Answers
The transformations needed to sketch the graph of [tex]h(x) = \sqrt[3]{1 - x}[/tex] are described as follows:
Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.
What is a transformation in a function?A transformation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.
The parent cube root function is given by:
[tex]y = \sqrt[3]{x}[/tex]
To have x -> x - 1, we reflect the function over the y-axis, hence:
[tex]y = \sqrt[3]{-x}[/tex]
To have -x -> 1 - x, we shift it one unit right, hence:
[tex]h(x) = \sqrt[3]{1 - x}[/tex]
The order of the transformations can be reversed, i. e., shift right then reflection.
Thus the correct statement to sketch the graph is given by:
Starting with the graph of the basic function [tex]y = \sqrt[3]{x}[/tex], horizontally shift the graph right one unit, and then reflected the graph about the x-axis.
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Related Questions
An earthquake of magnitude 7.7 occurred in 2001 in Gujarat, India. It was about 4900 times as strong as the greatest earthquake ever to hit Pennsylvania. What is the magnitude of the Pennsylvania earthquake?
Answers
The magnitude of the Pennsylvania earthquake is 4.
What is a logarithm function?An exponent is a logarithm. You may convert any exponential expression to logarithmic form. As an illustration, if 8 = 23, the base is 2, the exponent is 3, and the outcome is 8. This may be represented as 3 = log2 8 in logarithmic notation.
The equation y=logb(x+h)+k shifts the logarithmic function, y=logbx, by k units vertically and h units horizontally.
Using the formula,
log I₁ / I₂ = M₁ - M₂
M₁ = 7.7, I₁ / I₂ = 4900
log 4900 = 7.7 - M₂
log 4900 ≈ 3.69
On calculating,
M₂ ≈ 4
The magnitude of the Pennsylvania earthquake is 4.
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Two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, what is the speed (in mi/h) of the faster cyclist?
Answers
If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.
SpeedLet r represent the speed of one
Let 2r represent thee speed of the other
Total distance traveled by both the sisters = 30 miles
Time ×rate = Distance
Hence,
2(2r+r) = 30
2(3r)=30
6r=30
r=30/6
r=5 mph
Speed=5 mph and (5 mph×2)
Speed=5 mph and 10 mph
Therefore If two cyclists, 30 miles apart, start riding toward each other at the same time. one cycles 2 times as fast as the other. if they meet 2 hours later, The speed (in mi/h) of the faster cyclist is: 5 mph and 10 mph.
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The number of bacteria in a bacterial culture increased by 149% in 110 hours. How many bacteria were there after 55 hours if there were 4850 pcs. from the beginning?
Round the answer to whole tens.
a. 8980 pcs
b. 7650 pcs
c. 7890 pcs
d. 7760 pcs
Answers
HELPPPPPPPPPPPPP ILL MARK BRAINLIEST
Answers
Answer:
-9.2 or -9 1/5
Step-by-step explanation:
Hope it helps!
Answer:
m = -40
Step-by-step explanation:
Solve for m by simplifying both sides of the equation, then isolating the variable.
Find all the zeros of each function. y=x³-x²+x-1
Answers
The required zeros of the polynomial f(x) are 1 and ±√-1.
What are zeros of the polynomial?
All the possible values of x that will make the polynomial zero are called the zeros of the polynomial, p(x). Zeros of a polynomial can either be negative or positive.
Solving for the zeros of a polynomial
y = x³ - x² + x - 1
Let, f(x) = 0
x³ - x² + x - 1 = 0
Using heat and trial method, we get,
x =1 as one of the zero of the polynomial
It implies that (x-1) is the root of polynomial
Thus, dividing x³ - x² + x - 1 by x - 1, we get
x² + 1, which is then equated to 0 to obtain the zeros of the given polynomial
i.e. x² + 1 = 0
x = 1, ±√-1
Hence, the required zeros of the polynomial y are 1 and ±√-1.
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Mrs. Jones decided to buy some pencils for her class. She bought 5 packages of pencils, and each package contained 42 pencils. There are 14 students in her class and she divided up the pencils so that each student had the same amount of pencils. If there were no pencils left over, how many pencils did each student get?
