2. Write each of the following as a power function in the form f(x) = kx^p.
f(x) = -3/2x^5
Answers
The simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
What is power function ?
A function having a single term that is the sum of a real number, a coefficient, and a variable raised to a fixed real number is called a power function. Consider functions for area or volume as examples (a number that multiplies a variable raised to an exponent is known as a coefficient). A power function is a function where y = x n, where n is any real constant number. In reality, many of our parent functions, including linear and quadratic functions, are power functions.
Here ,
a) f(x) = [tex]\frac{-3}{2x^5}[/tex]
To write in the form of f(x)= [tex]kx^p[/tex]
=> f(x) = [tex]\frac{-3}{2}* \frac{1}{x^5}[/tex]
=> f(x) = [tex]\frac{-3}{2} x^-5[/tex]
b) g(x) = 5[tex]\sqrt[3]{x}[/tex]
Here we know that [tex]\sqrt[n]{a} = a^\frac{1}{n}[/tex] , then
=>g(x)=5[tex]x^\frac{1}{3}[/tex]
Hence the simplified power functions are a) f(x) = [tex]\frac{-3}{2} x^-5[/tex] and b)g(x)=5[tex]x^\frac{1}{3}[/tex] .
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Related Questions
Caroline was comparing the price of salmon at two stores. At SuperGrocery B, 3
pounds of salmon costs $24.63. The table below represents the total cost, in dollars
and cents, y, that it costs for a pounds of salmon at SuperGrocery A.
SuperGrocery A
Pounds (z) Total Cost (y)
2
$23.70
2.5
$29.63
3.5
$41.48
4.5
$53.33
How much more expensive is it, per pound, to buy salmon at
SuperGrocery A than at SuperGrocery B?
Answers
By the concept of basic arithmetic, it is $3.64 more expensive per pound, to buy salmon at Super Grocery A than at Super Grocery B.
What is meant by basic arithmetic?The area of mathematics known as arithmetic deals with the study of numbers and the numerous operations that can be performed on them. The four fundamental arithmetic operations in mathematics are addition (finding the sum), subtraction (finding the difference), multiplication (finding the product), and division (finding the quotient). These operations can be applied to all real numbers. The usage of fundamental arithmetic operations is the focus of the field of mathematics known as arithmetic.
At Super grocery B, 3 pounds of Salmon cost = $ 24.63
So, 1 pound will cost = $ 24.63/ 3
= $ 8.21
At Super grocery A, 2 pounds of Salmon cost = $ 23.70
So, 1 pound will cost = $23.70/ 2
= $ 11. 85
To buy salmon at SuperGrocery A than at SuperGrocery B expense per pound is given by
= $11.85 - $ 8.21
$ 3.64
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Examine the worked examples. Then, answer the questions.
Alessa's car uses 2 gallons of gas to drive 45 miles. How many miles can
Alessa's car drive using 15 gallons of gas?
Let m represent the number of miles and g represent the gallons of gas.
m=
11 L
m=
m=
Write an equation in the form y = kx for the number of
miles in terms of the gallons of gas.
(15) Substitute the value for the given quantity.
Evaluate the right hand side of the equation.
Alessa's car can drive
miles using 15 gallons of gas.
Answers
Answer: if you multiply you will end up with 675
Step-by-step explanation:
If 3 workers complete a certain task in 12 days, how many workers are needed to finish the same task in 4 days?
