This graph shows all the key characteristics of a particular polynomial function. Drag tiles to complete the function rule that could be represented by the graph
Answers
The function rule that could be represented by the graph is given as follows:
y = 2x³ + x - 3.
How to define the function?The first step in defining the function is looking at it's y-intercept, which is the value of y when the graph of the function crosses the y-axis.
This value is of -3, hence the function can be defined as follows:
f(x) = ax^n + x - 3.
Then we look at the behavior of the function. It has an inflection point, as it is concave down and then it becomes concave up, hence:
It's second derivative is of the first degree.It's first derivative is of the second degree.The function is of the third degree, hence n = 3.Thus:
f(x) = ax³ + x - 3.
Then we look at the x-intercept, meaning that when x = 1, y = 0, this the leading coefficient is obtained as follows:
0 = a + 1 - 3
a = 2.
Thus the function is defined as follows:
y = 2x³ + x - 3.
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Related Questions
a study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. one hundred participants are recruited to participate, and half are randomly assigned to participate in the intervention while the others serve as a control group. what study design is being used?
Answers
A study is conducted to see if a daily exercise intervention affects blood pressure among people with pre-hypertension. The study design being used is a randomized controlled trial (RCT).
What is a randomized controlled trial?Generally, In an RCT, the study participants are randomly assigned to either the intervention group or the control group. This helps to ensure that any differences between the two groups are not due to preexisting differences between them, but rather are due to the intervention being tested.
In this case, the intervention is a daily exercise intervention, and the outcome being measured is blood pressure among people with pre-hypertension.
The control group serves as a comparison group, and any changes in blood pressure observed in the intervention group can be attributed to the intervention rather than other factors.
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passes through (-2,6) with a slope of - 1/4
Answers
The equation of the line is y = x/4 + 13/2 .
What is a slope?A line's slope, sometimes referred to as its gradient in mathematics, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
And here we have the slope,
m = 1/4
And (x₁ ,y₁) = (-2,6)
then the equation of line is
y - y₁ = m (x - x₁)
y - 6 = (1/4) (x +2)
y = x/4 + 13/2
Therefore, the equation is y = x/4 + 13/2.
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Given the Trapezoid, BATS, where B (-4, 2), A (-2, 6), T (6, 6), S (8, 2). Graph and find the approximate area of BATS.
Answers
The graph of the trapezoid is shown below. The area is calculated as: D. 40 square units.
How to Find the Area of a Trapezoid?To find the area of a trapezoid, the formula used is given below:
Area of a trapezoid = 1/2 * (a + b) * h, where,
a = length of one of the basesb = length of one baseh = height of the trapezoid.The trapezoid BATS with the following vertices, B (-4, 2), A (-2, 6), T (6, 6), S (8, 2), ahs been plotted in the graph shown in the image attached below.
1 unit = 1 box, therefore, we have the following:
a = length of AT = 8 units.
b = length of BS = 12 units
h = 4 units
Plug in the values:
Area of trapezoid BATS = 1/2 * (8 + 12) * 4
Area of trapezoid BATS = 1/2 * (20) * 4
= 10 * 4
Area of trapezoid BATS = 40 square units.
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Explain how to solve 2^(x + 1) = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth
Answers
The solution of the given expression is equal to 2.17.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is [tex]2^{x+1} = 9[/tex]. The expression will be solved by using the logarithmic property below,
[tex]2^{x+1}=9[/tex]
Take logs on both sides,
(x+1) ln(2) = ln(9)
(x+1) = ln(9) / ln(2)
x + 1 = 3.17
x = 2.17
Hence, the expression will be solved by taking log on both sides.
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Fatimah ate f cookies. Satvinder ate six fewer than two times the number that Fatimah ate. If Satvinder ate 4 cookies, write and solve an equation to find f, the number of cookies Fatimah ate.
Answers
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Fatimah ate f treats. Satvinder ate six less than twice the number that Fatimah ate.
Let 's' be the number of cookies eaten by Satvinder. Then the equation is given as,
s = 2f - 6
If Satvinder ate 4 cookies, then the number of cookies that Fatimah ate will be given as,
4 = 2f - 6
2f = 10
f = 5
On the off chance that Satvinder ate 4 treats, the number of treats that Fatimah ate will be 5.
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Justin is going to invest $90,000 and leave it in an account for 19 years. Assuming
the interest is compounded quarterly, what interest rate, to the nearest hundredth of
a percent, would be required in order for Justin to end up with $216,000?