A. 70
B. 15
C. 19
D. 3
Answers
Answer:
B, 15 pencils
Step-by-step explanation:
Our equation: (5 x 42)/14
42 x 5 = 210
210/14= 15
Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion.
Answers
The expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).
How to illustrate the information?It should be noted that there are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each and the history museum gave the class 20% off as part of a group promotion.
Therefore, it should be noted that the expression to illustrate this will be:
= 20% × (10 × x) + (20 × y)
= 0.2 (10x + 30y)
Therefore, the expression to illustrate the information when Toby's seventh grade class is going on a field trip to a history museum will be 0.2 (10x + 30y).
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Toby's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion. What expression will illustrate this?
Let f(x)=4 x, g(x)=1/2x+7 , and h(x)=-2 x+4 . Perform each function operation. (f⁰g)(x)
Answers
The value of the composite function (h⁰ g)(x) calculated by function operation is 2x+28 .
A function is described as the relationship between a set's domain and range and its elements. f, g, or h are frequently used to denote functions.
Each element of an algebraic function, denoted by the formula y=g(x), is connected to a single value of x.
(h ∘ g)(x) can also be expressed as h[g(x)] , which signifies that the value of x=g(x) will be replaced in the function h, is referred to as a composite function.
A composite function is produced by combining two existing functions to produce a third, distinct function.
In h of g of x, the output of one function becomes the input of another.
Given functions are:
f(x)=4 x and g(x)=1/2x+7
Therefore (f ∘ g)(x)=f[g(x)]
=f(1/2x+7)
=4×(1/2x+7)
=2x+28
Therefore the value of the function operation (f⁰ g)(x) is 2x+28
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Identify each function for which f ( 2 ) = 3
Answers
The function which f(2) = 3 is the function with the equation f(x) = x + 1
How to identify the function?The function value is given as
f(2) = 3
The above means that the value of the function is 3 when x = 2
i.e., f(x) = 3 when x = 2 or we substitute 2 for x in f(x)
Next, we test the above function in the list of given options
So, we have
f(x) = x^2 + 1
Substitute 2 for x in f(x)
f(2) = 2^2 + 1
Evaluate the exponent in the above equation
So, we have
f(2) = 4 + 1
Evaluate the sum in the above equation
So, we have
f(2) = 5
f(x) = 2x + 1
Substitute 2 for x in f(x)
f(2) = 2 x 2 + 1
Evaluate the product in the above equation
So, we have
f(2) = 4 + 1
Evaluate the sum in the above equation
So, we have
f(2) = 5
f(x) = x + 1
Substitute 2 for x in f(x)
f(2) = 1 x 2 + 1
Evaluate the product in the above equation
So, we have
f(2) = 2 + 1
Evaluate the sum in the above equation
So, we have
f(2) = 3
Hence, the function which f(2) = 3 is the function with the equation f(x) = x + 1
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Possible question
Identify each function for which f (2) = 3
f(x) = x^2 + 1
f(x) = 2x + 1
f(x) = x + 1
f(x) = 2x^3 + 1
Multiply and simplify. 4√16 x⁸ . 4√x¹⁴
Answers
Solving the problem by multiplying and simplifying we have as a result 16x¹⁵
What is simplification?Simplification is a process of reducing terms to expressions, which do not generate changes or values.
What is multiplication?Multiplication is also known as product, and it is a mathematical operation of a successive sum, this operation consists of adding a number a certain number of times:
a x b the number "a" will be added "b" times.
The algebraic expression that we must simplify to its minimum expression is:
4√16 x⁸ . 4√x¹⁴
4×4x⁸ × 4x¹⁴/²
16x⁸× 4x⁷ ; multiply power of equal base
16x⁸⁺⁷
16x¹⁵
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DUE TONIGHTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT
Answers
The estimate for the side length of the square = the width of the rectangle (w) = √44.
What is the Area of a Rectangle?Area of Rectangle = (length)(width)
Given the parameters below:
Width of the rectangle = wLength of the rectangle = 2wArea of the rectangle = 88 square unitsIf this rectangle is divided to form two squares with equal areas, then the side length of each square would be equal to the length of the original rectangle = w.
(2w)(w) = 88
2w² = 88
w² = 88/2
w² = 44
√w² = √44
w = √44
Thus, an estimate of the side length of the square = the width of the rectangle (w) = √44.
