Can you please explain in a easy way please? Where I can understand step by step? Thank you!
Answers
A piecewise function is a function built from pieces of different functions over different intervals; in this case we have a piecewise function defined by two pieces.
The first piece tells us that if x is any value less than or equal to 3 the we need to use the expression 2x for the function.
The second piece tells us that if x is any value greater than 3 we have to use the expression:
\(\frac{1}{3}x^2-2x+9\)Now, to graph this function we need to make a table of values like any other function taking into acount on which interval is x in orther to use the proper expression for the output of the function:
In this table we use what we stated above; for example since 0 is less than 3 we have to use the expression 2x, then we have:
\(f(0)=2(0)=0\)and so on for the values one, two and three.
For the other values we notice that they are greater than 3 then we hace to use the second expression, for example:
\(\begin{gathered} f(4)=\frac{1}{3}(4)^2-2(4)+9 \\ f(4)=\frac{16}{3}-8+9 \\ f(4)=5.33\bar{3}-8+9 \\ f(4)=6.33\bar{3} \end{gathered}\)and so on for any value greater than 3.
Now we plot this points and join them to get the graph:
Related Questions
Quadrilateral MNPQ is rotated at 90 degrees counterclockwise about the origin and then rotated 270 degrees counterclockwise about the origin
Answers
After the double rotation, the vertices of the quadrilateral MNPQ are transformed to M'', N'', P'', and Q''. The shape of the quadrilateral may have changed, but the order of the vertices remains the same.
When a quadrilateral MNPQ is rotated counterclockwise at 90 degrees about the origin, each vertex undergoes a transformation.
The new positions of the vertices after this rotation can be denoted as M', N', P', and Q'. The order of the vertices remains the same.
Next, when the rotated quadrilateral M'N'P'Q' is further rotated counterclockwise at 270 degrees about the origin, each vertex undergoes another transformation.
The new positions of the vertices after this rotation can be denoted as M'', N'', P'', and Q''. Again, the order of the vertices remains the same.
It's important to note that a 270-degree counterclockwise rotation is equivalent to a 90-degree clockwise rotation.
The result of the double rotation is equivalent to a single clockwise rotation of 90 degrees.
For more such questions on Quadrilateral:
https://brainly.com/question/27991573
#SPJ8
The diagram below shows part of the graph of y=g(x) .
The function has stationary points at (0,−3) and (2,0) as shown.
Sketch the graph of the related function y=3−g(x).
Answers
9514 1404 393
Answer:
see attached
Step-by-step explanation:
The related function is reflected across the x-axis and translated up 3 units. Effectively, it is reflected across the line y = 3/2. The graph of the related function is shown in blue in the attachment.
Brent described two subatomic particles below:
Particle P: Non-charged particle
Particle Q: Negatively charged particle
Which of the following statements is correct based on the descriptions of each particle?
Particle P is a proton and Particle Q is an electron.
Particle P is an electron and Particle Q is a neutron.
Particle P is outside the nucleus and Particle Q is in the nucleus.
Particle P is in the nucleus and Particle Q revolves around the nucleus.
Answers
The descriptions of each particle is Particle P is in the nucleus and Particle Q revolves around the nucleus.
What is nucleus ?
The nucleus carries the genes, structures that contain the hereditary information, and controls and regulates the functions of the cell (such as growth and metabolism). Small bodies called nucleoli are frequently seen inside the nucleus. The nucleoplasm is the gel-like matrix in which the nuclear parts are suspended.
P is non-charged particle or neutron
Particle Q is negatively charged particle means electron
The nucleus, that dense central core of the atom, contains both protons and neutrons. Electrons are outside the nucleus in energy levels.
So, In nucleus, atom can contain both postively and no charged charged but outside the nucleus negatively charged particles are present that get attracted towards the nucleus.
Thus option d Particle P is in the nucleus and Particle Q revolves around the nucleus is correct
To learn more about nucleus visit:https://brainly.com/question/17704494
#SPJ1
Use the diagram below to answer the questions about the Law of Cosines.
Answers
Based on the Law of Cosines; it was proven that:
cos Θ = x/acos (180 - C) = x/aa² + b² + 2bx = c²Please note that the given equation on number 3 is wrong. The correct equation should be: a² + b² + 2bx = c². The explanation why the given equation is incorrect will be explained later.