Answers
Answer:
4.63%
Step-by-step explanation:
You want the interest rate that, compounded quarterly, will result in a balance of $216,000 for an investment of $90,000 after 19 years.
Compound interestThe formula for the balance of an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where P is the principal invested, r is the annual interest rate, n is the number of times per year interest is compounded, and t is the number of years.
ApplicationFilling in the given values, we can solve for r:
216000 = 90000(1 +r/4)^(4·19)
2.4 = (1 + r/4)^76 . . . . . divide by 90,000
2.4^(1/76) = 1 +r/4 . . . . . . take the 76th root
(2.4^(1/76) -1) = r/4 . . . . . . subtract 1
r = 4(2.4^(1/76) -1) ≈ 0.0463437 ≈ 4.63%
The required interest rate is about 4.63%.
7x+14y=21,-7x+7y=7 using elimation
Answers
Answer:(x,y)=(1/3 , 4/3)
Step-by-step explanation:
What is the radius of the circumscribed circle of ABC?
Answers
Answer:
Given: △ABC, m∠A=120°, AB=AC=1 Find: The radius of circumscribed circle
Step-by-step explanation:
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Which equation, when paired with y = 2x 5, creates an inconsistent system? 2x y = 5 y = 2x 5 2x – 4y = 10 2y – 4x = –10
Answers
The equation that creases an inconsistent system when paired with y = 2x + 5 is given as follows:
2y - 4x = -10.
What is an inconsistent system?A system of equations is called inconsistent when the number of equations of the system is of zero.
The system in this problem is composed by linear equations, which have the following format:
y = mx + b.
In which:
m is the slope.b is the y-intercept.For inconsistent system, we have that the equations:
Have the same slope.Have different intercepts.The function in this problem is given as follows:
y = 2x + 5.
Hence the inconsistent system is formed with:
2y - 4x = -10.
Which is simplified by 2 as follows:
y - 2x = -5.
y = 2x - 5.
Having the same slope of 2, but a different intercept.
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Answer: 2y – 4x = –10
Step-by-step explanation: trust.
What is the value of y in the equation?
6y + 2 = 4p - 10
Answers
6y=4p-10-2
Calculate difference
6y=4p-12
Divide
Solution
Y=2/3 p -2
One of the tallest ferris wheels in the world is in las vegas. It has a diameter, , of 520 feet. The circumference of the ferris wheel represents the distance traveled by a passenger after one full rotation. The circumference can be determined using the expression. What is the distance traveled, in feet, by passengers on each rotation of the ferris wheel? record your answer to the nearest tenth of a foot.
Answers
Answer:
Below
Step-by-step explanation:
Circumference of a circle = pi * diameter
circumference of ferris wheel = 3.14159 * 520=1633.6 ft
a vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a
Answers
A vocational counselor wishes to compare the mean scores on a paper-and-pencil test of anxiety for groups of physicians, lawyers, and accountants. the appropriate test is a two factor chi Square test.
The Pearson chi-square (χ²) test, often simply called the chi-square test, is one of the most common non-parametric tests. Nonparametric tests are used for data that do not follow the assumptions of parametric tests, especially the assumption of normal distribution.
To test hypotheses about the distribution of a categorical variable, you should use the chi-square test or another non-parametric test. Categorical variables can be nominal or ordinal and represent groups such as species or nationality. They can only have a small number of specific values, so they cannot have a normal distribution.
Bidirectional chi-square is one of several tests of goodness of fit between the actual values of two nominal or ordinal variables and the values expected if the variables were unrelated or independent. Chi-square is also known as Pearson Chi-square and Chi-square test of independence. The symbol for the chi-square test is the lowercase Greek letter chi (χ) with a superscript 2, such as χ2. χ2 is a test of significance and should be accompanied by an appropriate test of strength. The strength test should be chosen based on the number of rows and columns in the table of observations. In particular, one of the most commonly used strength tests is the π coefficient.
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2) the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. the bls reported in february 2012 that the labor force participation rate in the united states was 66.9% (calculatedrisk). a marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. what are the expected value and the standard error for a labor participation rate in the company's sample?
Answers
The expected value and the standard error for a labor participation rate in the company's sample is 0.0043
In the given question, the labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized.
The BLS reported in February 2012 that the labor force participation rate in the united states was 66.9% (calculate risk).
A marketing company asks 120 working-age people if they either have a job or are looking for a job, or the labor force.
We have to find the expected value and the standard error for a labor participation rate in the company's sample.
