What does the graph of f(x)=3x^2-2x+1 look like
Answers
Answer:
Below.
Step-by-step explanation:
This is a parabola.
As the coefficient of x^2 is positive it will open upwards ( shaped like a 'U').
If we convert to vertex form we can find the line of symmetry and the coordinates of the vertex:
f(x) = 3x^2 - 2x + 1
f(x) = 3(x^2 - 2/3 x) + 1
f(x) = 3[(x - 1/3)^2 - (1/3)^2] + 1
f(x) = 3(x - 1/3)^2 - 1/3 + 1
f(x) = 3(x - 1/3)^2 + 2/3
So the line of symmetry is x = 1/3 and
the vertex ( the minimum of the curve) is at (1/3, 2/3).
Related Questions
one interior angle of a regular polygon is 3.5 times the size of one of its exterior angles. how many sides are in the polygon?
Answers
By studying the characteristics of a polygon, it can be concluded that there are 9 sides in the polygon.
A polygon is a plane figure represented by a finite number of connected straight lines (the sides), thus forming a closed polygonal chain (or polygonal circuit).
Regarding the angles, the characteristics of polygons are:
the exterior angle is the supplement of the interior angle, thus the sum of them is 180°the sum of the exterior angles is 360°the sum of interior angles is (n − 2) × 180° where n is the number of sidesNow we take a look at the given problem. If we denote x as the exterior angle, then the interior angle is equal to 3.5x.
An exterior and interior angle are supplementary angles, so:
x + 3.5x = 180°
4.5x = 180°
x = 180°/4.5°
= 40°
The sum of the exterior angles is 360°, so the number of the sides (n) can be calculated as follows:
n * 40° = 360°
n = 360° / 40°
= 9
Thus, the polygon has 9 sides.
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Given points A(-1,4) and B(x,7), determine the value(s) of x if AB=5cm
Answers
The value of x is either 3 or -5 based on the distance formula.
What is a co-ordinate system?
In pure mathematics, a coordinate system could be a system that uses one or additional numbers, or coordinates, to uniquely confirm the position of the points or different geometric components on a manifold like euclidean space.
Main body:
according to question
Given points A(-1,4) and B(x,7)
Also AB = 5 cm
Formula of distance = \(\sqrt{(y1-y2)^{2}+(x1 -x2)^{2} }\)
here by using points ,
5 = \(\sqrt{(x+1)^{2} +(7-4)^{2} }\)
taking square on both side ,'
25 = \((x+1)^{2} +3^{2}\)
25-9 = (x+1)²
16 = (x+1)²
taking square root on both sides,
x+1= ±4
x = 4-1 = 3 or x = -4-1 = -5
Hence value of x is either 3 or -5.
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Amelia traces her protractor on a piece of graph paper. Then, she holds one corner of the protractor still while she turns the rest of the protractor 270° clockwise. Finally, she traces the protractor again. What type of transformation did Amelia perform?
Answers
Answer:
Rotation is the answer to your problem.
Step-by-step explanation:
The floor plan shows the dimensions of a room.
78 in.
102 in.
96 in.
126 in.
what is the largest square tile that could be used to exactly cover the floor without cutting a tile?
Answers
The largest square tile that could be used to exactly cover the floor without cutting a tile is 78 inches by 78 inches.
To determine the largest square tile that can cover the floor without cutting, we need to find the greatest common divisor (GCD) of the dimensions of the room. The GCD represents the largest side length that can evenly divide all sides of the room.
The dimensions of the room are given as 78 inches, 102 inches, 96 inches, and 126 inches. To find the GCD, we can use the Euclidean algorithm, which involves finding the remainder when dividing one number by another and repeating the process until the remainder is zero.
Let's find the GCD step by step:
Step 1: Find the GCD of 78 inches and 102 inches.
Dividing 102 by 78, we get a remainder of 24.
Now, divide 78 by 24, which gives a remainder of 6.
Finally, divide 24 by 6, which gives a remainder of 0.
Step 2: Find the GCD of 6 inches and 96 inches.
