1. replace f(x) with y
[tex]y=4x^3+1[/tex]2. Replace every x with a y and replace every y with an x
[tex]x=4y^3+1[/tex]3. Solve for y:
[tex]\begin{gathered} 4y^3=x-1 \\ y^3=\frac{x-1}{4} \\ y=\sqrt[3]{\frac{x-1}{4}} \end{gathered}[/tex]4. Replace y with f−1(x):
[tex]f^{-1}(x)=\sqrt[3]{\frac{x-1}{4}}[/tex]FAST PLS
Which brand of granola typically weighs more?
Brand A bags typically weigh more because the median of brand A is higher than that of brand B.
Brand B bags typically weigh more than brand A bags because there is a high outlier at 52.5.
Brand A bags typically weigh more than brand B bags because there are no outliers in the distribution.
Brand B bags typically weigh more because the range of weights is higher than that of brand A.
Answer:
brand A. The bag weights for brand A have less variability than the bag weights for brand B
Question 3 of 5
A Galapagos penguin can walk mile in an hour. How many hours would it
take the penguin to walk mile?
O A. x = hour
OB. +=
hours
O c.
hour
OD. + hours
-
Answer:
1 hour
Step-by-step explanation:
Since the penguin supposedly walks a 1 mile per hour, it would take one hour to achieve 1 mile
PLEASE HELP!!!!!!!!! It’s algebra
Answer:
See below
Step-by-step explanation:
From 5 to 10 mugs is 5 mugs
These cost 110 - 67.50 = 42.50
So each mug costs 42.50 / 5 = 8.50 each
With a 'base cost' of 25 dollars
(Base cost might be artwork, design, order processing, shipping or whatever.....but this amount is added to each order)
(As a check 20 mugs would be 25 + 20 (8.50) = 195 <====yep
150 mugs will then be 25 + 150 ( 8.50) = 1300 dollars
3/4+(1/2+1/4) 2⋅2
NEED HELP.
Answer:
15/8 for exact form
1.875 for decimal form
And
1 and 7/8 for mixed number form
hope this helps you!
(also already in the simplest form :)
Choose the number and type of roots of each quadratic function.
Function
f(x)=x²-9x + 21
f(x) = x² + 16x - 64
f(x) = -4x²-4x²10x +84
f(x) = 3x² + 24
The number and type of roots of each quadratic function are:
f(x) = x² - 9·x + 21, Has complex rootsf(x) = x² + 16·x - 64 has two real and distinct rootsf(x) = -4·x² + 10·x + 84 has two real and distinct rootsf(x) = 3·x² + 24 has complex rootsWhat determines the type of root that a quadratic function has?The type of roots of a quadratic function is given by the value of the discriminant, which is the value under the square root of the quadratic formula.
The types of roots of a quadratic equation are;
Two real and distinct rootsTwo real and equal rootsComplex rootsThe roots or solution to the quadratic equation, a·x² + b·x + c = 0, are given by the quadratic formula, [tex]x = \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2\cdot a}[/tex]
Where:
b² - 4·a·c is known as the discriminant of the quadratic equation.
The type of root of a quadratic equation is given by the discriminant, b² - 4·a·c, as follows:
If the discriminant, b² - 4·a·c is less than 0, then the quadratic equation has no roots or no real rootsIf b² - 4·a·c = 0, then the quadratic equation has two real and equal roots (or one real root)If the discriminant, b² - 4·a·c > 0, then the quadratic equation has two real and distinct roots.The given functions are:
f(x) = x² - 9·x + 21Comparing the above equation to the, general form of a quadratic equation, f(x) = a·x² + b·x + c, we have;
a = 1, b = -9, and c = 21
The discriminant is therefore, (-9)² - 4 × 1 × 21 = -3 < 0
The quadratic equation therefore, has complex roots.
