Yes, this equation is a quadratic equation.
What is a quadratic equation?
Quadratic equation are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c ∈ R and a ≠ 0.
The given equation 3x² + 5x + 9x² + 7x + 3 = 0 can be written as 12x² + 12x +3 = 0, which is a general form of quadratic equation where a = 12, b = 12 and c =3.
Hence, the equation is a quadratic equation.
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If f(x) is a third degree polynomial function and g(x) = f(2x) + 2, which of the following MUST be true?
F f(x) and g(x) have the same x-intercepts.
G f(x) and g(x) have the same y-intercepts.
H f(x) and g(x) have the same number of zeros.
J f(0)=g(0)−2
over the past several years, a random sample of 40 women athletes at the school showed that 23 eventually graduated. does this indicate that the population proportion of women athletes who graduate from the university is now less than 67%? use a 1% level of significance.
The population proportion of women athletes who graduated from the university is more than 67%.
A random sample of 40 women athletes at the school showed that 23 eventually graduated.
n=40 , X=23 , p0 =67% = 0.67 , alpha = 1% = 0.01
H0: : p0 = 0.67 Vs H1 : p0 < 0.67
Test statistics = (p-p0) / (square root ((p0(1-p0) / n))
p=X/n
H0::p0=0.67 Vs H1:p0<0.67
Test statistics = z = (p-p0) / ( square root ((p0(1-p0)/n))
p=X/n=23/40
z = (0.575-0.67) / (square root (0.67(1-0.67)/40))=-1.278
P - value = P(z < -1.278) = 0.1007
Since the p-value is 0.1007 that is less than the level of significance the decision is to reject the null hypothesis. In conclusion, there is a sufficient evidence to support that the population proportion of women athletes who graduated is now more than 67%.
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Gavin has a deck that measures 6 feet by
3 feet. He wants to increase each
dimension by equal lengths so that its
area is tripled. By how much should he
increase each dimension?
Answer:
feet
Each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
In mathematics, a dimension is the length or width of an area, region, or space in one direction.
area = length × width
a = l × w
But, we want to triple than area;
3A = 3 (l × w)
3A = (k × l) (k × w)
k² = 3
k = √3
The new dimensions will be: 6√3 and 3√3
Increased Dimension: 6√3 - 6 and 3√3 - 3
let x is the amount of increase in each side:
(x + 6) (x + 3) = 3(18)
x² + 3x + 6x + 18 = 54
x² + 9x + 18 = 54
x² + 9x - 36 = 0
∵ x = 4
Hence, each dimension should be increased by four times so that the area is tripled and each dimension is equal in length.
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Answer:3
Step-by-step explanation:
What are the 10 expressions?
The 10 expressions in Math are:
1. Sum 2. Difference 3. Product 4. Quotient 5. Exponent 6. Root 7. Absolute Value 8. Factor 9. Power 10. FractionUnderstanding the Basics of Math Through the 10 ExpressionsMath is a subject that can be intimidating to many, but it is a fundamental part of life that is necessary to understand. It is important to have a basic grasp of different expressions in order to be successful in math. This essay will explore the ten expressions of math and provide insight into their importance.
The first expression is the sum. This is the answer you get when adding two or more numbers together. For example, if you have the numbers 5, 7, and 8, the sum would be 20. Sums can also be used to find the total amount of a group of objects.
The second expression is the difference. This is the answer you get when subtracting two or more numbers. For example, if you have the numbers 8 and 5, the difference would be 3. Differences can also be used to find the difference between two amounts.
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what is the value of y if the slope of the line is 3 and two points on the line is (0,y) and (2,4)
The value of y is -2.
What is coordinate of point?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.
Given points are (0,y) and (2,4).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
The slope of the given line is (4 - y)/(2 - 0) = (4 - y)/2.
Again given that the slope of the line is 3.
Therefore,
(4 - y)/2 = 3
Multiply both sides by 2
4 - y = 6
Subtract 4 from both sides:
-y = 2
Multiply both sides by -1:
y = -2
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60% of all the students passed an exam. if a random sample of 10 students is selected, what is the mean and standard deviation ? write every rule you are going to use.