Dividing 96 by 6, we get a remainder of 0.
Step 3: Find the GCD of 6 inches and 126 inches.
Dividing 126 by 6, we get a remainder of 0.
Since the remainder is zero in both Step 2 and Step 3, the GCD of all the dimensions is 6 inches.
To cover the floor without cutting any tiles, we need to find the largest square tile that can evenly divide all sides. Since the GCD is 6 inches, the largest square tile would have side lengths of 6 inches.
However, if we interpret the question as asking for the largest square tile in terms of one side length, we can use the GCD to determine the size. In this case, the largest square tile would have a side length of 78 inches, which is the GCD of all the dimensions.
In summary, the largest square tile that could be used to exactly cover the floor without cutting a tile is either 6 inches by 6 inches (if considering one side length) or 78 inches by 78 inches (if considering the GCD of all dimensions).
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Consider a consumer whose utility function is:U(x1, x2) = log(x₁) + log(x₂) X1 ≤ 0.5 Suppose that p₂ = 1, m = 1, and p1 is unknown. There is rationing such that ** Part a. (5 marks) Find the minimal p₁, denoted by pi, such that the if P1 > Pi, then the consumer consumes x₁ strictly less than 0.5. ** Part b. (10 marks) Now suppose increases. mathematically show that whether the threshold on you found in Part a increases/decreases/stays the same.
Answers
Part a)Given, utility function of the consumer as:U(x1, x2) = log(x1) + log(x2)X1 ≤ 0.5Let p2 = 1 and m = 1, and p1 is unknown. The consumer has a budget constraint as: p1x1 + p2x2 = m = 1Now we have to find the minimal p1 such that the consumer consumes x1 strictly less than 0.5.
We need to find the value of p1 such that the consumer spends the entire budget (m = 1) on the two goods, but purchases only less than 0.5 units of the first good. In other words, the consumer spends all his money on the two goods, but still cannot afford more than 0.5 units of good 1.
Mathematically we can represent this as:
p1x1 + p2x2 = 1......(1)Where, x1 < 0.5, p2 = 1 and m = 1
Substituting the given value of p2 in (1), we get:
p1x1 + x2 = 1x1 = (1 - x2) / p1Given, x1 < 0.5 => (1 - x2) / p1 < 0.5 => 1 - x2 < 0.5p1 => p1 > (1 - x2) / 0.5
Now we know, 0 < x2 < 1.So, we will maximize the expression (1 - x2) / 0.5 for x2 ∈ (0,1) which gives the minimum value of p1 such that x1 < 0.5.On differentiating the expression w.r.t x2, we get:d/dx2 [(1-x2)/0.5] = -1/0.5 = -2
Therefore, (1-x2) / 0.5 is maximum at x2 = 0.
Now, substituting the value of x2 = 0 in the above equation, we get:p1 > 1/0.5 = 2So, the minimal value of p1 is 2.Part b)Now, we have to show mathematically that whether the threshold on p1 found in Part a increases/decreases/stays the same when p2 increases.
That is, if p2 increases then the minimum value of p1 will increase/decrease/stay the same.Since p2 = 1, the consumer’s budget constraint is given by:
p1x1 + x2 = m = 1Suppose that p2 increases to p2′.
The consumer’s new budget constraint is:
p1x1 + p2′x2 = m = 1.
Now we will find the minimal p1 denoted by pi, such that the consumer purchases less than 0.5 units of good 1. This can be expressed as:
p1x1 + p2′x2 = 1Where, x1 < 0.5
The budget constraint is the same as that in Part a, except that p2 has been replaced by p2′. Now, using the same argument as in Part a, the minimum value of p1 is given by:
p1 > (1 - x2) / 0.5.
We need to maximize (1 - x2) / 0.5 w.r.t x2.
As discussed in Part a, this occurs when x2 = 0.Therefore, minimal value of p1 is:
pi > 1/0.5 = 2
This value of pi is independent of the value of p2′.
Hence, the threshold on p1 found in Part a stays the same when p2 increases.