f(x) = x² + 16·x - 64The quadratic equation, f(x) = x² + 16·x - 64 has a discriminant given as follows;
The discriminant is: 16² - 4 × 1 × (-64) = 512 > 0, therefore, the quadratic equation two real roots, given by the equation;
[tex]x = \dfrac{-16\pm \sqrt{16^2 - 4\times 1 \times 64} }{2\times 1}= \dfrac{-16\pm \sqrt{512} }{2}= \dfrac{-16\pm 16\cdot \sqrt{2} }{2}[/tex]
x = -8 + 8·√2 or x = -8 - 8·√2
f(x) = -4x² + 10·x + 84The value of the discriminant is 10² - 4 × (-4) × 84 = 1444 > 0, therefore, the equation has two real and distinct roots, given by the equation;[tex]x = \dfrac{-10\pm \sqrt{1444} }{2\times (-4)}= \dfrac{-10\pm 38 }{-8}[/tex]
[tex]x = \dfrac{28 }{-8}= -3.5[/tex] and [tex]x = \dfrac{-48 }{-8}= 6[/tex]
f(x) = 3·x² + 24The discriminant of the above quadratic equation is; 0² - 4 × 3 ×24 = -288 < 0
Therefore, the quadratic equation, f(x) = 3·x² + 24, has no real roots or complex roots
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Find the radius of a cylinder whose height is 10 cm and the total surface area is 352 cm².
Answer: the radius of a cylinder is 4 cm
Step-by-step explanation:
[tex]S_{ts}=352\ cm\ \ \ \ H=10\ cm\ \ \ \ \ r=?[/tex]
The total surface area:
[tex]\displaystyle\\ S_{ts}= 2\pi r^2+2\pi rH\\\\S_{ts}=2\pi (r^2+rH)\\\\352=2\pi (r^2+10r)\\\\[/tex]
Divide both parts of the equation by 2π:
[tex]\displaystyle\\56=r^2+10r\\\\56-56=r^2+10r-56\\\\0=r^2+10r-56\\\\Thus,\\\\ r^2+10r-56=0\\\\D=(-10)^2-4(1)(-56)\\\\D=100+224\\\\D=324\\\\\sqrt{D}=\sqrt{324} \\\\\sqrt{D}=18\\\\ r=\frac{-10б18}{2(1)} \\\\r=-14\notin\ (r > 0)\\\\r=4\ cm[/tex]
Answer:
r ≈ 4 cm
Step-by-step explanation:
Total Surface Area of a cylinder
A = Base Area x 2 + Lateral Surface Area
A = 2(πr²) + 2πrh
where r = radius of base and h = height of cylinder
Solving for r we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{h^2 + 2 \dfrac{A}{\pi} }-\dfrac{h}{2}\\\\[/tex]
Given h = 10 cm and A = 325 we get
[tex]\displaystyle r = \dfrac{1}{2} \sqrt{10^2 + 2 \dfrac{352}{\pi} }-\dfrac{10}{2}\\\\\\[/tex]
[tex]\sqrt{10^2 + 2 \dfrac{352}{\pi} } =\sqrt{100+\dfrac{704}{\pi }}\\\\= \sqrt{100 + 224.09}\\\\\\[/tex]
= [tex]\sqrt{324.09}[/tex]
= 18.0025
1/2 x 18.0025 ≈ 9
So r ≈ 9 - 10/2 = 9 -5 = 4
r ≈ 4 cm
Part of the proceeds from a garage sale was 535$ worth of 5$ and 20$ bills. If there were 2 more 5$ bills than 20$ bills, find the number of each denomination
Using concept of Linear equation in two variables, we got 23 is denomination count of 5$ bills and 21 is denomination count of 20$ bills.
Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.
The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).
It is given that 5$ bills are 2 more than 20$ bills,
so let suppose 20$ bills denomination count is x,
then 5$ bills denomination count=x+2;
It is also given that 535$ worth is summation of 5$ bills and 20$ bills
Therefore,[5×(x+2)+(20×x)]=535
On solving for x, we get x=21
Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.
Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21
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it is decided that this barrel must be painted pink and the barrel's surface area is requested in order to determine the amount of paint needed. what is the surface area of the barrel g
The surface area of the barrel needs to be calculated in order to determine the amount of paint. The surface area of the barrel, including the lid, is 13 m²
Missing data from the problem:
radius of the barrel = 0.4 meters
height of the barrel = 1.2 meters
The shape of a barrel is cylinder. The surface area of the barrel, including the lid) is:
A = 2. πr² + 2. πr.h
Where:
r = radius
h = height
Plug the parameters into the formula:
A = 2. π(0.4)² + 2. π(0.4).(1.2)
A = 13 m²
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Your family used 27.5 gallons of gas to drive 654.5 miles. how many miles did you drive for each gallon?
