Three points on the graph of the function f(x) are {(0,4), (1,9), (2, 16)}. Which
equation represents f(x)?
○ ƒ(x) = 4 · (²)ª
Of(x) = 5x + 4
Of(x) = (x + 2)²
Of(x) = 7x+2
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Answers
Answer:
We can use the three given points to form a system of equations and solve for the coefficients of the polynomial function:
When x = 0, f(x) = 4:
4 = a(0)^2 + b(0) + c
4 = c
When x = 1, f(x) = 9:
9 = a(1)^2 + b(1) + c
9 = a + b + 4
When x = 2, f(x) = 16:
16 = a(2)^2 + b(2) + c
16 = 4a + 2b + 4
We can simplify the second equation by substituting c = 4:
9 = a + b + 4
a + b = 5
Solving for b, we get:
b = 5 - a
Now we can substitute this expression for b in the third equation:
16 = 4a + 2b + 4
16 = 4a + 2(5 - a) + 4
16 = 6a + 14
2 = 6a
a = 1/3
Substituting this value of a in the equation for b:
b = 5 - a
b = 5 - 1/3
b = 14/3
Now we know that the quadratic function that passes through the three points is:
f(x) = (1/3)x^2 + (14/3)x + 4
Therefore, none of the given equations represents f(x). The correct equation is f(x) = (1/3)x^2 + (14/3)x + 4.
Related Questions
1 point
What is Nick required to do for an hour before soccer on Saturdays?
laundry
O read his dad's dictionary
practice his soccer skills
clean his room
Please help please lease ASAP
Answers
Can the following quadrilateral be proven to be a parallelogram based on the given information? Explain.
(picture shown below)
A.) No. It cannot be proven because at least two of the adjacent angles are not congruent to each other
B.) Yes. It can be proven because both pairs of opposite sides are congruent.
C.) No. It cannot be proven because it does not have an angle that is supplementary to both of its consecutive angles.
D.) Yes. It can be proven because both pairs of opposite angles are congruent.
Answers
Answer:
Step-by-step explanation:
The answer is, no!
Step-by-step explanation:
The reason to that answer is that some other shapes are also, having the same properties as shown. An example for that property would also mean a rectangle and not always a parallelogram.
So, here is the given information on what we need to classify a shape as a parallelogram:-
1) Parallel Sides
2)Opposite Sides are equal.
3) Adjacent sides are not equal.
4) Opposite angles are equal.
5)Adjacent angles are not equal.
Based on this, we can classify a shape as a parallelogram.
Hope, this answer helps!
Call me Al ~ A 2009 study conducted by Dr. Douglas and Dr. Rowlinson at Newcastle University aimed to examine the human-animal relationship between dairy farmers and their cows. Douglas and Rowlinson surveyed 516 UK dairy farmers about how they thought human interaction could affect the productivity of dairy cattle. Analysis showed that farmers who called their cows by name produced more liters of milk per cow annually than farmers who did not.Laerte owns a dairy farm near Para de Minas, Brazil and he names all his cows. He wants to conduct a similar study in his home state of Minas Gerais. Minas Gerais is the country’s main milk producing state and accounts for approximately 28% of national milk production.Laerte imagines five sampling scenarios. Identify the type of sample Laerte imagined in each proposed scenario.
A. Simple Random
B. Systematic
C. Stratified
D. Cluster
E. Convenience
? A B C D E 1. Laerte develops a numbered list of all dairy farms in Minas Gerais, chooses a random number from 1 to 5 as a starting point, and includes every 5th farm on the list in his sample.
? A B C D E 2. Laerte knows that the most common dairy farm types in Minas Gerais are extensive grazing, semi-confinement, and full-confinement. He generates a list of farms for each farm type and randomly selects 30 farms from each list.
? A B C D E 3. Laerte visits a cattle auction near his farm and surveys all the dairy farmers he meets.
? A B C D E 4. The state of Minas Gerais is subdivided into 66 microregions. Laerte randomly selects 4 microregions and then surveys all the dairy farms in those 4 microregions.
? A B C D E 5. Laerte develops a numbered list of all dairy farms in Minas Gerais and uses a random number generator to select 90 farms to survey.
Once Laerte has determined which dairy farms to survey, he collects information on the following variables. Identify the type of each variable.
6. ? Numerical Ordinal Nominal How many dairy cows are owned by the dairy farm.
7. ? Numerical Ordinal Nominal Do the owners call the cows by name? (yes/no)
8. ? Numerical Ordinal Nominal Size of the dairy farm (small/mid-size/large/very large)
Answers
parameters are Sample = The 5 cows selected by the farmer. and Population = all of the farmer's dairy cows
Statistic = The five measurements collected on cows selected by the farmer.
Data = Variance in daily milk production among the cows in the farmer's sample
Parameter = a quantity equivalent to the volume of milk produced by a randomly selected cow
Population refers to all members belonging to a particular group of interest ; all the farmer's dairy cows
Sample : A small subset of observation selected from the sample; 5 selected cows from the population.
Statistic: Numeric characteristic of the observations derived from the sample
Parameter : Numeric characteristic of observation derived from the population.
Data: gathered figures calculated from either sample or population ; the variance in Daily milk production.
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expert that helps you learn core concepts.
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One item on a questionnaire asks students how many times in a typical week they eat at a fast-food restaurant. The responses for a sample of n = 10 students are summarized in the frequency distribution. What is the mean for this sample?
X f
5 or more 2
4 3
3 2
2 1
1 1
0 1
M = 4
M = 3.5
M = 31/10 = 3.1
The mean cannot be determined for these data.
Answers
The arithmetic mean for this value is M=3.1.we can calculate this data from frequency distribution.
what is arithmetic mean?It is sum of collection of number divided by the count of numbers.Its value can be positive or negative both.The collection is often a set of results from an experiments and observational study.
what is the use of arithmetic mean?It is often used as a parameter in statistical distribution or as a result to summarize the observations of an experiment survey.It is simplest way to used to measure the average.Its also measure frequency distribution by considering all of the observations.
Now we are using formula for arithmetic mean
A.M= Sum of (fx)/sum of (f)
by putting values in this formula we have
A.M= 31/10
A.M= 3.1
Hence 3.1 is the arithmetic mean for given frequency data.
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Find the unknown angle measure.
Answers
Answer:
54
Step-by-step explanation:
equilateral triangle= 2 angles equal
180-72=108
108/2 =54
x=54
The authors of the paper "Statistical Methods for Assessing Agreement Between Two Methods of Clinical Measurement"† compared two different instruments for measuring a person's ability to breathe out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter.
Subject Mini-Weight Meter Weight Meter
1 512 494
2 430 395
3 520 516
4 428 434
5 500 476
6 600 557
7 364 413
8 380 442
9 658 650
10 445 433
11 432 417
12 626 656
13 260 267
14 477 478
15 259 178
16 350 423
17 451 427
(a) Suppose that the Wright meter is considered to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. If the two types of meters produce different readings but there is a strong relationship between the readings, it would be possible to use a reading from the mini-Wright meter to predict the reading that the larger Wright meter would have given. Use the given data to find an equation to predict Wright meter reading using a reading from the mini-Wright meter. (Round your values to three decimal places.)
Answers
Answer:
Step-by-step explanation:
Given data;
n = 17
\(\sum x =7692\)
\(\sum x^2=3685124\)
\(\sum y =7656\\\\ \sum xy=3662682\)
Slope:
\(\hat B_1=\frac{n \sum xy - \sum x \sum y}{n \sum x^2 - ( \sum x)^2} \\\\=0.96994\)
≅ 0.970
y - intercept :
\(\hat B_0 = \frac{\sum y}{n} - \hat B\frac{\sum x}{n} \\\\=11.48178\)
≅ 11.482
a)
Equation :
\(\hat y = 11.482+0.970x\)
b)
Predicted wright meter reading
\(\hat y = 11.48178+0.96994(563)\\\\=557.558\)
c)Predicted wright meter reading
\(\hat y = 11.48178+0.96994(342)\\\\= 343.201\)
Find the simple interest owed for the following loan. The interest is $ (Do not round until the final answer. Then round to the nearest cer Principal Rate Time in Years 1 $2975 6.5% 3/12
Answers
The simple interest formula is given by
\(I=p\cdot r\cdot t\)where I is the interest, p is the principal, r is the interest rate and t the time in years.
In our case,
\(\begin{gathered} P=2975 \\ r=0.065 \\ t=3\frac{1}{2} \end{gathered}\)However, in order to use the above formula, we must convert the time into a simple fraction form, that is
\(3\frac{1}{2}=\frac{2\cdot3+1}{2}=\frac{7}{2}\)Then, by subsituting our values into the simple interest formula, we get
\(I=(2975)(0.065)(\frac{7}{2})\)which gives
\(\begin{gathered} I=\frac{13563.625}{2} \\ I=676.8125 \end{gathered}\)Then,by rounding to the nearest cent, the interest is $676.81
please help me asap!!!
Answers
Answer:
YZ = 4
Step-by-step explanation:
△XZW is simliar to △ YZV
Then use ratios to find the missing side
8/x = 12/6
12x = 48
x = 4
Also good luck on IXL that suuuucccckkksss
Roland has built a circuit, and is using a device called an
ammeter to measure how quickly electrical current is flowing
through the circuit. He calculates that the current should be
0.180 amps, but he measures the current as 0.173 amps. What
is Roland's percent error?
Answers
Roland's percent error is approximately 3.889%.
This means that his measured value differs from the actual value by 3.889% or 0.03889 in decimal form.
The positive sign indicates that Roland's measured value is slightly lower than the actual value.
To calculate Roland's percent error, we can use the formula:
Percent Error = (|Measured Value - Actual Value| / Actual Value) \(\times\) 100
Given that Roland measured a current of 0.173 amps while expecting a current of 0.180 amps, we can substitute these values into the formula:
Percent Error = (|0.173 - 0.180| / 0.180) \(\times\) 100
Simplifying the expression within the absolute value:
Percent Error = (|-0.007| / 0.180) \(\times\) 100
Since the absolute value of -0.007 is 0.007, we have:
Percent Error = (0.007 / 0.180) \(\times\) 100
Calculating the division:
Percent Error = 0.03889 \(\times\) 100
Percent Error = 3.889%.
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What value of x satisfies the equation
(793x)3 = 343q36?
Answers
The value of x satisfies the equation is 4
What are index forms?Index forms are described as mathematical forms that are used to represent numbers or values that are too large or small in more convenient ways.
From the information given, we have that;
(7q³ˣ)³ = 343q³⁶
expand the bracket for the values
7³. q⁹ˣ = 343q³⁶
Now find the common exponents, we have;
7³. q⁹ˣ= 7³. q³⁶
Divide the values, we have;
q⁹ˣ = q³⁶
Equate the exponents, we get;
9x = 36
Divide both sides by the coefficient of x, we get
9x/9 = 36/9
Divide the values
x = 4
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a right triangle had side lengths d,e,and f as shown below. use these lengths to find sin x cos x and tan x
Answers
Cos X=D/F
Tan X= E/D
Using soh-cah-toa we know sin is opposite/ hypotenuse. Cos is adjacent/ hypotenuse. And tan is opposite/ adjacent
Dominic took a 20-question online quiz. He received 5 points for every correct answer. For every question he answered
incorrectly, he lost 2 points. The quiz also had a 20-point bonus for finishing in one hour or less. Since Dominic finished
the quiz in less than one hour, his score S is determined by x, the number of questions answered correctly.
Drag and drop expressions into the function to correctly define S(a).
Answers
The function that correctly defines S(x) is S(x) = 5x - 2(20 - x) + 20
How to determine the function that correctly defines S(x)We have the following definitions in the question
Correct answers = xTotal questions = 20Points for correct answers = 5Points for incorrect answers = -2Bonus for finishing in one hour or less = 20If the total questions is 20, then
Incorrect answers = 20 - x
So, the points gained/lost are
Gained = 5 * x = 5x
Lost = -2 * (20 - x) = -2(20 - x)
Bonus = 20
Add the above points to get the function S(x)
S(x) = 5x - 2(20 - x) + 20
Hence, the definition is S(x) = 5x - 2(20 - x) + 20
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you can have the points
Answers
6-Please help me (50 points)
Answers
The graphed function g(x) belongs to the square root function family.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.For this problem, we have the square root function translated 3 units right, hence the function's family is the square root.
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John has 6 pairs of pants and 3 shirts. How many possible outfits consisting of one shirt and
one pair of pants can he select?
Answers
Answer:
4*5*7=140 ways
Step-by-step explanation:
First he has to decide on a pair of pants and he has 4 different choices.
For each of those choices he has a choice of 7 different shirts, so that gives him 4 times 7 = 28 different pant/shirt combinations. (I hope none of the pants are striped and none of the shirts have polka-dots).
For each those 28 possibilities, he has 5 different ties he could select, so altogether he has 28 times 5 = 140 different outfits, and some of them may be acceptable to wear in public.
It is simply , 4*5*7=140 ways.
the bookstore sold 8 books for 66$ at that rate how much would one book be.
Answers
7) +9 –
+16 = N
8) +85 –
+12 = N
9) –6 –
–2 = N
10) +13 –
+12 = N sorry
Answers
Hey there!
Is this all one complex equation or it this representing multiple? Reason I ask is it's a little hard to understand above.
on a recent trip a trucker traveled 220 miles at a constant rate because of road conditions the trucker then reduce the speed by 25 mph an additional 30 miles traveled at a reduced rate the entire trip took five hours find the rate of the tracker for the first 220 miles
Answers
55 mph
if we assume it takes an hour for the last 30 miles then the rest of the time the trucker could go 55
A container is 8/9 kg of berries is 2/3 full, how many kg can the container hold
Answers
Answer:
1.33kg of berries
Step-by-step explanation:
A container is 8/9 kg of berries is 2/3 full, how many kg can the container hold
2/3 of a container = 8/9kg
To get the amount of kg the container can hold, we will write;
1 container = x kg
Divide both expressions
2/3 = 8/9x
Cross multiply
2 * 9x = 3*8
18x = 24
x = 24/18
x = 1.33kg
Hence the container will hold 1.33kg of berries
What is the area of the trapezoid?
80 m²
96 m²
100 m2
120 m²
Answers
Answer:
Step-by-step explanation:
A=100
Use the figure above to answer the questions.
A Name the quadrilateral.
B. Name the sides.
C. Name the angles.
D. Identify the congruent angles and the congruent sides.
Answers
Answer:
the answer is d
Step-by-step explanation:
the shape of it as well
Need help with this question
Answers
Answer:
Yes, it is a solution because inserting 8 into the equation gives you 13.
Step-by-step explanation:
1/2(8) + 9 = 13
4 + 9 = 13
13 = 13
I need help with this math problem
Answers
⇒Perimeter is the summation of all the sides of a shape
⇒Note for some sides I will not be able to explain because I cannot draw to show you.
P=S+S+S+S+S+S
P=4+8+12+2+8+4
P=38
⇒For the Area Divide the shape into two shapes Note it will results into two rectangles with the 1st rectangle having measurements L=12 and W=2
and the 2nd rectangle having L=8 and W=4 After finding the areas of both these rectangles ADD the areas for they will give you the area of the whole shape
\(1^{st} _{rectangle area} =L*W\\1^{st} _{rectangle area}=12*2\\\\\\1^{st} _{rectangle area}=24\)
⇒\(2^{nd} _{rectangle area}=L*B\\2^{nd} _{rectangle area}=8*4\\2^{nd} _{rectangle area}=32\\\\total_{shape \\area}=24+32\\\)
The Area of the shape is 56
note if you were to insert the unit of measurement you were going to put in the square measurement.
Please do not hesitate to ask failure to understand.
Please help
sin (52) = cos(
Answers
Answer:
0.78801.
Step-by-step explanation:
In trigonometry, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right-angled triangle that includes that angle.
However, since the angle of 52 is not specified to be in degrees or radians, I will assume it is in degrees.
Using a scientific calculator, the sine of 52 degrees is approximately 0.78801. Therefore, sin(52) = 0.78801.
Factor
4y(3x+2)-2(3x+2)
Answers
Answer:
\(2(3x+2)(2y-1)\)
Step-by-step explanation:
Hope I helped!
Answer:
(4y − 2)(3x + 2)
Step-by-step explanation:
4y(3x + 2) − 2(3x + 2) = (3x + 2)[4y − 2]
what is 9-3 divided by 1/3 + 1 =
Answers
write an equation of the line in slope intercept form if its slope is 3 and y-intercept is "-5"
Answers
Use y = mx + b
m = 3
b = -5
The answer: y = 3x - 5
Plz!!!! need help algebra!!!
give a good answer... and you get brainlst!!
Answers
Answer:
What's the question?
Step-by-step explanation:
What is the value of c?
a)4 units
b)5 units
c)6 units
d)7 units
Answers
The value of c in the triangle is (b) 5 units
Finding the value of c in the triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The length c is the hypotenuse of one of the triangles and can be calculated using the following Pythagoras theorem
c² = sum of squares of the legs
Using the above as a guide, we have the following:
c² = 3² + 4²
Evaluate
c² = 25
Take the square roots
c = 5
Hence, the hypotenuse of the right triangle is 5
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Woodsmith magazine gave instructions on how to build a pine cupboard. Lumber will be needed for two shelves 11 1/4 inches long, two base sides 12 1/2 inches long, and two door stiles 28 1/8 inches long. Your lumber comes in 6 foot lengths.
a. How many feet of lumber will you need?
Answers
You will need 7.104 feet of lumber. (rounded to three decimal places)
There are four basic arithmetic operations in mathematics: addition, subtraction, multiplication, and division.
Among these four procedures, division is one of the most important in our everyday tasks. It is the division of a large group into equal smaller groups.
To find out how many feet of lumber you need, you need to add up the length of all the pieces and then divide by the number of inches in a foot (12).
First, we'll add up the length of all the pieces:
11 (1/4) + 11 (1/4) + 12 (1/2) + 12 (1/2) + 28 (1/8) + 28 (1/8)
= 85 (1/4) inches
Next, we'll convert this total length to feet by dividing by 12:
85 1/4 inches ÷ 12 inches/foot = 7.104 feet
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