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Type the correct answer in the box. Use numerals instead of words. Use / for the fraction bar.
A cooler contains 14 bottles of water and 10 bottles of lemonade.
Colleen randomly selects 2 bottles from the cooler without replacement.
The probability, as a fraction in simplest terms, that Colleen selected a bottle of water and then a bottle of lemonade is
Answers
The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is 35/138
What is probability and multiplication rule of probability?Probability is the measure of that how likely is an event can occur.
Probability of an event = Favorable outcomes of the event / total outcomes
Multiplication rule of probability states that probability of two events happening at the same time = (probability of one event )*(probability of another event )
Given that A cooler contains 14 bottles of water and 10 bottles of lemonade. Colleen randomly selects 2 bottles from the cooler
Total bottle = 14 +10 = 24
Let E be the event that Colleen selects a bottle of water first
Probability of E = 14/24
Let F be an event that Colleen selects bottle of lemonade when at the same time a bottle of lemonade is already taken out
Probability of F = 10/23
Therefore , The probability that Colleen selected a bottle of water and then a bottle of lemonade without replacement is
= Probability of E * Probability of F = (14/24)*(10/23) =35/138.
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An experiment will be conducted in which 20 pepper plants are randomly assigned to two groups. The plants in group 1 will receive the current fertilizer, fertilizer a, and the plants in group 2 will receive a new fertilizer, fertilizer b. All other growing conditions, including amount of sunlight and water, will be kept the same for the two groups. The growth of the pepper plants will be compared for the two groups. What are the experimental units in this experiment?.
Answers
Answer: E. The 20 plants in the two groups
Step-by-step explanation: experimental units are individuals on which the experiment is being performed. In this case the pepper plants are being used to test the effectiveness of the new fertilizer.
Please help with problem 10
Answers
Answer:
A. 0
Step-by-step explanation:
Slope tells you steepness or flatness of your line.
If you know two points on a line find slope by subtracting the y's and put that on top of a fraction. And subtract the x's and put that on the bottom of the fraction.
Subtract y's: 3 - 3
Put it on top: 0/...
Subtract x's: 5 - -4
same as 5+4
Put that on the bottom: 0/9
slope, usually called m, is 0/9, which is 0.
Notice if you graph these two points its a hOrizOntal line. HOrizOntal lines have zerO slope.
a conical frustum has bases with radii of $9$ and $12,$ and a height of $4.$ the total surface area of the frustum is $a$, in square units, and the volume of the frustum is $v$, in cubic units. find $a v.$
Answers
Slant height of the conical frustum, l = 5 units.
Total surface area of the conical frustum, a = 329.87 square units.
Volume of the conical frustum, v = 1394.87 cubic units.
Given,
Radii of bases of a conical frustum,
r₁= 9
r₂ = 12
Height = 4
We have to find the total surface area of the frustum and volume of the frustum.
Formula for total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]
Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]
Here l is the slant height.
Slant height, l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]
First we have to find the slant height.
l = [tex]\sqrt{(r_{1} -r_{2} )^{2} +h^{2} }[/tex]
l = [tex]\sqrt{(9-12)^{2}+4^{2} }[/tex]
l = [tex]\sqrt{(-3)^{2} +16}[/tex]
l = [tex]\sqrt{9+16}[/tex]
l = [tex]\sqrt{25}[/tex]
Slant height, l = 5 units
Now,
Total surface area, a = [tex]\pi l(r_{1} +r_{2}[/tex][tex])[/tex]
a = [tex]\pi[/tex] × 5 × ( 9 + 12)
a = [tex]\pi[/tex] × 5 × 21
a = 329.87 square units.
Then,
Volume of the frustum, v = [tex]\frac{1}{3} \pi h(r_{1} ^{2} +r_{2} ^{2} +(r_{1} r_{2} )} )[/tex]
v = [tex]\frac{1}{3}[/tex] × π × 4 × (9² + 12² + ( 9×12))
v = [tex]\frac{1}{3}[/tex] × π × 4 × (81 + 144 + 108)
v = [tex]\frac{1}{3}[/tex] × π × 4 × 333
v = 1394.87 cubic units.