Based on the unshaded triangle, we can find that:
cos Θ = x/a
Next, we will prove that: cos (180 - C) = x/a
Remember that:
cos (A + B) = cos A cos B - sin A sin B
Law of Cosines: c² = a² + b² - 2ab. cos C
cos C = - [c² - (a² + b²)] /2ab ... (i)
Then:
cos Θ = cos (180 - C)
cos (180 - C) = cos 180 . cos C - sin 180 . sin C
We subtitute equation (i):
cos (180 - C) = (-1) (- [c² - ((a² + b²)] / 2ab) - 0 sin C
cos (180 - C) = [c² - (a² + b²)]/ 2ab ... (ii)
If we focus on the unshaded triangle, we can find an equation of a, where:
a² = h² + x² ... (iii)
And if we combine both triangle into a giant triangle, we can make another equation of c. where:
c² = (x + b)² + h² ... (iv)
We will subtitute equation (iv) into equation (ii):
cos (180 - C) = [c² - (a² + b²)]/ 2ab
cos (180 - C) = [(x + b)² + h² - (a² + b²)] / 2ab
cos (180 - C) = [x² + b² + 2bx + h² - a² - b²] / 2ab
cos (180 - C) = [x² + 2bx + h² - a²] / 2ab ... (v)
We subtitute equation (iii) into equation (v):
cos (180 - C) = [x² + 2bx + h² - a²] / 2ab
cos (180 - C) = [a² + 2bx - a²] / 2ab
cos (180 - C) = 2bx / 2ab
cos (180 - C) = x/a --> PROVEN!
Next, we will try to show why the given equation of a² + b² - 2bx = c² is incorrect.
We know that:
a² + b² - 2ab cos C = c²
c² = (x + b)² + h²
We will try to find the value of cos C:
a² + b² - 2ab cos C = (x + b)² + h²
a² + b² - 2ab cos C = x² + b² + 2bx + h²
a² - 2ab cos C = a² + 2bx
- 2 ab cos C = 2bx
cos C = - x/a
We will subtitute the value of cos C under the Law of Cosines:
c² = a² + b² - 2ab cos C
c² = a² + b² - 2ab (- x/a)
c² = a² + b² + 2bx --> PROVEN!
Learn more about Law of Cosines here: brainly.com/question/9261858
#SPJ1
Find the distance between the two numbers on a number line. Write your answer as a mixed number.
−212,−534
The distance between the two numbers is....
(Answer it correct ill give you brainly)
Answers
Answer:
We conclude that the distance between the two numbers on a number line will be: 322
Step-by-step explanation:
Given the numbers
-212
-534
There can be a lot of ways to determine the distance between the two numbers on a number line like counting every number between them.
But, we can use a more efficient method in terms of determining the distance by taking the absolute value of the difference between those numbers.
so
Distance between the numbers:
\(\left|-212-\left(-534\right)\right|\)
Apply rule: -(-a) = a
\(=\left|-212+534\right|\)
\(=\left|322\right|\)
Apply absolute rule: \(\left|a\right|=a,\:a\ge 0\)
\(=322\)
Therefore, we conclude that the distance between the two numbers on a number line will be: 322
What is the name of the property for : a + ( − a ) = 0 ?
Answers
Answer:
Inverse Property of Addition
Step-by-step explanation:
figure 2-18 shows four paths along which objects move from a starting point to a final point, all in the same time interval. the paths pass over a grid of equally spaced straight lines
Answers
The ranking based on average speed is 1 > 2 > 4 > 3
(a) Based on the given information, we have:
V1 = V2: The objects on paths 1 and 2 have the same average velocity.
V3 < V4: The object on path 4 has a greater average velocity than the object on path 3.
(b) Average speed is simply the distance traveled divided by the time interval. If the objects move at a constant speed along each path, then the paths with the greatest distances will have the greatest average speeds. Therefore, the ranking based on average speed is:
1 > 2 > 4 > 3
Note that this ranking is based only on the distances traveled along each path, and does not take into account the directions of motion or any changes in direction.
Learn more about average velocity here https://brainly.com/question/862972
#SPJ4
Using the information in the Box-and-Whisker plot shown, below what value is three quarters of the data?
A. 7
B. 10
C. 12
D. 17
Answers
Answer:
Step-by-step explanation:
A
What is -4w + 7 = -10w + 37?
Please show me how to get it!
Answers
Part b c and d please help
Answers
Answer:
b) Y =5.73X +4.36
C) =5.73225*(21)X +4.359
124.73625
D) 163.728 = 5.73X +4.36
X = (163.728 - 4.36)/5.73
X = 27.81291449
Year would be 2027
Step-by-step explanation:
x1 y1 x2 y2
4 27.288 16 96.075
(Y2-Y1) (96.075)-(27.288)= 68.787 ΔY 68.787
(X2-X1) (16)-(4)= 12 ΔX 12
slope= 5 41/56
B= 4 14/39
Y =5.73X +4.36
elisa was going to sell all of her stamp collection to buy a videos game then she changes her mind then she bought 8 more how many did she start with if she now has 36
Answers
Answer:
24 (not sure)
Step-by-step explanation:
36 - 8 = 24
im not sure if this is what the question is asking for.
