the question could be as follow,
What is the relationship between the base and height of triangle?
The sampling distribution of the sample mean _____.a. shows the distribution of all possible values of μb. is an unbiased estimatorc. is the probability distribution showing all possible values of the sample meand. is used as a point estimator of the population mean μ.The standard error of the proportion will become larger as _____.a. p approaches 1b. n increasesc. p approaches 0d. p approaches .5
C- is the probability distribution showing all possible values of the sample mean. D- p approaches 0.5
The sampling distribution mean is the physical to the population mean. A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
Thus, the correct answer is C
The term "standard error" refers to the sampling standard deviation of the sample statistic or sample proportion. The population percentage can be accurately estimated using the sample proportion.
Thus, the correct answer is D
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The sampling distribution mean is the physical to the population mean. A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
Write an expression that can be used to find 65% of 120.
write two linear expressions that have a sum of 6x + 9
Please help I will give brainliest
Answer:
I know how to do this problem, but before I do, this isn't a live test, correct?
I recognize that your photo is from an eCampus quiz. I want to make sure I don't violate the honor code when answering.
Express the given product as a sum containing only sines or cosines.
sin (50) cos (20)
The zeros are thetas btw
Pls help I don't have much time
Answer:
s (50) c (20) s (50) c (20) = 0
Step-by-step explanation:
Hope this helps
The ize of a rectangle i 25 cm by 16 cm. A quare ha the ame area a the rectangle. Find the
perimeter of the quare
The square has a 48 centimeter perimeter.
To find the perimeter of the square, we need to calculate its side length. The area of a rectangle is given by its length multiplied by its width, so we can use the given measurements of the rectangle to calculate its area: 25 cm x 16 cm = 400 cm². The area of a square is given by the square of its side length, so we can use the area of the rectangle to calculate the side length of the square: √400 cm² = 20 cm.
Thus, the perimeter of the square is equal to 4 times its side length, or 4 x 20 cm = 80 cm.
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Two angles of a quadrilateral measure 133⁰ and 188°. The other two angles are in a ratio of
6:7. What are the measures of those two angles?
Answer:
18 and 21
Step-by-step explanation:
We take those two angles as 6x and 7x
133⁰ + 188° + 6x + 7x = 360(Sum of angles of a quadrilateral)
321+13x=360
13x=360-321
13x=39
x=39/13
x=3
6x=6x3=18
7x=7x3=21
Find the measure of each rectangle indicated. Round to the nearest tenth
The value of θ or the measurement m∠B of is 69°.
What is 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. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The hypotenuse of △ABC is AB = 14.
The base of △ABC is AC = 5.
The cosine is a trigonometry ratio and cosine of an angle is ratio of base to hypotenuse.
cos θ = Base/ hypotenuse
Putting Base =5 and hypotenuse = 14
cos θ = 5/14
Taking inverse of cosine on both sides:
θ = cos⁻¹(5/14)
θ = 69.0
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use the binomial theorem to determine the number of ways 1, 2, 3, and 4 heads can occur when four fair coins are flipped
If you write everything down, you can get 0,1,2,3 or 4 heads. The probabilities are: 1/16, 4/16, 6/16, 4/16, and 1/16. Notice, the probabilities add up to 16/16 = 1. You toss 4 fair coins.
What is probabilities?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
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How to do algebra Grade 6?
The steps for solving an algebraic problem can be summarized as follows Identify the problem and what you need to find (the variable). Determine what information you have about the problem, including any equations or other relevant information. Develop a plan for how to approach the problem and solve the variable. Implement your plan and perform the necessary calculations to solve for the variable. Check your solution to make sure it makes sense in the context of the problem and that it satisfies the original equation or conditions.