Answer:
total distance = 654.5
Total gas used = 27.5
Distance per gallon = 654.5 ÷ 27.5 = 23.8
We drove 23.8 miles for each gallon of gas
The graphs below have the same shape. What is the equation of the blue graph? G(x) = _ A. G(x) = x2 + 5 B. G(x) = (x + 5)2 C. G(x) = x2 - 5 D. G(x) = (x - 5)2
The blue graph is represented by the equation g(x) = (x - 5)²
How to determine the equation represented by the blue graph?The possible graph that completes the question is added as an attachment
From the attached graph, we have the following parameters
Red graph = f(x)Blue graph = g(x)Also from the graph, we have the equation of the function f(x) to be
f(x) = x²
Solving further, we can see that:
The function g(x) is on the same level as the function f(x) Also, the function has the same size as .f(x)The only difference is that, f(x) is shifted to the right by 5 units
This means that
g(x) = f(x - 5)
So, we have
g(x) = (x - 5)²
Hence, the blue graph equation is g(x) = (x - 5)²
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Jenna buys three boxes of cocoa.
She gives one box to Keanu and one box to Jacoby.
What fraction of cocoa did Jenna give to her friends?
Answer: 2/3
Jenna had 3 boxes of cocoa and gave away 2, for each friend the fraction is 1/3 therefore 1/3 +1/3 =2/3.... the final fraction is 2/3.
Answer: 2/3
Step-by-step explanation:
total, Jenna had 3/3, then she gave 1/3 to two of her friends. Which makes the total boxes 2/3 of what she gave away with a remaining of 1/3. (1 box of the three boxes)
20, 33, 44, 53, 69, 75, 89, 90 Find the mean and the standard deviation. Round to the nearest thousandth.
The mean and the standard deviation of the following numbers 20, 33, 44, 53, 69, 75, 89, 90 are 59.125 and 22.461 respectively
What are mean and standard deviation?The mean is the average value in a collection and a standard deviation is the average amount of variability in a data.
mean= sum of data in the collection/ number of data
= (20+33+44+53+69+75+89+90)/8 = 473/8 = 59.125( nearest thousandth)
standard deviation= sum of √(x- mean)^2/ number of data while x is each number in the data
finding (x- mean)^2 for each value of x
(20-59.125)^2=848.266
(33-59.125)^2=682.516
(44-59.125)^2=228.766
(53-59.125)^2=37.516
(69-59.125)^2=102.516
(75-59.125)^2= 260.016
(89-59.125)^2= 907.516
(90-59.125)^2= 968.766
S.D= √(848.266+682.516+228.766+37.516+102.516+260.016+907.516+968.766)/8 =
√504.484
Therefore S.D =22.461 ( to the nearest thousandth)
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Evaluate the expression. Explain your process. 3x+2. for x=4
Answer:
14
Explanation:
To evaluate the expression, we need to replace x by 4. So, the expression is equal to:
3x + 2
3(4) + 2
12 + 2
14
Therefore, the value of the expression is 14
A bacterial colony starts with 120 cells and quadruples in size each day. Write an equation that relates the population of cells in this colony (P) at the start of each day and the number of days (d). Find the population on day 8.
Answer:
P = 120*([tex]2^{2d-2}[/tex])P(8) = 1, 966, 080Step-by-step explanation:
Since the population quadruples each day, the population for the subsequent day would be 4*(population of the previous day).
Thus, the evolution of the population value takes the form of a geometric progression, with a common ratio, r = 4
The n-th term of a geometric progression is given by:
[tex]a_{n}[/tex] = [tex]ar^{n-1}[/tex] (1)
Where a is the 1st term of the progression.
From (1), our population would generally take the form:
[tex]P_{d}[/tex] = [tex]P_0r^{d-1}[/tex] (2)
In this case, the initial value (1st term) [tex]P_{0}[/tex] = 120.