Working age people sample n = 120
The labor force participation rate in the United States was 66.9% = 0.669
The Expected value is μ = p = 0.669
The standard error:
SE = √p(1-p)/n
SE = √0.669(1-0.669)/120
SE = √0.669*0.331/120
SE = √0.2214/120
SE = √0.001845
SE = 0.043
Hence, the expected value and the standard error for a labor participation rate in the company's sample is 0.0043.
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Find the y intercept y = – 17 x + 12.
Answers
Answer: 12
Step-by-step explanation:
The y-intercept in the equation that is in slope-intercept form is the constant.
Which polynomial is prime?
O x² +7
Ox²-25
O3x²-27
O 2x²-8
Answers
Explanation:
All of the polynomials listed are quadratic polynomials, which have the general form ax^2 + bx + c, where a, b, and c are constants and x is a variable. A polynomial is considered prime if it cannot be factored into the product of two or more polynomials with integer coefficients.It is not possible to determine whether any of the given polynomials are prime without further information, such as the values of the constants a, b, and c. For example, the polynomial x^2 + 7 could be prime, but it could also be factored into the product of two linear polynomials (x + 3)(x + 3), which would make it composite. Similarly, the polynomial x^2 - 25 could be prime, but it could also be factored into the product of two polynomials of the form (x + 5)(x - 5), which would make it composite. Without more information, it is not possible to determine whether any of the given polynomials are prime.
21. Is the following ordered pair (3, 6) a solution of the linear inequality y < -5x + 1?
Answers
The pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
What is linear inequality?
A linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
y < -5x + 1
Substitute the points and see if they are true
(3, 6)
6 < -5*(3) + 1
6 < -15 + 1
6 < -14
Not true not a solution
Hence, the pair (3, 6) is not a solution of the linear inequality y < -5x + 1.
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What i cot of tiling a rectangular plot of land 500m long and 200m wide at the rate r 8 per q m
Answers
The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
Area of rectangle = length × breadth
Area of rectangular plot = 500× 200 = 1,00,000 sq m
Cost of tilling 1 sq m of land = Rs. 8
Cost of tilling 1,00,000 sq m of land = 8 × 1,00,000 = Rs. 8,00,000
Thus, The cost of tilling a rectangular plot of land 500m long and 200m wide at the rate of rs 8 per sq m is Rs. 8,00,000.
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If Santa Claus ate two cookies from every child on Earth, how many cookies would he eat over one Christmas Eve?
Answers
Answer:
three billion eight hundred million
Step-by-step explanation:
1. 5x - 8 < 17
It needs to be graphed on a number line.
Answers
Answer: x < 5
What does this mean?
This simply means that any point that is five or below is going to be outlined.
How do I do it?
It's as simple as drawing a point at value 5, and everything below is going to contain a line.
Representation
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find the slope of the line that passes Through the points (2.5, 1) and (1,-3.5)
Answers
Answer:
3
Step-by-step explanation:
slope m = (y - y1)/(x - x1)
m = (-3.5 - 1)/(1 - 2.5) = (-4.5)/(-1.5) = 3
suppose a juice box contains 30% juice with the remaining portion of the drink composed of water. what is the solute in this type of juice box?
Answers
Suppose a juice box contains 30% juice with the remaining portion of the drink composed of water alcohol is the solute in this type of juice box.
Ethanol; Ethanol, a drab liquid with a pleasing scent this is produced evidently from fermentation through yeasts and different microorganisms. It is utilized in alcoholic beverages, as a solvent, and withinside the manufacture of different chemicals. Ethanol is a fairly poisonous and colorless compound.
Alcohol is the solute in this type of juice box is the solvent as alcohol is easily soluble as the solvent and has best property of a solute and csn pass through the semipermeable permeability and others solvent also. The alcohol is actually acting as the solute here to dissolve the solvent.
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Simplify 4x - 7 + 12x - 3.
Answers
Answer:2(8x-5)
Hope this helps!
What is an equation of a line that passes through the points (1, 4) and (2, 9) in
5)
point-slope form? Analyze the steps and fill in the blanks. (4pts)
First, use the two given points to find the slope.
m=
Уг-У1
Use the slope and one point to write an equation of the line in
point-slope form.
Point-slope form of a linear equation.
Substitute
Answers
The equation of line in point-slope form of the line, is y = 5x - 1.
What is point - slope form of the line?
The general form of a linear equation is y - y1 = m(x - x1).
It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Given:
The line passes through the points (1, 4) and (2, 9).
We have to find the equation of line in point - slope form.
First to find the slope from the given points.
Since,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex](x_1, y_1) = (1, 4), (x_2, y_2) = (2, 9)[/tex]
So, [tex]m = \frac{9-4}{2-1} = 5[/tex]
Now consider, the point slope form of the line
[tex]y-y_1=m(x-x_1)[/tex]
Plug [tex]m = 5, (x_1, y_1) = (1, 4)[/tex]
⇒
[tex]y - 4=5(x-1)\\y-4=5x-5\\y=5x-5+4\\y=5x-1[/tex]
Hence, the equation of line in point-slope form of the line, is y = 5x - 1.
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Deposited (dollars)
12,500
10,000
7,500
$5,000
rate of change=
2,500 initial value=
Time (years)
y
dollars per year
dollars
Answers
The rate of change is $2500 per year.
The initial amount is $5000.
What is slope?The value of the steepness or the direction of a line in a coordinate plane is known as the slope of a line, often known as the gradient. Given the equation of a line or the coordinates of points situated on the straight line, slope can be determined using a variety of techniques.
The formula for slope between two points (x₁, y₁) and (x₂, y₂) is,
m = (y₂ - y₁)/(x₂ - x₁)
In the given graph,
The initial value that deposited at x = 0 is $5000.
To find the rate of change in amount per year,
Find slope of the line, because rate of change will be equal to slope.
Let two points are (0, 5000) and (1, 7500)
The slope = (7500 - 5000 / 1 - 0) = 2500
The rate of change is $2500 per year.
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A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do
not have brown hair, while 80% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest
marginal relative frequency and its interpretation?
A. 0.56; Individuals with brown eyes
B. 0.70; Individuals with brown eyes
C. 0.80; Individuals with brown hair
D. 0.83; Individuals with brown hair
Answers
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C
What is the marginal relative frequency?Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.
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read the picture plsss
Answers
Answer:
Step-by-step explanation:
If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value. 17. f[g(–2)]
a. 7 b. 10 c. 30 d. 100
Answers
Answer:
d.) 100
Step-by-step explanation:
To solve, first find the value of g(-2):
[tex]g(-2)=5(-2)\\g(-2)=-10[/tex]
Next, use this value to find f(-10):
[tex]f(-10)=(-10)^2\\f(-10)=100[/tex]
The formula for the volume of a cylinder is V=\pi r^2 h,V=πr
2
h, where rr is the radius of the cylinder and hh is the height of the cylinder. Rewrite the formula to solve for hh in terms of rr and V.V.
Answers
The formula to solve for height(h) is given as, if the volume of the cylinder is, V = π r² h, is h = V / π r².
What is volume?An object's volume is a measurement of the amount of space it occupies in three dimensions. This indicates that an elephant's volume is more than a mosquito's volume.
Given:
V = π r² h
Here, r is the radius of the cylinder, V is the volume, and h is the height of the cylinder. The value of π is 3.14.
Take the remaining term of the right side to the left as shown below,
V / π r² = h
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When Lisa increased her speed in letter c,
the increase took two seconds. What was her acceleration?
Answers
Lisa's change in speed is 4 miles per hour.Lisa's acceleration is 2 miles per hour.
What was her acceleration?According to the question,
The speed of Lisa is = 3 miles per hour
A dog starts to chase her, and she speeds up to seven miles per hour.
The change in speed after dog chase her is,
= 7 miles per hour - 3 miles per hour
= 4 miles per hour
Lisa's change in speed is 4 miles per hour.
When Lisa increased her speed in letter c, the increase took two seconds.
Then,
The Lisa acceleration is,
Acceleration = Change in speed/Change in time
Acceleration = 4/2
Acceleration = 2 per mail.
Hence, Lisa's acceleration is 2 miles per hour.
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for what values of x and y are the triangles congruent by HL?
Answers
For the given congruent triangles, the values of x = -1 and y = 3.
What do you mean by congruence of triangle?Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other.
The congruence symbol is "≅".As both the triangles are congruent therefore their corresponding sides will be equal.
3y + x = y + 5 ...........(1)
y - x = x + 5 ..............(2)
Equation
1:3y + x = y + 5
3y - y = 5 - x
2y = 5 - x
x = 5 - 2y ..............(3)
Substitute this value of x in equation (2)
y - x = x + 5 y = x + x + 5y
= 2x + 5 y = 2(5 - 2y) + 5y
= 10 - 4y + 54y + y = 15
5y = 15 y = 15/ 5
y = 3
Substitute this value of y in equation (3) x = 5 - 2(3) = 5 - 6 = -1
Therefore, x = -1 and y = 3
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