There are several basic steps that can help you solve algebraic equations in grade 6:
Read the problem carefully and determine what you are trying to find (the variable).Identify the operation(s) that need to be performed to solve the equation.Use the order of operations to determine the sequence in which the operations should be performed.Perform the operations in the correct order, starting with any operations inside parentheses or brackets.Simplify the equation by combining like terms on either side of the equal sign.Solve the equation by performing the opposite operation on both sides of the equal sign to isolate the variable.Check your solution by substituting it back into the original equation to make sure it works.Here's an example of how to use these steps to solve an equation:
Solve the equation 3x + 7 = 11.The variable we are trying to find is x.The operation we need to perform is to get x by itself on one side of the equal sign.There are no parentheses or brackets, so we can start by performing the operation on the right side of the equal sign.Subtract 7 from both sides of the equation: 3x = 4.Divide both sides by 3: x = 4/3.Check the solution by substituting it back into the original equation: 3(4/3) + 7 = 11, which is true.So, the solution to the equation is x = 4/3.Learn more about algebra at
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What is the difference in value between the three's in the numeral below? 632 387
Answer:
One is 30,000 and the other is 300
How do you find the standard deviation of a sample given the mean and sample size?
Using the sample mean and the provided sample size, We can find the sample standard deviation by using the formula [tex]\sqrt \frac {\sum {(x-\bar x)^{2}}}{n-1}[/tex] .
What do you mean by sample?Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.
What is mean and standard deviation?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a series of findings from a survey, experiment, or observational study.
The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
sample mean = [tex]\bar x[/tex]
sample size = n
sample standard deviation = [tex]\sqrt \frac {\sum {(x-\bar x)^{2}}}{n-1}[/tex]
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What percent is a 3 to 1 slope?
The percent of 3 to 1 is:
Slope Ratio: 3:1 or 3 to 1
Percent Slope: 33%
What was the slope?There is a picture of what the slope is down below:
Therefore, The percent of 3 to 1 is:
Slope Ratio: 3:1 or 3 to 1
Percent Slope: 33%
11. If the perimeter of ABCD is 600 ft. and AD=2x-10 find AB.
Answer:balls
Step-by-step explanation:
balls
Why is the square root of 4 undefined?
A negative number is not a real number which, squared, is negative. Hence square root of -4 undefined
What is the square root?
The square root of a number is the factor that we can multiply by itself to get that number. The symbol for square root is √ .Finding the square root of a number is the opposite of squaring a number.
According to the given question:
A negative number is not a real number which, squared, is negative.
You can't get square a number and get a negative. If you square a negative number, it'll become positive, therefore you can't square root a negative number because it doesn't exist. Hence square root of -4 is undefined.
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How do I determine if this equation is a linear function or a nonlinear function?
An equation is considered linear if it is in the form of [tex]y = mx + c[/tex] where m is the slope of the equation and b is the y-intercept.
Notice how here, x can only be to the power of one. In here, the conditions are just simply m,c ∈ R.
Some examples include [tex]y = 8x + 9, 2y = x-7, 8y=0[/tex] and even some like [tex]x=4[/tex].
As you can see here, all of the following equations are represented using a straight line.
An equation is considered “non-linear” when it is not graphed using straight lines. Some examples include [tex]y = 3x^{2} +8, 4y =2x^{4}-6, y = x^{5} +86[/tex].
In conclusion, a linear equation will always be in the form of , where m is the slope of the equation, and b is the y-intercept of the equation.
Note: To determine if an equation is a linear function, it must have the form (in which m is the slope and b is the y-intercept). A nonlinear function will not match this form.
In a linear equation, the variables appear in first degree only and terms containing products of variables are absent. But in the case of nonlinear equations, at least one variable is not of the first degree or the equation contains a product of variables.
An equation is linear if its graph forms a straight line. This will happen when the highest power of x is . Graphically, if the equation gives you a straight line then it is a linear equation. Else if it gives you a circle, or parabola, or any other conic for that matter it is a quadratic or nonlinear equation.
If the highest power of x in the equation is one then it is a linear equation else if the power of x is greater than one then it is nonlinear.
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We can determine if this equation is a linear function or a nonlinear function by looking at their graph.
What are linear functions and non-linear functions?
Simplify the equation as closely as possible to the form of y = ax + b.
