In two or more complete sentences, define the key features of the graph below and explain how to write its equation using function notation.
Answers
This means that for each value of f (x) there are two possible values of x.
The absolute value function is:
f (x) = lxl
y = f (x) - 2 shifts the graph 2 units down.
y = f (x + 3) moves the graph 3 units to the right.
Finally:
The function that best fits this graph is:
f (x) = l-x + 3l-2
Answer:
The function notation of the graph is f(x) = |x-3| - 2
Step-by-step explanation:
From the graph it is evident that it is the graph of the absolute value of the function i.e. f(x) = |x| and we know that 'Translation' is a transformation that shifts the graph of a function in any direction.
Now, as we can see that the graph is shifted towards the right of the y-axis at point x=3, this means that it is translated by 3 units to the right of y-axis.
Therefore, the function becomes f(x) = |x-3|.
Furthermore, it is also shifted downwards at the point x= -2, this means that it is translated by 2 units downward from the x-axis.
Hence, the new function is f(x) = |x-3| - 2.
It can also be seen from the figure below that the graph of above f(x) is same as that of the provided image.
Related Questions
In a raffle, one ticket is randomly chosen from 80 tickets to receive free haircuts for a year. If Jake entered 6 tickets, what is the probability that he is not chosen to receive the free haircuts? Express your answer as a fraction in simplest form, percent, and decimal.
Answers
Final answer:
The probability that Jake is not chosen in the raffle is 37/40, 92.5%, or 0.925.
Explanation:
The question asks for the probability that Jake is not chosen to receive free haircuts for a year from a raffle of 80 tickets, where he entered 6 tickets.
First, we compute the probability that Jake is chosen, which is the number of tickets he entered divided by the total number of tickets, resulting in 6/80 or 3/40.
To find the probability that Jake is not chosen, we subtract this probability from 1 (the total probability space), yielding 1 - 3/40 = 37/40.
In the simplest form, this is already reduced. As a percent, this probability is 92.5%, and as a decimal, it is 0.925.
The two-way table shows the number of students in a school who like music and/or dance.
Like Music
Do Not Like Music
Total
Like Dance
23
?
42
Do Not Like Dance
15
11
26
Total
38
30
68
What is the missing number in the table?
19
31
53
65
Answers
The missing number in the two-way frequency table will be 19 so option (A) will be correct.
What is a frequency table?
A frequency table is a list of objects with the frequency of each item shown in the table.
The quantity of times that an event or value occurs is its frequency.
In other words, a frequency table is a table in which we have some data and their frequency.
Given,
Total number of students who like dance= 42
Out of which 23 like music
Remaining = 42 - 23 = 19
So there will be total 19 students who like dancing but not music.
To learn more about the frequency table
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Rank the nine career characteristics in order of their importance to you with the first being the most important
Answers
2. Farmers
3. Army Forces/ Police
4. Doctors
5. Education Administrators
6.Engineers
7. Lawyers
8.Construction Workers
9. Shopkeepers and other workers
That took a lot of thought, and I doubt I may have covered the most important careers of our society. I hope this helps and I'm extremely sorry if I left out a career and I hope nobody gets offended in any way.
Answer:
dont listen to the other dude
Step-by-step explanation:
explain why the amount of propane in a grill’s tank and the time spent grilling could represent an inverse variation
Answers
The obvious answer is because propane is a gas at room temperature, while 2-propanol is a liquid at room temperature.
That happens because the intermolecular forces that exist between 2-propanol, or isopropyl alcohol, molecules are stronger than those that exist between propane molecules.
The amount of propane in a grill's tank and the time spent grilling represent an inverse variation. As the amount of propane in the tank decreases, the time spent grilling increases.
Explanation:In the context of a propane grill, the amount of propane in the grill's tank and the time spent grilling represent an inverse variation. In an inverse variation, as one variable increases, the other variable decreases, and vice versa. In this case, as the amount of propane in the tank decreases (more grilling time), the time spent grilling increases. This is because the more propane that is used up, the less time you have left to grill before running out of gas.
In what range do the closing costs on a home loan typically fall?
a. 1% to 3%
b. 3% to 5%
c. 5% to 7%
d. 7% to 10%
Answers
Answer:
The answer is b.
Step-by-step explanation:
Answer:
b. 3% to 5% is the right choice.
Step-by-step explanation:
When a person buys a house, he will pay anywhere between 2 to 5 percent of the actual home price or the purchase price in the closing fees.
For example - if a home costs $200,000, a person can pay between $4000 and $10000 in closing costs.
So, option B : 3% to 5% is the correct answer.
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
x y
2 3
4 5
6 7
8 9
A. Initial value: 1, rate of change: 2 (Not the answer)
B. Initial value: 1, rate of change: 1
C. Initial value: 2, rate of change: 2 (Not the answer)
D. Initial value: 3, rate of change: 2
Answers
B. Initial value: 1, rate of change: 1
D is completely off. To get the initial value on a table you have to find the place where the input is zero.
So, you would take (2,3) and decrease both slots by 2 until x reaches zero. Now, we have (0,1). 1 is now our Initial Value.
To find the rate of change, you simply see how much the values increase/decrease. For example, let's take (6,7) and (8,9). As I said before, the input and output value increase by 2. Now, you put the change in 'y' over the change in 'x' and you have 2/2. After simplification, you are left with 1 as a whole number.
-Hope that wasn't too confusing, lol. I got a hundred on my test so I can assure you B. is correct. Good luck on your quiz :)
Answer:
Initial value: 1, rate of change: 1
Step-by-step explanation:
Took the FLVS test
A rectangle has a length of 1111 inches less than 33 times its width. if the area of the rectangle is 592592 square inches, find the length of the rectangle
Answers
A = L*W
592 = L*(L +11)/3
It is convenient to let a graphing calculator find the solution to this.
L = 37 . . . . inches
1,220,000,000 in scientific notation?
0.0287 in scientific notation?
Answers
= 1.22 × 109
(scientific notation)
= 1.22e9
(scientific e notation)
= 1.22 × 109
(engineering notation)
(billion; prefix giga- (G))
= 1220000000
(real number)
_________________________________________________
Answer:
= 2.87 × 10-2
(scientific notation)
= 2.87e-2
(scientific e notation)
= 28.7 × 10-3
(engineering notation)
(thousandth; prefix milli- (m))
= 0.0287
(real number)
Answer:
1.22*10^9
Step-by-step explanation:
Three consecutive integers whose sum is 138
Answers
Hope this helps!
X → first integer
X + 1 → second integer
X + 3 → third integer
X + X + 1 + X + 2 = 138
3x + 3 = 138
-3 -3
3x = 135
÷3 ÷3
X = 45
X + 1 = 46
X + 2 = 47
Four consecutive integer numbers add to 2. What are the numbers?
Answers
Hope this helps
Four consecutive integer numbers add to 2. What are the numbers?
Let the smallest integer=x
The three consecutive integers will be x+1,x+2, x+3
Sum of four consecutive integers=2
So, x+x+1+x+2+x+3=2
Adding like terms, we get
4x+6=2
Subtract 6 from both sides
4x+6-6=2-6
4x+0=-4
4x=-4
To solve for x, let us divide by 4 on both sides
4/4x=-4/4
x=-1
So, the four consecutive integers are =x=-1
x+1=-1+1=0
x+2=-1+2=1
x+3=-1+3=2
So, the four consecutive integers are:= -1,0,1,2
A student earned grades of C, A, B, and A in four different courses. Those courses had these corresponding numbers of credit hours: 4, 5, 1, and 5. The grading system assigns quality points to letter grades as follows: A = 4, B = 3, C = 2, D = 1, and F = 0. Compute the grade point average (GPA) and round the result to two decimal places.
Answers
To compute the GPA, multiply each grade by its corresponding credit hours, sum up the grade points, and divide by the total number of credit hours. In this case, the GPA is 3.40.
Explanation:To compute the grade point average (GPA), we need to multiply each grade by its corresponding number of credit hours to get the grade points. Then, we sum up the grade points and divide by the total number of credit hours. Here are the calculations:
Course 1: C grade (2 grade points) x 4 credit hours = 8 grade pointsCourse 2: A grade (4 grade points) x 5 credit hours = 20 grade pointsCourse 3: B grade (3 grade points) x 1 credit hour = 3 grade pointsCourse 4: A grade (4 grade points) x 5 credit hours = 20 grade pointsTotal grade points = 8 + 20 + 3 + 20 = 51 grade points
Total credit hours = 4 + 5 + 1 + 5 = 15 credit hours
GPA = Total grade points / Total credit hours = 51 / 15 = 3.40
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Seventy-five bottles of water are randomly tested from the large inventory in a warehouse. Which term refers to the large inventory of water bottles in the warehouse
Answers
Luiza delivers newspapers in her neighborhood. If you plot the points (−1, 1), (4, 1), (4, −2) and (−1, −2), you will create a representation of the route she takes, in miles. How many miles does her route cover?
Answers
We have then that the resulting figure is a rectangle.
We must find the perimeter of the rectangle that is given by:
P = 2L + 2W
Where,
L: long
W: width
Restoring the values:
P = 2 * (5) + 2 * (3)
P = 16
Answer:
her route cover 16 miles.
Answer: 16 i just did this
Step-by-step explanation:
(-6,12,-24...) What is the common difference? Is it Arithmetic or Geometric
Answers
In an aptitude test if am given a question like this I wouldn't even solve it because the answer is in the question...
How???
"what is the common difference " then you asked" is it Arithmetic or geometric"
I would have chosen arithmetic because common difference is only typical to arithmetic progression... But this question is a typical Geometric sequence "we use Common ratio"
Common ratio = T₂/T₁
Common difference = T₂-T₁
T₂ = 12 and T₁ =-6
∴Common ratio = 12/-6 = -2......
Meaning each number in the sequence in creases by a factor of -2....
Multiply T₁ by -2 you'll have 12[T₂]
Multiply T₂ by -2 you'll have -24[T₃] and the sequence continues .........
Hope this helped......?
helpppppppppppppppppppppppppp
Answers
The fourth function is just a constant (with exponent 0), so it is an even function.
1. f(x) = (x-1)^2 = x^2 - 2x + 1
f(-x) = (-x-1)^2 = x^2 + 2x + 1
These two don't match, not an even function
2. f(x) = 8x
f(-x) = -8x
These two don't match, not an even function
3. f(x) = x^2 - x
f(-x) = (-x)^2 - (-x) = x^2 + x
These two don't match, not an even function
4. f(x) = 7
f(-x) = 7
Match, is an even function
A Web site defines a regular polygon as “a polygon with all sides the same length.” Is this definition valid?
A. Yes, because all regular polygons fit this definition.
B. Yes, because a square is a regular polygon.
C. No, because some polygons that are irregular fit this definition.
D. No, because not all regular polygons fit this definition.
Answers
Final answer:
The definition of a regular polygon as a polygon with all sides the same length is incomplete because it does not include the requirement that all angles must also be equal. Therefore, the best answer choice is C, as some polygons with equal sides do not have equal angles and are not regular.
Explanation:
The definition of a regular polygon as “a polygon with all sides the same length” is not entirely accurate, because it overlooks an important aspect of regular polygons. For a polygon to be considered regular, it must not only have all sides of equal length but also all angles must be equal. Therefore, the correct answer is C. No, because some polygons that are irregular fit this definition. For example, an equilateral triangle and a square are both regular polygons because they satisfy both conditions. However, a rhombus may have all sides of equal length but can have angles that are not equal, which makes it an irregular polygon.
A rational expression that will be undefined at x=1?
Answers
[tex]r(x)= \dfrac{p(x)}{q(x)} [/tex]
will be undefined for the zeros of the expression [tex]q(x)[/tex]. For an expression with a zero equal to 1, the simplest way is to use [tex](x-1)[/tex] as a factor in [tex]q(x)[/tex]. In can be your only one, or you can mix in other factors.
But, so long as the denominator of [tex]r(x)[/tex] is equal to zero, as it is when [tex]q(x)=x-1[/tex], the expression will be undefined at that point x, because it would involve division by zero.
You could use as your sample:
[tex] \dfrac{x-7}{x-1} [/tex]
You can try to get fancy and square some factors or add in some radicals or trigonometric functions or anything else, so long as the 1 makes the denominator equal to zero!
WILL GIVE BRAINLIEST!!!!!! PLEASE HELP ME!!! 12 POINTS!!!!!
The acceleration of any object can be found using the expression v - u over t , where v is final velocity, u is intial velocity and t is the time interval.
This expression can be interpreted as the _____
Given choices: (sum, difference, product, quotient)
of the _____
Given choices: (sum, difference, product, quotient)
of _____
Given choices: (v subtracted from u, u subtracted from v, v subtracted from t, u subtracted from t)
divided by _____.
Given choices: (u, v, t)
Answers
_____
That's precisely how you would read (v -u)/t.
This is actually the *average* acceleration over the time interval t.
hhhhhhhellllllllp.....................................
Answers
28/3 = 9.3333
The pen will be 9.3333 by 9.3333 meters
The radius of the circular lens of a magnifying glass is 4 centimeters.
What is the area, in square centimeters of the glass?
Answers
Answer: 50.24 square centimeters.
Step-by-step explanation:
Given: The radius of the circular lens of a magnifying glass = 4 centimeters
The area of a circle is given by :-
[tex]\text{Area}=\pi r^2[/tex], where r is the radius of the circle.
Then the area of the circular lens of a magnifying glass is given by :-
[tex]\text{Area}=\pi (4)^2=(3.14)(16)=50.24\text{ square centimeters }[/tex]
Hence, the area of the circular lens of a magnifying glass = 50.24 square centimeters.
Please answer this question! Its easy
Answers
1 of all it's not easy and second the 1 one is A
Answer:
A
Step-by-step explanation:
The answer to the first question is A
ich sequence of transformations would result in a figure that is similar, but not congruent, to the original figure? Select all that apply. a dilation with a scale factor of 0.6 followed by a translation of 2 units up a reflection across the y-axis followed by a rotation about the origin of 10 a translation 2 units up followed by a translation of 2 units to the left a rotation about the origin of 50° followed by a dilation with a scale factor of 8
Answers
The 1st and 4th selections apply.
When multiplying 2 fractions is the product greater than the factors?
Answers
What is the midpoint of the segment whose endpoints are (-6,5) and (4,-7)?
Answers
(-6+4)/2=x
(-2)/2=x
-1=x
(5+-7)/2=y
(-2)/2=y
-1=y
To start, the formula to find the midpoint coordinate pair of two given coordinates is as follows:
([tex] \frac{x1+x2}{2} [/tex], [tex] \frac{y1+y2}{2} [/tex])
Knowing this, plug in your given values (the two x values are -6 and 4; the two y values are 5 and -7) and simplify:
([tex] \frac{-6+4}{2} [/tex], [tex] \frac{5+-7}{2} [/tex])
=([tex] \frac{-2}{2} [/tex], [tex] \frac{-2}{2} [/tex])
=(-1,-1)
Therefore, the midpoint of the coordinates (-6,5) and (4,-7) would be (-1,-1).
Hope this helps and have a marvelous day! :)
What z-score value separates the top 10% of a normal distribution from the bottom 90%??
Answers
Find the area of the following ellipse Use = 3.14 and round to nearest tenth. a = 7 in.; b = 9 in.
Answers
Round to the nearest tenth
197.82~ 197.2 in^2
Answer:
197.82
Step-by-step explanation:
A radius is an angle that connects any point on the circle to the center of that circle. A. True B. False
Answers
Answer:
IT REALLY IS FALSE FOREHEADS
Step-by-step explanation:
Classify the following expression by degree and term: (2 points)
x2y − 7xy + xyz + x
Answers
xyz - 5xy + x
Remember to always arrange terms in your polynomial in descending order according to the degree.
Now for degree, just get the sum of the exponents to determine the highest degree. The first term in the new equation has 3 variables, x,y, and z. Each of them, even when the power is not expressed are each raised to the power of 1. There are three variables so it will be:
1+1+1 = 3
The first term is classified as 3rd degree, which is the highest. So now you can conclude that this expression is a 3rd degree trinomial.
The given expression is a third-degree polynomial and consists of four terms: x^2y, -7xy, xyz, and x. Each term has a degree based on the sum of the exponents of the variables within it.
The expression in question is x2y − 7xy + xyz + x. To classify this expression by degree and by term, we need to look at the exponents of the variables in each term. The term 'degree' of a term in a polynomial is the sum of the exponents of the variables in that term.
x2y: The degree is 3 (2 from x2 and 1 from y).−7xy: The degree is 2 (1 from x and 1 from y).xyz: The degree is also 3 (1 from x, 1 from y, and 1 from z).x: The degree is 1, as there is only one occurrence of x.So the expression is a polynomial of third degree with four terms.
Kristen owns a bakery called Kristen’s cakes and such and is considering lowering the price of her cakes Kristen pulls her customers and determines that she can sell 100 cakes each week when she charges $25 each she also discovers that for every one dollar decrease in the price of the cake she will sell five more cakes the graph below represents Christians projected weekly revenue for each decrease in the price at what price she Christian sell her cakes in order to meet her maximum potential revenue
Answers
Suppose a triangle has two sides of the length 2and 3 and that the angle between these two sides is 60 what is the length of the third side of the triangle
Answers
.. c^2 = a^2 +b^2 -2ab*cos(C)
.. c^2 = 2^2 +3^2 -2*2*3*cos(60°)
.. c^2 = 7
.. c = √7 ≈ 2.6458
The third side of the triangle is √7, about 2.6458.
Answer: √7
Step-by-step explanation:
took the test