What is the value of 55 x 2 ÷ 11 - 10
A) 0
B) 1
C) 9
D) 27.5
Answers
Answer: 0
Explanation: Divide 2 and 11, and you get 2/11 and multiply that with 55 you get 10 and 10 - 10 equals 0! ^^
Find the distance between a point (–7, –19) and a horizontal line at y = 3. Question 18 options: A) 13 B) 22 C) –16 D) 16
Answers
Answer: B) 22
Step-by-step explanation:
y coordinate of line = 3
y coordinate of point = -19
On a number line, distance between 3 & -19 = 22
A number cube is rolled. Event A is rolling an odd number, and event B is rolling a factor of 12. What is P(AU B)?
Answers
Explanation:
A = set of odd numbers = {1,3,5}
B = set of factors of 12 = {1,2,3,4,6}
A U B = union of set A and set B
A U B = {1,3,5} union {1,2,3,4,6}
A U B = {1,3,5, 1,2,3,4,6}
A U B = {1,2,3,4,5,6}
The set union operation combines two sets into one bigger set. Duplicates are tossed out.
There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.
Therefore, the probability event A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.
Side notes:
A U B can be read out as "event A or event B"; so P(A U B) is "the probability event A happens or B happens or both".A intersect B = {1,3} = values that are in both set A and set B at the same time. These are both odd and a factor of 12.Choose the situation that represents a function.
A) The number of raisins in an oatmeal raisin cookie is a function of the diameter of the cookie.
B) The inches of rainfall is a function of the day’s average temperature.
C) The time it takes to cook a turkey is a function of the turkey’s weight.
D) The number of sit-ups a student can do in a minute is a function of the student’s age.
Answers
Answer:c
Step-by-step explanation:
Answer: The answer is C.
Hope this helps you!
DUE IN 30 MINS (6th grade) PLEASE PLEASE HELP ME ASAAP
The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 40 to 95. There is one dot above 45 and 80. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
No, there is no outlier. This means that the people were all the same age.
No, there is no outlier. This means that the people are all around the mean age.
Yes, there is an outlier of 45. This means that the average person at the center is 45 years old.
Yes, there is an outlier of 45. This means that one person's age was 45, which is 25 years younger than the next closest age
{Please follow the rules Dos and Don't}
Do :
Answer the question correctly
Leave a positive Comment
Make sure you have reviewed it before submitting
Don't
Answer incorrectly
Be Rude to the community
Spam/Send links to inappropriate Websites
Answers
Answer: Yes, there is an outlier of 45, This means that one person's age was 45, which is 25 years younger than the next closest age.
Hope this helps! :)
Step-by-step explanation:
Answer:
D
GIVE HIME BRAINLIEST
Step-by-step explanation:
Can somebody please help?? i’ll give Brainliest to whoever answers first.
There are 625 students in Leon's school. He takes a random sample of 75 students from the entire school population. In the sample, 33
students are planning to attend the end of year picnic.
Based on his data, how many students from the entire school are planning to attend the end of year picnic? Show ALL your work!
Answers
Answer:
The answer is 275 students.
Step-by-step explanation:
In 75 students, 33 students attend.
So the ratio is 33/75.
so multiply with 625.
625 x 33/75 = 275
3
1 point
Find the area of the composite figure below:
16.4 cm
5.5 cm
7 cm
Answers
The area of the composite figure is 159.9 cm²
Calculating the area of the composite figureFrom the question, we are to determine the area of the given composite figure
In the given diagram, the area of the composite figure = Area of triangle + Area of rectangle
First, we will calculate the area of the triangle
Area of triangle = 1/2 × base × height
Thus,
Area of the triangle = 1/2 × 16.4 × 5.5
Area of the triangle = 45.1 cm²
Calculating the area of the rectangle
Area of rectangle = Length × Width
Thus,
Area of the rectangle = 16.4 × 7
Area of the rectangle = 114.8 cm²
Therefore,
The area of the composite figure = 45.1 cm² + 114.8 cm²
The area of the composite figure = 159.9 cm²
Hence, the area is 159.9 cm²
Learn more on Calculating the area of the composite figure here: https://brainly.com/question/10254615
#SPJ1
Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48
Answers
Answer:
D) 48
Step-by-step explanation:
Let s = Scott
Let j - James
s = 5
s + 43 = j Substitute 5 for s
5 + 43 = j
48 = j
Solve y = ax² + c for x.
Answers
Answer:
\(x=\pm \sqrt{\frac{y-c}{a}}\)
Step-by-step explanation:
\(y=ax^2 + c \\ \\ ax^2 =y-c \\ \\ x^2=\frac{y-c}{a} \\ \\ x=\pm \sqrt{\frac{y-c}{a}}\)
Listed below is a table showing the number of employees. 20 years or older by gender in the United states
Answers
The total number of workers that were studied can be found to be 139,340,000.
The percent of workers unemployed would be 5. 4 %.
Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.
How to find the employment figures ?Number of employed workers :
= 74,624,000 + 64, 716, 000
= 139,340,000
Percentage unemployed :
= ( 4, 209,000 + 3,314,000 ) / 139,340,000
= 5. 4 %
Percentage of unemployed men :
= 4,209,000 / 74,624,000
= 5.6 %
Percentage of unemployed women:
= 3,314,000 / 64, 716, 000
= 5. 1 %
Find out more on unemployment at https://brainly.com/question/13280244
#SPJ1
The full question is:
a. How many workers were studied?
b. What percent of the workers were unemployed?
c. Compare the percent unemployed for the men and the women.
I need help ASAP on this question.
Answers
How to find measure of an angle
Answers
Write an equation of the line that passes through the points (1,-4) and (-1,3) in point slope form and then in slope intercept form
Answers
Answer:
point slope form: y-(-4)=-3(x-1)
Slope intercept form: y=-3x-3
Step-by-step explanation:
Point slope form formula: y-y1= m(x-x1)
(1,-4), (-1,3)
Slope formula x2-x1/ y2-y1
Plug in the information 3-(-4)/-1-1
Simplify: 6/-2 or -3
Use one of the coordinates for the equation: y-(-4)=-3(x-1)
I used the first coordinate.
Slope intercept form formula: y=mx+b
Slope=-3
Plug in information: y= -3x+b
To find b, plug in one of the coordinates.
-4=-1+b, subtract to isolate b
b=-3
Your equation: y=-3x-3
Hope this helps!
The following angles are supplementary to each other.
m∠C = (x + 19)° and m∠D = (3x − 19)°
Determine x.
60
45
38
19
Answers
Answer:
45
Step-by-step explanation:it gives you the answer chiices if you plug each number into x and then do the equation you will get 180
Answer: 45
Step-by-step explanation:
Did the test.
Find the standard deviation for n = 10 and p = 0.6 when the conditions for the binomial distribution are met. (Round your answer to two digits after the decimal point.)
Answers
Given the values of n and p to be;
\(\begin{gathered} n=10 \\ p=0.6 \end{gathered}\)We can calculate the standard deviation using the formula below;
\(\sigma=\sqrt[]{n\cdot p\cdot(1-p)}\)substituting the given values;
\(\begin{gathered} \sigma=\sqrt[]{10\cdot0.6\cdot(1-0.6)} \\ \sigma=\sqrt[]{2.4} \\ \sigma=1.55 \end{gathered}\)Therefore, the standard deviation for the distribution is;
\(\sigma=1.55\)When the polynomial 4x4–13x2–2x + 1 is divided by the polynomial x –2, what is the remainder?
A) -23
B) 1
C) 9
D) 17
Answers
Step-by-step explanation:
answer is C
the process is shown in picture
The answer is either A or D
Ty bought a new computer for $499. This brand depreciates at a rate of 12% of the original price per year. The value y of Ty's computer, x years after he purchased it, is found using an equation in the form y = mx + b. What is the approximate value of m?
Answers
Answer:
the approximate value of m is -0.12, indicating that the value of Ty's computer decreases by 0.12 (or 12%) each year.
Step-by-step explanation:
o express this depreciation rate as a slope in the equation y = mx + b, we need to determine how much the value changes (the "rise") for each year (the "run").
Since the value decreases by 12% per year, the slope (m) would be -12%. However, we need to express the slope as a decimal, so we divide -12% by 100 to convert it to a decimal:
m = -12% / 100 = -0.12
The constraints of a problem are listed below. What are the vertices of the feasible region?
\(x+y\leq 7\\x-2y\leq -2\\x\geq 0\\y\geq 0\)
Answers
The vertices of the feasible region is (4, 3)
What are the vertices of the feasible region?From the question, we have the following parameters that can be used in our computation:
x + y ≤ 7
x - 2y ≤ -2
x ≥ 0
y ≥ 0
Express as equations
So, we have
x + y = 7
x - 2y = -2
Subtract the equations
3y = 9
So, we have
y = 3
Next, we have
x + 3 = 7
This gives
x = 4
Hence, the vertex of the feasible region is (4, 3)
Read more about linear programming at
https://brainly.com/question/14309521
#SPJ1
10. The ordered pairs (1, 2), (2, 8), (3, 18), and (4, 32) represent a function. What is a rule that represents this function?
It also gives me these numbers:
a. 2x
b. 2x + 2
c. x^2
d. 2x^2
Answers
Answer:
d. 2x^2
Step-by-step explanation