On a Cartesian Plane, a linear function is a function where the graph is a straight line. The line can go in any direction, but it's always a straight line. The linear functions don't have any exponents higher than 1. Some of them don't have variables at all, and if they do, they have just plain x, which is equal to x to the first power. When a linear function is written in its simplest form, it looks like[tex]y = a + bx[/tex], where [tex]a[/tex] and [tex]b[/tex] are both constants. For example, here are some linear functions:
y = 3 + 5x
y = 2 - 6x
y = 4x
On a cartesian plane, a non-linear function is a function where the graph is never a straight line it is always curved may be a parabola, hyperbola or something else. Non-linear functions all have atleast one variable raised to the power of two or more. There's no one formula for non-linear functions because they're all different. For example, here are some non-linear functions:
y = 3x^3 + x^2 - 7
y = 5x^5 - 3x^2 +2
We can determine if this equation is a linear function or a nonlinear function by looking at their graph.
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-x+10x=9x+5 i need x please
Answer:No answer
Step-by-step explanation: Simplify like terms first if possible
on LS=-X+10X=9X
9X=9X+5
We need to get Xs on one side to solve equation
We aim to have the Xs on the left side
we take 9X from both sides
9X-9X=9X-9X+5
0=5
No solution
Is the relationship between volume and moles of gas proportional or inversely proportional?
The volume of the gas approximately directly proportional to its number of moles of gas when both temperature and pressure are constant.
Explain the Mole-Volume Relationship - Avogadro’s Law?The volume of a gas being directly proportional to the amount of moles of that gas, according to a plot illustrating the relationship between temperature and volume of a gas under constant pressure. Avogadro's law is cited in support of this: When the pressure (P) and temperature (T) are constant, the volume (V) of an ideal gas (n) directly varies depending on the number of moles of the gas (n).V∝ n at constant P and T
V = constant × (n)
Vn = constant
This can be mathematically stated as follows: As before, we can anticipate what will change to the volume of the a sample of gas as we adjust the number of moles using Avogadro's law.
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A flat rectangular piece of aluminum has a perimeter of 60 inches. The
length is 14 inches longer than the width. Find the width.
please add all the steps and explanation thank you.
Answer:
width = 8 inches
Step-by-step explanation:
⭐ What is the formula for the perimeter of a rectangle?
perimeter = 2(length) + 2(width)We are given that the length is 14 inches longer than the width, and the perimeter of the rectangle is 60 inches.
So, let's substitute these values into the perimeter formula and solve for the width. Let w = width.
[tex]60 = 2(14 + w) + 2(w)[/tex] Multiply the 2 into the parentheses
[tex]60 = 28 + 2w + 2w[/tex] Add like terms (terms with the same variable)
[tex]60 = 28 + 4w[/tex] Subtract 28 on both sides
[tex]32 = 4w[/tex] Divide both sides by 4 to isolate the variable
[tex]8 = w[/tex]
∴ The width is 8 inches.
A basketball player made 5 out 6 free throws. What percent of the free throws did he miss? (1 point)
Answer:
5/6 = 0.83
multiply the decimal by 100 to get the answer in percentage = 83%
83% is what they made
100 - 83 = 17% this is what he missed
Answer:
adfftep explanation:
ADFWAD
Por favor ayuda con el gráfico y la tabla pls
If the length of a rectangle is increased by 30% and the width is decreased by 30%, then the area:.
The area of the given rectangle will decrease by 9 % .
What is a rectangle?
The rectangle is a geometrical figure in which opposite sides are equal.
Area of rectangle = length × width.
Perimeter of rectangle = 2( length + width ).
Area of rectangle is given by = Length ( L ) × Width ( W )
The length of a rectangle is increased by 30%
New length L' = 1.3L
width of the same rectangle is decreased by 30%
New width( W' ) = 0.70W
Now,
New area = L'W'
1.3L × 0.70W = 0.91LW = 0.91 Old area
Hence the percentage decrement
(Old area - 0.91 old area)/old area × 100 = 9%.
Hence, The area of the given rectangle will decrease by 9 %
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The odds in favor of an event are 8 to 3. What is the probability of the event?
The answer to your Question is 3:8