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Jesse is saving the money he earns in his piggybank. He had already earned
$60 from previous work. He charges $15 to mow one lawn. After mowing 4
lawns, how much total money will he have in his piggybank?
Answers
Answer:
Jesse will have $120.
Step-by-step explanation:
First you need to set up your equation. We know Jesse has $60 already and that he charges $15 per lawn. Your equation will look something like this:
15x+60=?
Then you plug in the 4 lawns he did:
15(4)+60=
Then you solve and get 120! :)
PS Parenthesis mean you are multiplying. Same thing as saying
15 x 4 + 60= 120
Clara lends half her collection of formal dresses, d, to her sister, Susan. Clara then buys four more dresses. If she has 12 now, write an equation to show how many dresses Clara had originally.
Answers
Answer:
16
Step-by-step explanation:
a:2+4 =12
a:2=12-4
a:2=8
a=8 ×2
a=16 dresses
Angle DEB is 71°. State the size of angle ABD, giving a reason for your answer.
Answers
Check the picture below.
suppose you have 50 students and need to assign them to two independent groups. describe a randomization procedure that would achieve this.
Answers
To assign the 50 students to two independent groups, a randomization procedure can be used. The procedure involves first listing all the students in a random order. It minimizes bias and ensures an equal chance of assignment to either group.
To assign 50 students to two independent groups using randomization, follow these steps:
1. Start with a list of all 50 students.
2. Assign a unique number to each student, such as from 1 to 50.
3. Use a random number generator to generate 25 distinct random numbers from 1 to 50. These random numbers will represent the students for the first independent group.
4. The remaining 25 students, represented by the numbers not selected in step 3, will form the second independent group.
5. Assign the students to their respective groups based on the random numbers.
This procedure ensures that the students are assigned to two independent groups through randomization, reducing potential biases and ensuring a fair distribution of students across the groups.
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A. 22
B. 23
C. 24
D. 33.75
Answers
Answer:
c
Step-by-step explanation:
7.5 + 7.5 + 4.5 +4.5 = 24
convenience sampling allows for generalizations to a larger population, and probability sampling does not. group of answer choices true false
Answers
Probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
Explain the term convenience sampling?Convenience sampling is any non sampling technique where units are chosen for the sample based on their accessibility to the researcher.
This may be as a result of close proximity geographically, availability at a specific moment, or willingness to take part in the study. Convenience sampling, sometimes known as inadvertent sampling, is a non-random sampling technique.Research projects in qualitative and medical fields frequently employ convenience sampling.In medical science, convenience sampling frequently entails choosing clinical cases or volunteers who are accessible nearby (such as at a hospital) or from a database of medical information.Convenience sampling is frequently employed in qualitative research in the social sciences and in education where it is practical to use which was before groups, including such students.Thus, probability sampling is not "wrong," and convenience sampling allows allowing generalizations to a wider group.
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Ava earns 9.20 per hour for the first 6 hours she works each day then time and a half.
What is her pay if she works for 9 hours?
Answers
What decimal is equivalent to 1/8
Answers
Answer:
0.125
Step-by-step explanation:
Becuase math
a. 51 b.102 c.112 d.258
Answers
find the equation for (a) the tangent plane and (b) the normal line at the point p0(2,0,2) on the surface 2z−x2=0.
(a) The equation for the tangent plane is
nothing.
(b) Find the equations for the normal line.
xequals=nothing,
yequals=nothing,
zequals=nothing
Answers
(a) The equation for the tangent plane at point P₀(2,0,2) on the surface 2z−x²=0 can be found by taking the partial derivatives of the surface equation with respect to x, y, and z at point P₀.
Then we can use these derivatives to construct the equation of a plane in the form of Ax + By + Cz + D = 0.
(b) To find the equations for the normal line, we first need to determine the normal vector to the tangent plane at point P₀. The normal vector will have components equal to the coefficients of x, y, and z in the equation of the tangent plane. Once we have the normal vector, we can write the parametric equations of the normal line using the coordinates of point P₀.