Answers
A total of 9 workers are needed to finish the same task in 4 days
How to determine the number of workers?From the question, we understand that:
3 workers can complete a certain task in 12 days
This means that
3 workers = 12 days
The proportionality constant is then calculated as
Proportionality constant = Number of workers x Number of days
Substitute the known values in the above equation So, we have the following equation
Proportionality constant = 3 * 12
Evaluate
Proportionality constant = 36
When the number of days is 4, we have
Days = 4
So, we have
Proportionality constant = Number of workers x Number of days
This gives
36 = Number of workers x 4
Divide both sides by 4
Number of workers = 9
Hence, the number of workers is 9
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Calculate the simple interest and maturity value
Answers
The simple interest is $420 and the maturity value is $$6,720
How to find the simple interest?Using this formula to find the simple interest
Simple interest = Principal × Interest rate × Time
Where:
Principal = $6300
Interest rate =4% or 0.04
Time = 20 month = 20/12 = 1.6666666
Let plug in the formula
Simple interest = $6,300 × 0.04 × 1.6666666
Simple interest = $420
Using this formula to find the maturity value
Maturity value = Principal + Interest
Maturity value = $6,300 + $420
Maturity value = $6,720
Therefore the interest is $420.
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Add the 2 polynomials:
(-77x²¹ +
2
·x² + x
3
+[52*+
1
-
Answers
Answer:
Step-by-step explanation:
If q is 2.00 what is the distance from C to A?
Answers
Answer: 4.00
Step-by-step explanation:
If the q is 2.00 A to C is double the q. So, 2.00x2= 4.00.
Answer:
AC = 4.00Step-by-step explanation:
Given is a parallelogram.
One of the properties of a parallelogram is its diagonals bisect each other.
It gives us:
AC = 2qAC = 2*2.00 = 4.00Sets A, B, and C are subsets of the universal set U.
These sets are defined as follows:
U= {f, g, h, p, q, r, x, y, z}
A= {f, g, p, q}
B= {g, h, q, x, y}
C={ p, q, x, y, z}
Find (A' u B) ∩ C'.
Write your answer in roster form or as Ø.
Answers
=====================================================
Explanation:
Unfortunately the U from "universal set" and the union symbol look almost identical.
What I'll do to avoid confusion is to let E represent the set of everything we care about, aka universal set.
E = {f, g, h, p, q, r, x, y, z}
Feel free to use other notation if it makes better sense to you.
From this set, we'll erase items that are found inside set A = {f, g, p, q}
So we go from this
E = {f, g, h, p, q, r, x, y, z}
to this
A' = {h, r, x, y, z}
Everything found in here is guaranteed to not be inside set A.
------------------------
The next step is to union set A' with set B. This is where we combine those two sets into a larger set of items. Toss out any duplicates. Each unique letter is to be listed once.
A' u B = {h, r, x, y, z} U {g, h, q, x, y}
A' u B = {h, r, x, y, z, g, h, q, x, y}
A' u B = {g, h, q, r, x, y, z}
It's recommended you sort the items in a consistent fashion.
Set this result aside for now, and come back to it later.
------------------------
Go back to the set of everything, aka universal set.
E = {f, g, h, p, q, r, x, y, z}
Cross off stuff found in set C, so we guarantee to form the opposite or complement set C'
C' = set of everything NOT found in C
C' = erase "p,q,x,y,z" from set E
C' = {f, g, h, r}
------------------------
To recap we found
A' u B = {g, h, q, r, x, y, z}C' = {f, g, h, r}Intersect those sets by looking at what they have in common. This is the overlapped region between the sets.
The three items in common are: {g, h, r} which forms the final answer.
On an architect's blueprint, 1 inch corresponds to 4 feet. Find the length of a wall represented by a line 1 inches long on the blueprint
Answers
The length of wall in real life is 4 feet.
Given that on an architect's blueprint, 1 inch corresponds to 4 feet.
In this architect's plan, a wall represented by a line 1 inches long on the blue print.
So, the length of wall in real life is = 4 feet.
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Answer:
4ft
Step-by-step explanation:
If 1 inch corresponds to 4 ft on the blueprint. The ratio is 1 inch on the blue print for every 4 ft in real life.
what is the total change in the cats weight for all 3 months?
Answers
The total change in the cats weight for all 3 months is -0.5 pounds.
How to find the total change?Since we have 3 months which is from April to June, Now let add up the change in weight in pounds so as to find the total change
Let x represent the total change
x = -0.7 + 0.5 + (- 0.3 )
x = -0.5 pounds
Therefore the -0.5 pound is the change in weight.