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
Probability , p = 0.6 (60%=60/100)
Number of trial,n = 10(selected)
Mean = number of trial ✕ probability
= 10 ✕ 0.6
= 6.0
Mean is 6.0
Standard deviation :
σ = np(1-p)
= 10 ✕ 0.6 ✕(1- 0.6 )
= 2.4
Standard deviation = 1.5492
If a random sample of 10 students is selected from 60% passed students,with mean 6 and standard deviation 1.5492.
Rules of Probability : The first rule of probability used in this essay is the definition of a random sample. A random sample is a set of data taken from a larger population that is chosen by a method that gives each element of the population an equal chance.
The mean and standard deviation of a random sample of 10 students can be calculated in order to determine the probability that a given student has passed an exam. This requires knowledge of some basic principles of statistics and probability.
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8. Solve the Right Triangle.
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.
The Pythagoras theorem formula is given as
H² = P² + B²
The hypotenuse is 30 m and the base is 22 m. Then the length of the perpendicular is given as,
30² = P² + 22²
900 = P² + 484
P² = 900 - 484
P² = 416
P = 20.4 m
The length of the perpendicular of the right-angle triangle will be 20.4 meters.
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When two angles and a non-included side of one triangle are congruent to the corresponding pieces of another triangle?
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
We know that the AAS (angle-angle-side) theorem says that when two angles and any side of a triangle are congruent to two angles and any side of other triangle, then the triangles are said to be congruent.
If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.
Whereas the Angle-Angle-Side Postulate (AAS) tells us that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.
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How do you find the inverses?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.
Inverse function
An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.
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What are 3 odd consecutive numbers of 75?
The three consecutive odd numbers of the number 75 are:
77, 79 and 81
What are consecutive numbers?Consecutive numbers are those numerical values that are found just after a specific number or value, for example consecutive numbers from 5 will be 6 onwards.
In our case we have a specific value and this is the number 75, if we want to know the consecutive numbers immediately we add +1, +2 and so on.
But as we only want the odd numbers we will add +2, +4 and +6, having as a result the following numbers:
75 + 2 = 7775 + 4 = 7975 + 6 = 81The consecutive and odd numbers will be 77, 79, 81.
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Does parallel equal 180?
The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°.
Parallel lines are straight lines that never meet each other no matter how long we extend them
Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.
Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).
The fundamental characteristics listed below make it simple to recognise parallel lines.
Parallel lines are defined as straight lines that are always the same distance apart.
No matter how far apart they are from one another, parallel lines can never intersect.
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Please Help ASAP, end of term is the 15th and I’m super behind!!
What is the rate of change of the line in the graph below?
(Picture below)
The rate of change is 1 and the y-intercept is 1/2.
How do you find the rate of change on a line graph?
To get the slope of a graphed function, use the average rate of change formula. Divide the change in y-values by the change in x-values to determine the average rate of change.
The slope, rise over run, or change in over the change in of a line determines its rate of change. A graph's slope triangle or two points in a table can be used to compute the slope.
It is frequently referred to as rate of change when determining the slope of real-world scenarios. "Rate of change" and "slope" have the same meaning. Use the slope formula or create a slope triangle if you are asked to determine the rate of change.
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need your help please
Answer:
Hi ! the answer is .38!
Step-by-step explanation:
3) Part of the population of 4,500 elk at a wildlife preserve is infected with a parasite. A random sample of 50 elk shows that 8 of them are infected. How many elk are likely to be infected?
Using percentage on the population size, the number of infected is 720
Probability SamplingProbability sampling is a technique in which the researcher chooses samples from a larger population using a method based on probability theory. For a participant to be considered as a probability sample, he/she must be selected using a random selection.
In this question, we can find the percentage of infected in a sample size of 50.
Percentage of infected = (8 / 50) * 100
Percentage of infected = 0.16 * 100
Percentage of infected = 16%
Using this value, we can further calculate the total number of infected in the population.
16 % of 4500 = ?
16 / 100 = x / 4500
0.16 = x / 4500
x = 4500 * 0.16
x = 720
The number of infected are 720
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i need help i dont understand how to solve
By using the concept of depreciation, it can be calculated that
Value of x is 3.6%
What is depreciation?
Depreciation is the exponential decrease in the value of an asset or population or cost of an article at a certain rate over a certain period of time.
Now opposite of depreciation is growth.
Growth is the exponential increase in the value of an asset or population or cost of an article at a certain rate over a certain period of time.
Here concept of depreciation has been used
Number of deer in 2005 = 1480
Rate = x%
Time = 7 years
Number of deer after 7 years = 1141
[tex]1141 = 1480(1-\frac{x}{100})^7\\(1 - \frac{x}{100})^7 = \frac{1141}{1480}\\(1-\frac{x}{100}) = (\frac{1141}{1480})^{\frac{1}{7}}\\1 - \frac{x}{100} = 0.964\\\frac{x}{100} = 1 - 0.964\\\frac{x}{100} = 0.036\\x = 0.036 \times 100\\[/tex]
x = 3.6 %
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What are the roots of the quadratic equation 2x² 5x 3?
The roots of the quadratic equation 2x^2 + 5x + 3 are the two values of x that make the equation equal to 0. These two values are x = -3 and x = -1/2.
The roots of a quadratic equation are the two values of x that make the equation equal to 0. To find the roots of the equation 2x^2 + 5x + 3, we need to set the equation equal to 0 and solve for x. We can do this by using the Quadratic Formula, which states that the two roots of a quadratic equation ax^2 + bx + c = 0 are x = [-b +/- sqrt(b^2 - 4ac)] / 2a. In this equation, a = 2, b = 5, and c = 3. We can plug these values into the formula to get x = [-5 +/- sqrt(25 - 24)] / 4. Simplifying this expression gives us x = -3 and x = -1/2, which are the two roots of the equation 2x^2 + 5x + 3.
x = [-5 +/- sqrt(25 - 24)] / 4
x = [-5 +/- sqrt(1)] / 4
x = [-5 +/- 1] / 4
x = -3 and x = -1/2
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What are the properties of the circumcenter of a triangle quizlet?
For different types of triangle, The circumcenter has different properties. The properties varies for acute, obtuse and right angle triangles.
What do you mean by a triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes.
What do you mean by circumcenter of triangle?The spot where the three perpendicular bisectors of a triangle's sides meet and which is equally spaced from the triangle's three vertices.
Properties of circumcenter of triangle are:
In an acute-angled triangle, circumcenter lies inside the triangle. In an obtuse-angled triangle, it lies outside of the triangle. Circumcenter lies at the midpoint of the hypotenuse side of a right-angled triangle.To learn more about circumcenter visit:
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What do you mean by 3 more than 7?
The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10
In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y
If a given number let's say Z is Y less than X then the value of Z will be
Z=X-Y
More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value
So, 3 more than 7 means 7+3 = 10
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help it is an assignment
Answer:
13. Given below is a graph showing the number of Hindi movies released in the first six months of 2005. Which of the following questions can be answered from this graph?
D. How many movies were released during the period 1st Match to 31st May 2005?14. The table below gives the dimensions of some rectangles.
D. rectangles that are equal in perimeter could have different areas.Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer + Explanation:
13. A. can be answered - add all the monthly figures using the bar height.
B. cannot be answered - the graph shows May has the least movies but the graph doesn't tell you WHY it has the least movies, it does not give any reason.
C. can be answered - look at the highest bar height (it's February)
D. can be answered - calculate March, April and May figures together.
As such, circle A , C and D.
14.
A. Wrong - perimeter does not change in the table despite increase in area (all the perimeters in the table are the same).
B. Wrong - none have equal areas that have equal perimeters.
C. Wrong - none of the rectangles with equal perimeters have equal areas.
D. Correct - All the rectangles with the equal perimeter do not have equal areas (areas can be different).
So circle only D.
Finding angle measures of a triangle given two angles of a similar triangle
ok
Answer:
the answer would be this 5,8,3
What are the 4 theorems that can be used in proving congruence in right triangles?
Answer: The leg-leg theorem, the hypotenuse-leg theorem, the hypotenuse-angle theorem, and the leg-angle theorem.
Step-by-step explanation: Search it up.
How do you sum a column in Excel on a Mac?
To see the steps of sum a column in Excel on a Mac.
Now, According to the question:
1. Click the first empty cell below a column of numbers.
2. Do one of the following: Excel 2016 for Mac: : On the Home tab, click AutoSum. Excel for Mac 2011: On the Standard toolbar, click AutoSum. ...
3. Press RETURN .
How do you sum cells on a Mac?
Once the cells are selected, press the Command key and the = (equal sign) key at the same time. This will automatically sum the selected cells. If you want to sum a specific range of cells, you can do so by selecting the first cell in the range, pressing the Shift key, and then selecting the last cell in the range.
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If dx-2=h, then x is equal to?
Answer:
x=h+2 divided by d x = h+2/d
Step-by-step explanation:
statistical significance: a. indicates a high likelihood that your results are due to your treatment versus due to chance. b. is more likely to be reliable if you have a small sample size versus a large sample size. c. is a requirement of the data from a scientific experiment. d. indicates that the hypothesis should be rejected. e. depends on large data sets.
Answer:
Step-by-step explanation:
sean
Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.
The number of simulation trials that would be likely to produce results that are closest to the actual probability is 25. The correct option is C).
The following steps can be used in order to determine the number of simulations:
Step 1 - Remember the maximum number of trials gives the maximum chance to produce results that are closest to the actual probability.
Step 2 - Now, check all the options given in the question and choose the largest one.
From the above steps, it can be concluded that the correct option is C) 25.
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Full question :
Which number of simulation trials would be likely to produce results that are closest to those predicted by probability theory?.
A. 10
B. 15
C. 25
D. 20
How do you find the slope of a perpendicular line with an equation and point?
First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.
By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
A line's slope often indicates the steepness and direction of the line.
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m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line may be shown as
tan θ = Δy/Δx
Is the mean of the following data is 18.75 then find the value of p?
The value of p is 20
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean = (Sum of all the observations/Total number of observations)
Is the mean of the following data is 18.75 then find the value of p?
Xi 10 15 p 25 30
Fi 5 10 7 8 2
We may prepare th frequency table as given below:
mean=(∑Fi *Xi) / ∑Fi
= (5*10 + 10*15 + 7*p + 8*25 + 2* 30)/ (5 + 10 +7 +8 +2)
= (460+7p)/ 32
=18.75
460+7p=(18.75×32)
⇒(460+7p)=600
⇒7p=140
⇒p=20
The value of p is 20
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How will I know if my SSS loan is approved?
You can log into your My.SSS account to see the status of your SSS salary loan.
Your salary loan has been granted if you see the message "SSS Loan Application Has Been Granted." Logging into your My.SSS account will allow you to view the status of your SSS salary loan. Select "Inquiry" first, followed by "Loan Info." Your SSS loan status and other loan information can be found here. If the loan funds have already been credited to your disbursement account, you will also get another SMS message.
The loan must be repaid by the borrower in 24 monthly installments. The second month after the loan's origination date is when the monthly amortization starts.
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Philip wants to enclose his garden using 32 meters of fence. What is the largest interger value area, in square meteres, that he can enclose? what are the dimensions of the rectangular enclosure for his garden?.
The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.
Given :
Let x represent the length of the garden and y represent the width of the garden.
Perimeter = 2(x + y)
32 = 2(x + y)
x + y = 16
y = 16 - x
Area (A) = length * width
A = xy
A = x(16 - x)
A = 16x - x²
Maximum area is at dA/dx = 0:
dA/dx = 16 - 2x
0 = 16 - 2x
2x = 16
x = 8.0 m
y = 16 - x = 15 - 7.5 = 8.0 m
The dimensions of the rectangular enclosure for his garden is length of 8.0 m and width of 8.0 m.
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If line a has a slope of -8, what would be the slope of a line perpendicular to line a?
If line a has a slope of 2/5, what would be the slope of a line perpendicular to line a?
The slope of each of the perpendicular lines are:
a. 1/8
b. -5/2.
What is the Slope of Perpendicular Lines?The slope of two lines that are perpendicular to each other have values that are negative reciprocals. That is to say, their product will be equal to -1.
For example, if the slope of two perpendicular lines are -a and 1/a, therefore, their product will be (-a)(1/a) = -1.
a. Line a has a slope that is equal to -8. The negative reciprocal of -8 is 1/8.
Therefore, the slope of the perpendicular to line a would be 1/8.
b. Line a has a slope that is equal to 2/5. The negative reciprocal of 2/5 is -5/2.
Therefore, the slope of the perpendicular to line a would be -5/2.
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