It seems that the equation for the tangent plane and the equations for the normal line are missing from the provided options. Without the specific equations, it is not possible to provide the exact values for x, y, and z in the equations for the normal line.
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The Environmental Protection Agency (EPA) fuel economy estimates for automobiles can be described by a normal model with mean E(X) = / = 29 miles per gallon and standard deviation SD(X) 6 = 5.85 miles per gallon. What is the median miles per gallon for automobiles according to EPA estimates, that is, what is the miles per gallon k such that P(X > k) = P(X < k) = 0.50? Right-click this link standard normal table to open a standard normal table in a separate window or tab. () 29.85 () 28.15 () 29 () 30.7 () 30.96
Answers
We are given the following:
Mean, E(X) = 29 miles per gallon
Standard Deviation, SD(X) = 5.85 miles per gallon
P (X > k) = P (X < k) = 0.50
We are required to find the median miles per gallon according to the EPA estimates.
The question mentions a normal distribution, which is also known as a Gaussian distribution. Gaussian distributions are those that have equal values for mean, median and mode. This type of distribution is of continuous probabilities.
From the above explanation, we can deduce that since, Mean= Median = Mode, and the value of mean is given in the question,
The median miles per gallon is 29 miles per gallon.
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If you eat a diet with 2,000 kilocalories and 45 percent of those calories come from protein, about how many grams of protein did you eat?
Answers
The amount of Protein intake is 900 kilocalorie.
We have - 2000 Kilocalories of diet and 45 Percent of calories come from Proteins.
Wе have to find out the amount of protein intake.
If ' x ' students out of total ' n ' students in a class are infected by virus. Then, what percentage of students are infected.Percentage of students affected are - \(\frac{x}{n} \times 100\)
In the question given -
Let the amount of Protein intake be y.
Then -
45 = y % of 2000
45 = \(\frac{y}{2000} \times100\)
y = \(\frac{45\times2000}{100}\)
y = 900 Kilocalorie
Hence, the amount of Protein intake is 900 kilocalorie.
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Mya uses a potato chip can to store small items. each cylindrical can has a radius of 2.5 inches and a height of 9 inches. what is the approximate surface area of the can? (use 3.14 for π.)
Answers
The approximate surface area of the can is 180.55 sq.inches
A cylinder's surface area is the area that its surface takes up in three dimensions. A three-dimensional structure known as a cylinder has circular bases that are parallel to one another. There are no vertices on it. Area of three-dimensional shapes often refers to surface area. Square units are used to denote the surface area. Examples include cm2, m2, and so forth. A group of circular discs placed on top of one another might be thought of as a cylinder. The cylinder has both surface area and volume since it is a solid with a three-dimensional geometry.
The area of the cylinder is determined by adding the areas of its two circular bases and curving surface.
The Surface Area of Cylinder = Curved Surface + Area of Circular bases
S.A. (in terms of π) = 2πr (h + r) sq.unit
Where, π (Pi) = 3.142 or = 22/7
r = Radius of the cylinder
h = Height of the cylinder
cylindrical can has a radius of 2.5 inches and a height of 9 inches
surface area =2πr (h + r) sq.unit
= 2π*2.5(9+2.5)
=180.55 sq.inches
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\(245 \div 7\)
Answers
Answer:
35
Step-by-step explanation:
\(245\) ÷ \(7\) :-
\(245\) ÷ \(7 = 35\)
∠A and \angle B∠B are supplementary angles. If m\angle A=(5x+25)^{\circ}∠A=(5x+25) ∘ and m\angle B=(3x+19)^{\circ}∠B=(3x+19) ∘ , then find the measure of \angle B∠B.
Answers
Answer:
Measure of angle B is 70 degrees
Step-by-step explanation:
If they are both supplementary, it means that add up to be 180 degrees
Thus;
5x + 25 + 3x + 19 = 180
8x + 44 = 180
8x = 136
x = 136/8
x = 17
Measure of angle B will be;
3(17) + 19
= 51 + 19 = 70 degrees
Angle 1 and angle 2 are ____.