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X
0
123
4
f(x)
36
54
81
121.5
182.25
کے
Using the given table, what are the y-values of the table?
Answers
Using the given table, the y-values are 36, 54, 81, 121.5, and 182.25.
We are given a table. Mathematical tables are collections of numbers that represent the outcome of a computation with varied arguments. The table has two columns and five rows. The first column shows the x-values. The second column shows the f(x) values. We know that y = f(x). So, the second column shows the y-values. The y-value is the vertical value in a pair of coordinates. It denotes how high or low the point is. In an ordered pair of coordinates, the y-coordinate is always written second (x, y). The five rows show the data points with corresponding x-values and y-values.
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What is -1/6 divided by 2/9
Answers
Answer:
Step-by-step explanation:
1. List out the numbers and divide
-1/6/2/9=
2. In division for fractions, the number or numbers on the right of the division side flip and change to multiply!
-1/6/2/9= -1/6*9/2= -9/12
3. Simplify!
-9/12= -3/4
Answer:
-3/4
Step-by-step explanation:
so you leave -1/6 but then you change the sign to multiply and the other fraction change it so if you had 2/9 it will be 9/2
so we get -1/6×9/2.
if you don't know how to multiply fractions i can explain just ask.
In the triangle below, with right angle I, suppose that m< J= (2x+22)° and m < K = (5x-2)
Find the degree measure of each angle in the triangle.
m < I =
M< J =
m < K =
Answers
Answer:
Step-by-step explanation
so basically you need to see what m<I equals and do the same for the rest of them and you should get your answer and that would be let me see and m<k= -44 degrees and m<I and J= -10 degrees and there you have if this is not right i tried have the same step and ask another person
If India works overtime, she receives an
hourly rate of 1-times her regular hourly 1/2
rate. What is her hourly overtime rate?
Answers
After solving, 50% is her hourly overtime rate.
In the given question,
India works overtime, she receives an hourly rate of 1-times her regular hourly 1/2 rate.
We have to find her hourly overtime rate.
India is working overtime so her regular hourly rate is 1/2.
Evaluating the expression
We find her hourly overtime rate in percentage.
She receive overtime rate for 1 time is 1/2 rate.
We can write 1/2 as 0.5.
To express it as percentage we multiply and divide by 100.
= 0.5 × 100/100
= 50%
Hence, 50% is her hourly overtime rate.
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PLEASE HELP EXTRA POINTS select all true statements
Answers
Answer: C
PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!
You can afford a $1100 per month mortgage payment. You've found a 30 year loan at 8% interest.
a) How big of a loan can you afford?
b) How much total money will you pay the loan company?
c) How much of that money is interest?
Answers
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
What is interest ?The cost of borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR).Lenders may charge interest to borrowers for using their funds, or borrowers may charge interest to lenders for using their funds.Interest is frequently regarded as simple interest (based on the principal amount) or compound interest (based on principal and previously-earned interest).Credit cards, mortgages, auto loans, personal loans, savings accounts, and penalty assessments are all frequently linked with interest.The macroeconomic policy set by the Federal Reserve's federal funds rate has a significant impact on interest rates.Calculation
Given,
d=$1100
N= 30 years
r = 8% or 0.08
a) Loan amount that can be afforded
[tex]=\frac{d[1- (1+\frac{r}{k})^{-Nk} }{\frac{0.08}{12} }[/tex]
[tex]=\frac{1100[1- (1+\frac{0.08}{12})^{-30*12} }{\frac{0.08}{12} }[/tex]
= $149911.84
b) Total money you pay = d×N×k
=1100×30×12
=$39600
c) Interest paid = Total money paid – loan amount
⇒39600–14911.84 = $246088.16
Hence,
a) $149911.84 can be afforded
b) $39600 is the total money you will pay the loan company
c) $246088.16 is the interested amount
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Line x is the perpendicular bisector of segment ZY
what does b=
Answers
Based on the definition of perpendicular bisector, the value of b = 5.