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what is the midpoint of a line segment with the endpoints (8,-3) and (-5,-9)
Answers
Answer: (3/2,-6)
Step-by-step explanation:
Answer:
Formula for midpoint is given as [(x1+x2)÷2, (y1+y2)÷2] where x and y are the coordinates of the points.
Midpoint = [(8+(-5))÷2, (-3+(-9))÷2]
= (3/2, -12÷2)
= (3/2, -6)
Help quick pls
Question two:
ABC is rotated ____ degrees ____ around point ____ to create abc
Answers
Triangle ABC is rotated 85° around the point D to create A'B'C'.
What is rotation?Rotation is a transformation in which a figure is turned around a point . This point is fixed and is called the center of rotation.
From the given diagram we can see that the triangle is rotated about the fixed point D with an angle of 85° such that A' is new location of A and B' and C' are new locations of B and C respectively.
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Solve the following absolute value equation.
|4x - 12| = 16
Answers
The absolute value of the given modulus function are -1 and 7.
What is defined as the modulus function?A modulus function returns this same magnitude of a number regardless of its sign. It's also acknowledged as the absolute value function. This same modulus function, signified by |x| in mathematics, gives the modulus of such a real number x. It returns a non-negative value for x. The modulus but rather absolute value of a number too is known as the number's distance from the origin or zero.The given modulus function is;
|4x - 12| = 16
Removing modulus sign will provide two values;
4x - 12 = ±16
Solve for positive value of modulus function;
4x - 12 = 16
Add 12 on both side;
4x - 12 + 12 = 16 + 12
4x = 28
Dive both side by 4.
x = 7
Now, solve for negative value of modulus function.
4x - 12 = -16
Add 12 on both side;
4x - 12 + 12 = -16 + 12
4x = -4
Divide both side by 4;
x = -1
Thus, the two value of the given modulus function are -1 and 7.
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A/an is calculated by dividing the difference between a data value and the mean by the standard deviation.
Answers
Answer:
z score
Step-by-step explanation:
2-2n=3n+17 solve for n
Answers
Answer:
n=-3
Step-by-step explanation:
2-2n=3n+17
-2n=3n+15
-5n=15
n=-3
Steve had the option to buy a new computer at the $4250.00 cash price or to rent it for $595.00 per month for 10 months. after which he will own the computer. What percentage more than the cash price would the rent option cost him?
Answers
Answer:
I believe it's 25% .............
Answer:
40%
Step-by-step explanation:
The cash price = $4,250
If Steve rents the computer for $595 for 10 months he would have to spend $595 x 10 = $5,950
The difference in money = 5950 - 4250 =$1700
As a percentage of the cash price this would be
1700/4250 x 100 = 40%
Answer:
Rent option is 40% more than the cash price 40%
We can verify this by noting that if there is an increase of r% in the price of an item then
Increased price = Old price + Increase
= Old price + Old price x r/100
In this case, Old price = 4250
r = 40%, r/100 = 0.04
New price = 4250 + 4250 x 0.04 = 4250(1 + 0.04) = 4250(1.04) = 5950 which tallies with given figures
Evaluate each expression for the given value of x
4ˣ+1 for x=1
Answers
The correct answer for the given expression is 5.
A formula is a statement containing at least two numbers/variables and at least one mathematical operation. An expression is a combination of terms combined by mathematical operations such as subtraction, addition, multiplication, and division. The terms that appear in the formula are:Constant: A constant is a fixed number.Variables: Variables are symbols that do not have fixed values.Term: A term can be a single constant, a single variable, or a combination of variables and constants combined with multiplication or division.Coefficient: A coefficient is a number that is multiplied by a variable in an expression.Given,
evaluate the expression 4ˣ + 1
By putting x= 1,
we get 4¹ + 1
= 4+ 1
= 5
So, the the answer for the question, evaluate 4ˣ + 1 is 5.
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A figure is multiplied by a scale factor of 1/3. Did the figure get smaller or larger? How do you know?
I will give Brainiest answer
Answers
Answer:
Smaller
Step-by-step explanation:
When you multiply something by 1/3, basically what you are doing is multiplying that thing by one and dividing it by 3.
To put it in a better perspective, let's say you have something that is 5 inches long and you multiply it by a scale factor of 1/3. The equation would be: (5*1)/3.