Answers
Answer:
adjacent
Step-by-step explanation:
Answer:
adjacent angles
Step-by-step explanation:
Hope this Helps! :)
What is the solution to 5(2x−2)=30? solve for x
Answers
Answer:
x=4
Step-by-step explanation:
5(2x-2)=30
divide both sides
2x-2=6
move the constant to the right
2x=6-2
caculate
2x=8
divide both sides
x=4
Select the equation in point-slope form for the line that passes through the point (1, -1) and has a slope of 4.
O A y + 1 = 4x-1
B. y 1= 4x + 1
Answers
Answer:
y + 1 = 4(x−1)
Step-by-step explanation:
y - y1 = m ( x - x1 )
PLS HELP ME ILL GIVE U BRAINLIEST THXX Find (F-g)(2)
Answers
Answer:
-9 is the correct answer
1
Robert has a piece of string that is 62 cm long. He cuts off 39 cm of the string.
How long is the string that is left?
Answers
Answer:
23cm
Step-by-step explanation:
62-39=23cm
Change the order of integration in the integral \( \int_{0}^{1} \int_{y^{2}}^{\sqrt{y}} f(x, y) d x d y \). Reverse the order of integration. \[ \iint f(x, y) d y d x \] (Type exact answers.)
Answers
To reverse the order of integration in the integral
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Find the missing variable!! Will mark brainliest!!THANK YOU!
Answers
Answer:mark me it pls
meme of the day: Gote aka my friend
Explain how to describe the data on a histogram.
Answers
Answer:
visual interpretation. of numerical data
Step-by-step explanation:
A histogram is a graphical representation of discrete or continuous data. To put it another way, it gives a visual representation of numerical data by displaying the number of data points that fall within a given range of values.
On friday night, the owner of chez pierre in downtown chicago noted the amount spent for dinner for 28 four-person tables. 110 118 124 185 129 128 122 139 120 95 119 99 191 130 84 110 149 123 76 175 143 83 110 76 165 67 102 151. click here for the excel data file.
(a) Find the mean, median, and mode. (Round your answers to 2 decimal places.) NOTE - (It also asks for the count)
(b) Are the data symmetric or skewed? If skewed, which direction?
multiple choice
a. Symmetric
b. Skewed right
c. Skewed left
Answers
- Mean: 119.43- Median: 118.50- Mode: 110 - Count: 28
To find the mean, we add up all the values and divide by the number of observations. In this case, the sum of the values is 3342, and since there are 28 observations, the mean is 3342/28 = 119.43.
The median is the middle value when the data is arranged in ascending order. In this case, there are 28 observations, so the median is the average of the 14th and 15th values. When the data is ordered, the 14th value is 118 and the 15th value is 124. Therefore, the median is (118 + 124)/2 = 118.50.
The mode is the value that appears most frequently in the dataset. In this case, the value 110 appears three times, which is more than any other value. Hence, the mode is 110.
The count simply refers to the number of observations in the dataset, which is 28 in this case.
(b) The data is skewed right.
When data is symmetric, it means that the values are evenly distributed around the mean, resulting in a bell-shaped curve. In this case, the data is not symmetric. Looking at the dataset, we can observe that there are several smaller values on the left side, while the right side has a few larger values. This indicates a right skew or positive skewness.
Skewness refers to the asymmetry of a distribution. In a right-skewed distribution, the tail of the distribution extends towards the right, indicating a longer right tail. Therefore, the correct answer is b. Skewed right, indicating that the data is positively skewed.
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What calculator is used for pre-calculus?
Answers
A scientific calculator is typically used for pre-calculus.
This type of calculator is designed to handle more advanced mathematical functions, such as trigonometry, logarithms, and exponents, which are commonly used in pre-calculus.
It is important to have a scientific calculator for pre-calculus because it allows you to easily solve more complex equations and perform calculations quickly and accurately.
Additionally, many scientific calculators have graphing capabilities, which can be useful for visualizing equations and understanding how they behave. Overall, a scientific calculator is an essential tool for pre-calculus and can help you succeed in the course.
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