What is a Perpendicular Bisector?A perpendicular bisector can be described as any line that bisects another line segment at right angles.
This means, the measure of the angles at the point of bisection are right angles (90 degrees).
Therefore:
12b + 30 = 90 [definition of perpendicular bisector]
Solve for b
12b + 30 - 30 = 90 - 30
12b = 60
Divide both sides by 12
12b/12 = 60/12
b = 5
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Franks’s annual salary is $80000. About 25% of her salary is deducted for taxes.
How much tax is deducted?
Explain.
Answers
Paula stands on the side of a river and sights the opposite bank at an angle of depression of 7 degrees. if Paula is 5.5 feet tall, approximately how wide is the river, to the nearest foot?
Answers
The width of the river to the nearest foot will be 45 feet.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Paula remains on a waterway and sights the contrary bank at a point of the wretchedness of 7 degrees.
If Paula is 5.5 feet tall.
Let 'w' be the width of the river. Then the width of the river will be given as,
tan 7° = 5.5 / w
0.12278 = 5.5 / w
w = 44.79
w ≈ 45 feet
The width of the river to the nearest foot will be 45 feet.
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In the diagram ray MO bisects the measurement of
Answers
2x+30 = 15
X=15
You are then able to plug 15 in for the variable of X.
Ray ML
3(15)-20
45-20
= 25°
Ray MN
(15) + 10
= 25°
Or you could assume they are the same measurement as they are equal.
A group of 16 people is choosing a chairperson and vice-chairperson. They put all 16 people's names into a hat. The first name drawn becomes chair. The second name drawn becomes vice-chair. How many possible combinations of chair and vice-chair are there?
Answers
Based on the number of people present, the total number of combinations of Chairperson and Vice Chairperson is 240 combinations.
How to carry out Probability combinations?In order for us to find out the total possible combinations, we will use the formula as:
Total possible combinations = Number of possible chairpersons * Number of possible vice chairpersons
We are given that;
Number of possible chairpersons = 16
Number of possible vice chairpersons = 15 (This is because a chairperson is chosen first and leaves 15 people.)
Thus, we can say that;
Total possible combinations = 16 * 15
Total possible combinations = 240 combinations
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4 yd.
3 yd.
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
yards
Answers
Answer:
5 yds
Step-by-step explanation:
i am assuming that 4 yd and 3 yd are the legs
so
to find the hypotenuse you square both legs add them and then take the square root of that
so
4^2 + 3^2 = c^2
16 + 9 = c^2
25 = c^2
c = 5
the final side is 5
Milan has been given a list of bands and asked to place a vote. His vote must have the names of his favorite, second favorite, and third favorite bands from the list. How many different votes are possible?
Answers
The number of possible different votes for Milan, based on the list of bands is 60 different votes.
How to find the number of possible votes?There are 5 lists of bands that Milan has to choose from to place a vote and there are only 3 bands to be chosen out of the 5 lists.
The total number of different votes possible is therefore possible by performing a permutation:
= 5! / ( 5 - 3) !
= 5 ! / 2 !
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= 60 different votes
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f(x) = √3x
g(x) = 3x + 2
Find (4) (2). Include any restrictions on the domain.
Answers
Option A is correct. The value of function (f/g)(x) is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3.
What exactly is a function composition?In mathematics, function composition is an operation in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
What is the sum of two functions?The new function obtained by performing f first and then g is the combination of two functions g and f.
Given:
f(x) = [tex]\sqrt[3]{3x}[/tex]
g(x) = 3x + 2
(f/g)(x) = [tex]\sqrt[3]{3x}[/tex]/(3x+2)
Also, the denominator should not be equal to 0.
So, 3x + 2 ≠ 0
x ≠ -2/3
Therefore, the value of function is found to be [tex]\sqrt[3]{3x}[/tex]/(3x+2) where the condition is that x ≠ -2/3. So, Option A is correct
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Find the equation in slope intercept
Answers
Answer:
y=-1/4x+4
Step-by-step explanation:
The graph starts on 4 so that is your y-intercept
Use slope formula to get the slop (y2-y1 over x2-x1)
Use 2 coordinates for formuls (In your case (0,4) and (4,3))
3-4=-1 4-0=4
slope is -1/4
y= -1/4x+4
Which parabola will have one real solution with the line y=x-5?
Answers
The equation of the parabola that has one real solution with the line y = x - 5 is y = x² + 7·x + 4
What is the standard form of the equation of a parabola?The standard form of the equation of a parabola is y = a·x² + b·x + c
The equation of the line is; y = x - 5
The parabola that has one real solution with the line is given by the parabola that is equal to both (x - 5) and the equation for the parabola;
Analyzing the quadratic equations of the parabolas with the equation y = x - 5, gives;
y = x² + x - 4 = x - 5x² + x - 4 - x + 5 = 0
x² + 1 = 0
x² = -1
x = ±√(-1) (Complex solution)
y = x² + 2·x - 1 = x - 5x² + x + 4 = 0
The discriminant, b² - 4·a·c is 1² - 4 × 1 × 4 = -15 < 0 (Complex solution)
x² + 6·x + 9 = x - 5x² + 5·x + 14 = 0
The discriminant, b² - 4·a·c is 5² - 4 × 1 × 14 = -31 < 0 (Complex solution)
x² + 7·x + 4 = x - 5x² + 6·x + 9 = 0
The discriminant, b² - 4·a·c is 6² - 4 × 1 × 9 = 0 One real solution;The quadratic equation that gives one real solution with the equation y = x - 5 is therefore;
y = x² + 7·x + 4
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A road is 8/9 of a mile long. A crew needs to repave 2/5 of the road. How long is the section that needs to be repaved?
Answers
19 is what percent of 500?
Answers
Answer:95
step by step explanation
Complete the model to find-9 + 3 Show your work
Answers
Answer:
Answer is 0. If you have to owe someone 9 dollars and they give you nine back it is 0. You can also rearrange the problem to 9-9 (same thing) which is 0
A cube box is 20 cm x 20 cm x 20 cm. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.
Answers
The surface area of the largest size sphere that can fit in this box is 400π
What is the surface area of the sphere?
The surface area of a sphere is the space that the sphere's outer surface occupies. A sphere is a circle in three dimensions. A circle is a two-dimensional (2D) shape, whereas a sphere is a three-dimensional (3D) shape, which is the difference between the two.
Here, we have
The diameter of the biggest sphere will be equal to the side of the sphere.
radius = 20/2
= 10
The surface area of the sphere = 4πr²
=4π(10)²
= 400π
Hence, the surface area of the largest size sphere that can fit in this box is 400π.
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Question 8 of 10
What is the complete factorization of the polynomial below?
x3+3x²+ 9x+27
OA. (x+3)(x+3/)(x-3)
OB. (x-3)(x+3)(x+3)
OC. (x-3)(x+3)(x-3/)
D. (x+3)(x+3)(x+3/)
Answers
The factorization of the expression [tex]x^3+3x^2+9x+27[/tex] is [tex](x+3)(x^2+9)[/tex].
What is factorization?
The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. A factorization is just the procedure by which an algebraic expression gets expanded in the opposite direction. The greatest common factors among the terms in the provided algebraic expression are identified, and the terms are then grouped in accordance with these factors to factorise the equation. Factorization is the reverse process of expansion of an algebraic statement. If an algebraic expression is a product of prime factors, it has undergone complete factorization.
Here the given polynomial expression is ,
=> [tex]x^3+3x^2+9x+27[/tex]
=> [tex]x^2(x+3)+9(x+3)[/tex]
=> [tex](x+3)(x^2+9)[/tex]
Hence the complete factorization of the given expression is [tex](x+3)(x^2+9)[/tex].
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