*Please mark brainliest answer
A recipe says it produces the best summer drink the recipe calls for 1/2 cups of lemonade for every 1 1/2 cups of iced teas if 16 cups of the summer drink are made how many of those are cups of lemonade use the table to help you find your answer
Answers
The solving of fraction shows that there are 4 cups of lemonade use the table.
What is fraction?A fraction seems to be a part of a whole. The number is expressed in arithmetic as a quotient, which is the numerator divided by that of the denominator. Both are integers in a simple fraction. A complex fraction has a fraction in both the numerator and the denominator.
Why is it critical to understand fractions?Fractions help children know the nature of numbers but instead their interactions (e.g., the meaning of division) (e.g., the meaning of division). If a child does not grasp how fractions work, he will struggle to understand algebra later in life.
According to the given data:Based on the given conditions, formulate:
= [tex]16 \times \frac{1}{2} \div\left(\frac{1}{2}+1 \frac{1}{2}\right)[/tex]
Convert the expression into a fraction:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{1}{1}+\frac{1}{2}\right)\right)}[/tex]
Expand the fraction to get the least common denominator:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{1 \times 2}+\frac{1}{2}\right)\right)}[/tex]
Calculate the product or quotient:
= [tex]\frac{16}{2 \times\left(\frac{1}{2}+\left(\frac{2}{2}+\frac{1}{2}\right)\right)}[/tex]
Write the numerators over common denominator:
= [tex]\frac{16}{2 \times \frac{1+2+1}{2}}[/tex]
Write the numerators over common denominator:
= [tex]\frac{16}{2 \times \frac{3+1}{2}}[/tex]
Calculate the sum or difference:
= [tex]\frac{16}{2 \times \frac{4}{2}}[/tex]
Calculate the sum or difference:
= 16 /2
Cross out the common factor:
= 4
This shows that there are 4 cups of lemonade use the table.
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11 People fit comfortably in a 6 feet by 6 feet area. Use this value to estimate the size of a crowd that is 18 feet by 30 feet
Answers
(2x+5)(2x+9) Express as a trinomial
Answers
Answer:
Step-by-step explanation:(2x+5)(2x+9)
use foil method ([tex]4x^{2}[/tex]+18x+10x+45)
[tex]4x^{2}[/tex]+28x+45
Read each question. Then write the letter of the correct answer on your paper.Use the sum of cubes formula to factor x³+64 .
(A) (x+4)(x²-4 x+4) (B) (x+4)(x²+4x+4) (C) (x+4)(x²-4 x+16) (D) (x+4)(x²+4 x+16)
Answers
The solution of factorization of x ³ + 64 is ( x + 4 )( x ² - 4 x + 16 ) [ Option C ].
The question asks to factorize the given polynomial, that is, x ³ + 64.
The question clearly states that we need to use the sum of cubes formula to factor the given polynomial x ³ + 64.
Sum of cube formula is given as
a ³ + b ³ = ( a + b ) ( a ² - a b + b ² ).
Substitute the values of variable a and b from the given polynomial x ³ + 64
x³ + 64 can be written as x ³ + 4 ³
=> a = x and b = 4
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 4 ² )
=> x ³ + 4 ³ = ( x + 4 ) ( x ² - 4 x + 16 )
This matches with the option c among the multiple choices for this question.
Therefore, we get the solution of factorization of x ³ + 64 as ( x + 4 )( x ² - 4 x + 16 ).
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Need help with this question image attached
Answers
explanation:
First, translate (-3, 0) to the origin: (-3, 0) → (-3+3, 0) = (0,0)
Translate (-4,1) in the same manner: (-4,1) → (-4+3, 1) = (-1,1)
Rotate (-1,0) counterclockwise 180° about the origin: (-1, 1) → (1,-1) [(x,y)→(-x,-y)]
Translate (1,-1) by "undoing" the original translation: (1,-1) → (1-3,-1) = (-2,-1)
Do the ratios 5:3 and 50:30 form a proportion?
Answers
if A= [2 6] prove that (A')' = A
3 7
4 9
Answers
Answer:if A= [2 6] prove that (A')' = A
3 7
4 9
Step-by-step explanation: