Which of the ten basic functions in
our toolkit have graphs that look the
same when reflected of the y-axis
and then reflected over the x-axis?
Answers
Answer:
a) x³, 1/x, x, sin(x)
Step-by-step explanation:
You want to know which list of functions has the same graph when reflected across both the y- and x-axes.
Odd functionReflection across the y-axis transforms the function to ...
f(x) ⇒ f(-x)
Reflection across the x-axis transforms the function to ...
f(x) ⇒ -f(x)
Hence, reflection across both axes transforms the function to ...
f(x) ⇒ -f(-x)
A function that has the characteristic that f(x) = -f(-x) is an odd function. Its graph is symmetrical about the origin. We can check to see if the functions of interest match this definition of an odd function:
x³ = -(-x)³ . . . . true
1/x = -(1/-x) . . . . true
x = -(-x) . . . . true
sin(x) = -sin(-x) . . . . true
cos(x) = -cos(-x) . . . . false
e^x = -e^-x . . . . false
|x| = -|-x| . . . . false
The basic functions that are odd are ...
x³, 1/x, x, sin(x)
Related Questions
What is the horizontal shift of y = cos(0 – ³7) + 3?4A. noneOB.-37OC. 3rD. 3Reset Selection
Answers
The horizontal shift will be the term that is subtracting the angle, in this case: -3pi/4= B .
7x+12=x-6
I need help!!!!
Answers
Answer:
x = -3
Step-by-step explanation:
You have to isolate x:
7x + 12 = x - 6
7x = x - 6 - 12 = x - 18
6x = -18
x = -3
For
f(x) = 4x
and
g(x) = x10,
find the following.
(a)
(f + g)(x)
(b)
(f − g)(x)
(c)
(f · g)(x)
(d)
(f/g)(x)
,
x ≠ 0
Answers
The addition, subtraction, multiplication and division of the two functions are 4 · x + x¹⁰, 4 · x - x¹⁰, 4 · x¹¹ and 4 / x⁹, respectively.
How to determine the expression resulting from operations between functions
In functions there are two fundamental operations (addition, multiplication) and two derivate operations (subtraction, division). In this problem we must look for the following definitions:
Addition
(f + g)(x) = f(x) + g(x)
Subtraction
(f - g)(x) = f(x) - g(x)
Multiplication
(f · g)(x) = f(x) · g(x)
Division
(f / g)(x) = f(x) / g(x), for x ≠ 0.
If we know that f(x) = 4 · x and g(x) = x¹⁰, then the expression behind the operations are, respectively:
Addition
(f + g)(x) = 4 · x + x¹⁰
Subtraction
(f - g)(x) = 4 · x - x¹⁰
Multiplication
(f · g)(x) = (4 · x) · x¹⁰ = 4 · x¹¹
Division
(f / g)(x) = (4 · x) / x¹⁰ = 4 / x⁹
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What is the solution to this equation?
x+8 = -3
OA. x = -5
OB. x = 5
OC. x = 11
OD. x=-11
Answers
[tex]x + 8 = - 3 \\ x = -3 - 8 \\ x = - 11[/tex]
OPTION (D) SUITS ..IT IS THE SOLUTION.
Which of the following linear equations represents the data chart?
Answers
Answer:
y = -x + 7
Step-by-step explanation:
let's use the first numbers as an example.
x=1 and y=6
now to get this we need to find the difference between the two numbers and we can do this by simply doing - 1 + 7 = 5
therefore making the answer y = -x + 7
About how many times heavier is the largest dog when compared with the smallest dog?
Answers
The number of times heavier that the largest dog is when compared with the smallest dog is B. 41.
How to illustrate the information?It should be noted that from the information given, the biggest dig is the St Bernard and it has 145 pounds.
Also, it should be noted that the smallest dog is Yorkie and it had 3.5 pounds. Therefore, it should be noted that the number of times heavier will be:
= Weight of biggest fog / Weight of smallest dog
= 145 / 3.5
= 41.
It is 41 times heavier.
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find the ratio of 15k to 65k
Answers
Answer:
Step-by-step explanation:
If its 15000:65000
Then we divide both sides by 1000 first :
15 : 65
Then we divide both sides by 5 :
3 : 13
This is simplified
If K is a unit then it will be 3k : 13k by doing the above steps but skipping the first.
Hope this helped and have a good day
Now answer the question:
Juan and his children went into a grocery store and he bought $4 worth of apples and
bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 6
apples and bananas altogether. Determine the number of apples, x, and the number
of bananas, y, that Juan bought.
Juan bought apples and
bananas.
Answers
X=2 and Y=4
Answer:
2 apples and 4 bananas
Step-by-step explanation:
Given info:
He bought $4 worth of apples and bananas. Each apple costs $1 and each banana costs $0.50. He bought a total of 6 apples and bananas altogether.Question given:
Determine the number of apples, x, and the number of bananas, y, that Juan bought.
Solution:
Since, we know that;
apples = x
bananas = y
Cost of each apple = $1 & Cost of each banana = $ 0.50
Total = 6
The equation that represents the following information:
x + y = 6
x + 0.5y = 4
We can multiply the top equation by -1 so it becomes -x -y = 6
-x - y = 6
x + 0.5y = 4
Now, we can use elimination to cancel out the x.
-0.5y = -2
y = 4
Because y=4, x must be 2 since x+y=6. So,
x = 2 and y = 4
Which means;
Juan bought 2 apples and 4 bananas.
~kavinsky
:) Please help!!!!!!
Answers
Answer:
1/2, 1/5, 1/7, 1/9, 1/28
7/14, 7/21, 7/42, 7/49
10/18, 10/20, 10/50, 10/100
HELP I WILL GIVE YOU POINTS!
Describe in words the one transformation that maps
ΔABC to ΔA'B'C'
∆ABC to ∆A′B′C′
. Make sure that you include specific details (Reflection – over which axis, Rotation – direction, degrees, and center of rotation, Translation – direction(s) and number of units). 15 points
Answer:
ΔABC
∆ABC
is transformed by a:
Type of Transformation:
Details of transformation:
Answers
The description of the one transformation that maps ∆ABC to ∆A'B'C' is a rotation counterclockwise, 90 degrees, with the center at the origin
What is a rotation transformation?A rotation transformation can be described as the angular motion of a rigid, geometric figure around a point
The vertices on the triangle ∆ABC are;
A(-5, -2), B(-7, -4), C(-5, -5)The vertices on the triangle ∆A'B'C' are;
A'(2, -5), B'(4, -7), C'(5, -5)The rotation of a point A(x, y), 90° counterclockwise about the origin gives the point A'(-y, x)
The reflection of a point (x, y) across the y–axis gives the point A'(-x, y)
Therefore;
The coordinates of the vertices of∆ABC following a 90° counterclockwise rotation gives;
A(-5, -2) → A'(2, -5)
B(-7, -4) → B'(4, -7)
C(-5, -5) → C'(5, -5)
Therefore;
The transformation that maps ∆ABC to ∆A'B'C' is therefore a rotation of 90° counterclockwise about the origin
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Gavin has a smart phone data plan that costs $20 per month that includes 6
GB of data, but will charge an extra $10 per GB over the included amount.
How much would Gavin have to pay in a month where he used 2 GB over the
limit? How much would Gavin have to pay in a month where he used went
over by x GB?
Total cost when over by 2 GB:
Total cost when over by x GB:
Answers
Total cost is given by the function $(20 + 10x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is referred to as the function's domain, and the set Y is referred to as the function's codomain. Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).
Total cost is given by the function $(20 + 10x)
Total cost when over by 2 GB = $(20 + 10x2) = $(20+20) = $40
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Question 1 (1 point)Given the graph below, is this relation a function?MathMLXBlarSubmit
Answers
To be a function, a relation can't have more than 1 value of 'y' for the same value of 'x'
For example, if you have points (3,7) and (3,-6) does not represent a function but points (3,7) and (-3,7) does.
In this problem, none of the graphed pairs have 2 or more values of 'y' for a single value of 'x'. They are all different, so yes, this relation is a function
hi can you please help me
Answers
The area of the kitchen will be:
[tex]\begin{gathered} A=w\cdot l \\ \text{where:} \\ w=\text{width}=36-24=12ft \\ l=\text{length}=8ft \\ A=12\cdot8 \\ A=96ft^2 \end{gathered}[/tex]Two splice plates are cut from a piece of sheet steel that has an overall length of 18 3/4 in. The plates are 10 1/2 in. and 6 15/16 in. long. How much material remains from the original piece if each saw cut removes 1/16 in.?
Answers
Total material remains from original piece if overall length of sheet is
[tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
As given,
Overall length of steel sheet=[tex]18\frac{3}{4}[/tex] in
=(75 /4) in
=(300 /16)in
Length of two plates is [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in
Total length of two plates=[tex]10 \frac{1}{2} + 6\frac{15}{16}[/tex]
=(21 /2) +(95/16)
=(168 +95)/16
=263 /16
Total length of saw cut=(1/16) +(1/16)
=2/16
Material remains from original piece=(300/16) - (263/16 +2/16)
= 35 /16
Therefore, total material remains from original piece if overall length of sheet is [tex]18\frac{3}{4}[/tex] in and two plates are cut of length [tex]10\frac{1}{2}[/tex] in and [tex]6\frac{15}{16}[/tex] in ,two saw of length 1/16 in is 35 / 16 in.
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Estimate the product of 653.2×4.6
Answers
Answer: 3004.72
Step-by-step explanation: i used a calculator
Mandy and 6 of her teammates each sold an equal number of
shirts to raise money for their tennis team. If a total of 56 shirts
were sold, how many shirts did each person sell?
Answers
Each person will sell 8 shirts if 56 shirts were sold
How to calculate the number of shirts sold by each person ?Mandy and 6 of her teammates each sold an equal number of shirt
Mandy is one person, let add 1 plus six to get the total number
1 + 6
= 7
The total number of shirts sold is 56 shirts
Since there are 7 people, the number of shirt that each person will sell can be calculated by dividing 56 by 7
= 56/7
= 8
Hence 8 shirts will be sold by each person
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Betsy's Bakery packages muffins in boxes of one dozen. If Besty bakes 1,152 muffins on Saturdays, how many boxes are ready to sell?
Answers
Answer:
96 boxes of muffins
Step-by-step explanation:
so how you would get to this answer would be 1152÷12
12 is equal to a dozen and so that is why you divide it by 12
the answer would be 96
factor of the following expression:
81x^4-16y^2
Answers
Answer:
See below
Step-by-step explanation:
(9x^2 - 4 y ) * (9x^2 + 4 y )
(-2,-5) (-3,5) fin the slope from the pair of points
Answers
The slope of the line from the pair of given points would be [tex]m = 5[/tex].
Hope this helps!
Bill and ross are twins, their brother mark was born on the same day as twins but is three year older. if mark was born in 1990, in what year did the three boys get total age 21
Answers
Step-by-step explanation:
x = age of one of the twin boys
when they had together 21 years of age,
Bill was x years old
Ross was x years old
Mark was x+3 years old
so, we have
x + x + (x + 3) = 21
3x + 3 = 21
3x = 18
x = 6
Bill and Ross were 6 years old.
Mark was 6+3 = 9 years old.
Mark was born in 1990.
1990 + 9 = 1999
so, it was 1999 when they had together 21 years of age.
q=p(r+s)
Solve for p
Answers
If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the
formula
v = vo -32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 4 seconds is 41 ft/s.
-
Answers
= 170 ft/s
Explanation:
• given equation is v=Vo-32t
.. (i)
an initial velocity, Vo, in feet per second
(ft/s)
vin ft/s = 42 ft/s
† is time in seconds = 4 seconds
Putting the values in (i) , we get
42 = Vo - 32 x 4
multiply
42 = Vo - 128
add 128 to both sides
42 + 128 = Vo - 128 + 128
Simplify and add
170= Vo
Hence, the initial velocity of an object = 170
ft/s
On a piece of paper, graph y + 2 > -3x - 3. Then determine which answer
choice matches the graph you drew.
A
D
(0,-5)
• A. Graph A
• B. Graph B
C. Graph C
D. Graph D
Answers
Answer:
D
Step-by-step explanation:
The line needs to be dotted since the boundary is not included.
Eliminate A and C.The line should be shaded above because of the > sign.
Eliminate B.I’m begging help me out with this, please
Answers
For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.
As given in the question,
Given function:
f(x) = 8 / (x+2)
g(x) = 4x² +2
Evaluation of the composition of function f(x) and g(x) we get,
(fog)(x)
= f(g(x))
Substitute g(x) = 4x² + 2
= f(4x² +2)
= 8/(4x² +2+2)
= 8/(4x²+4)
= 2/(x²+1)
Substitute x =-1 in the above function
(fog)(-1) = 2/ ((-1)² +1)
= 2/ 2
=1
Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.
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During a sleepover, Carissa played karaoke with her friends. Her song was 6 minutes long. She had already sung for 4 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 6
x + 4 = 10
x + 4 = 6
x − 4 = 6
Brett has a box of colored pencils. He uses 78 pencils and has 120 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
78 + p = 120
p − 78 = 120
120 + p = 78
p = 120 − 78
Answers
Answer:
for the first one it is x + 4 = 6
for the second one it is 78 + p = 120
Step-by-step explanation:
i hoped this helped!!!
Answer:
x+4=6
Step-by-step explanation:
x represents the missing number 4 represents the time she had already sang and 6 is the total
is the relation in this graph a function ?
Answers
Answer:
No it's not a function
Step-by-step explanation:
You can use the vertical line test to determine whether it's a function or not. If the vertical line touches the graph at more than one point, the graph is not a function therefore the answer is no.
In a game of cornhole, Sasha tossed a bean bag and it landed at the edge of the hole. The hole can be represented by the equation x2 + y2 = 5, and the path of the bean bag can be represented by y = 0.5x2 – 1.5x – 4. To which points could she have tossed her bean bag?
A. (–1, –2) or (–2, 1)
B. (1, –2) or (2, 1)
C. (–1, 2) or (–2, –1)
D. (1, 2) or (2, –1)
Answers
The points are (1, -2) or (2, 1).
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
The equation for the hole
x² + y² = 5.............(1)
and, equation for bean bag can be represented by
y = 0.5x² – 1.5x – 4............................(2)
By solving above two equation we get
0.25 [tex]x^4[/tex] + 1.5 x³ -0.75 x² -12 x +11 =0
we het x1=1 and x2 = 2
then y1= -2 and y2 = 1
hence, the points are (1, -2) or (2, 1).
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Consider the following function.
f(x) = (x − 3)2, x ≥ 3
Find the inverse function
f −1.
Answers
The inverse equation of the function is f'1(x) = 3 + √x
What are inverse functions?Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x)
How to determine the inverse function?The function f(x) is given as
f(x) = (x - 3)^2, x ≥ 3
As a general rule, we start by writing f(x) as a variable (say f(x) = y).
So, the equation of the function becomes
y = (x - 3)^2
The next step is to switch/swap the positions of x and y in the equation
The equation becomes
x = (y - 3)^2
Make y the subject of the formula in the equation
The equation becomes
y = 3 + √x
Express as an inverse function
f'1(x) = 3 + √x
Hence, the equation of the inverse function is f'1(x) = 3 + √x
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What is the surface area of the prism?
77.25 cm2
154.5 cm2
225 cm2
309 cm2
Answers
The surface area of the prism represented by the net diagram is 154.5 cm^2
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the surface area of the prism?The given parameter is in the figure
In the figure, we have the net of a rectangular prism
From the net of a rectangular prism, we have the following dimensions
Length = 8 1/2 cm
Width = 4 1/2 cm
Height = 3 cm
The surface area of the prism is then calculated as
Surface area = 2 * (Length * Width + Length * Height + Width * Height)
Substitute the known values in the above equation
So, we have the following equation
Surface area = 2 * (8 1/2 * 4 1/2 + 8 1/2 * 3 + 4 1/2 * 3)
Evaluate the products
So, we have the following equation
Surface area = 2 * (38 1/4 + 25 1/2 + 13 1/2)
Evaluate the sum
So, we have the following equation
Surface area = 2 * 77 1/4
Evaluate the products
So, we have the following equation
Surface area = 154.5
Hence, the surface area of the prism is 154.5 cm^2
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he figure on the left represents a scale drawing of the figure on the right.
pls help its due in 10 min
Answers
The scale of the drawing is expressed as, 1 inch : 2.5 yards.
What is a Scale Factor?A scale factor describes to what size an original image has been reduced or enlarged. If the scale factor of an enlargement is 2, it means every side lengths of the original image is increased times two to get the new image after enlargement.
On the other hand, if the reduction was done using a scale factor of 0.5 or 1/2, it means the size of the original image was reduced by half to get the new side lengths of the new image.
How to Find the Scale Factor of a Scale Drawing?The scale factor of a scale drawing = dimension of new image/corresponding dimension of original image.
The figure by the right is the original figure, while the one on the left is the scale drawing which is the new figure.
Scale of the drawing = 1 inches to 5/2 yards
Scale = 1 inch : 2.5 yards.
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