So putting r and [tex]P_{0}[/tex] into (2):
P(d) = 120*([tex]4^{d-1}[/tex])
Noting that 4 = 2²:
P(d) = 120*([tex]2^{2(d-1)}[/tex])
P(d) = 120*([tex]2^{2d-2}[/tex])FOR d = 8:
P(d) = 120*([tex]2^{2d-2}[/tex])
becomes:
P(8) = 120*([tex]2^{2(8)-2}[/tex])
P(8) = 120*([tex]2^{16-2}[/tex])
P(8) = 120*([tex]2^{14}[/tex])
P(8) = 120*(16,384)
P(8) = 1, 966, 080WATER DEPTH An echo sounder is a device used to determine the depth of water by measuring the time it takes a sound produced just below the water surface to return, or echo, from the bottom of the body of water. The accuracy of an echo sounder is the positive difference between the depth of water reading on the echo sounder and the actual depth of water w. Write two absolute value expressions equivalent to the accuracy of an echo sounder.
The absolute value expressions of the echo sounder are |r - w| and |w - r|
How to determine the absolute value expressions of the echo sounder?The statement in the question is represented as
The accuracy of an echo sounder is the positive difference between ...
To solve further, we use the following representations
Depth of water reading = r
Actual depth = w
So, the statement becomes
The accuracy of an echo sounder is the positive difference between r and w
The difference can be represented as
Difference = r - w or Difference = w - r
Represented as absolute value expressions
Difference = |r - w| or Difference = |w - r|
Hence, the expressions are |r - w| and |w - r|
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The length of a rectangle is 3 inches greater than the width. (Hint: draw a pictureand label itA. Write a polynomial that represents the area of the rectangle.B. Find the area of the rectangle when the width is 4 inches..
We are given that the length of a rectangle is 3 inches greater than the width.
Let us draw a rectangle and label the width and length.
Part A:
Let the width of the rectangle is x inches.
Then the length of the rectangle is (x + 3) inches.
Now recall that the area of a rectangle is given by
[tex]A=L\cdot W[/tex]Where L is the length and W is the width of the rectangle.
[tex]\begin{gathered} A=(x+3)\cdot x \\ A=x^2+3x \end{gathered}[/tex]Therefore, the above polynomial represents the area of the rectangle.
Part B:
We are given that the width is 4 inches.
Substitute the width (x = 4) into the equation of the area that we found in part A.
[tex]\begin{gathered} A=x^2+3x \\ A=(4)^2+3(4) \\ A=16+12 \\ A=28in^2 \end{gathered}[/tex]Therefore, the area of the rectangle is 28 square inches.
What is (9 x 10^4) (6 x 10^-7)?
Answer:0.0008994
Step-by-step explanation:
i don't get it could you please help me? also please could it be quick because I have soccer practice too
The number of cups of bananas is represented by x
The number of cups of strawberries is represented by y
Note that:
[tex]\begin{gathered} 1\frac{2}{25}\text{ = }\frac{27}{25} \\ 5\frac{2}{5}=\text{ }\frac{27}{5} \\ 2\frac{18}{25}=\text{ }\frac{68}{25} \\ 13\frac{3}{5}=\text{ }\frac{68}{5} \end{gathered}[/tex]27/5 cups of strawberry is used for 27/25 cups of banana
1 cup of strawberry is used for x cups of banana
x = 27/25 ÷ 27/5
x = 27/25 x 5/27
x = 1/5
1/5 cups of banana is used for 1 cup of strawberry
Comparing the values of x with values of y in the table and writing the relationship in the form y = kx:
y = 5x
where k = 5
The constant of proportionality = 5
PLEASE HELP NOW DUE AT 11 PM. Are the linear expressions equivalent? Drag the choices to the boxes to correctly complete the table. .
In these linear expressions one is equivalent which is 3- 2( - 2.6x + 2.1) = 5.2x - 1.2 and one is not .
What are linear expressions?An algebraic expression known as a linear expression has terms that are either constants or variables raised to the first power.
Alternatively pluging; we will see that none of the exponents can be greater than 1.
2x - 3(1.3x - 2.5) = 5.9x + 7.5
2x -3.9x + 7.5 = 5.9 + 7.5
-1.9x + 7.5 ≠ 5.9 + 7.5
thus linear expression is not equivalent.
3- 2( - 2.6x + 2.1) = 5.2x - 1.2
3 + 5.2x - 4.2 = 5.2x - 1.2
5.2x - 1.2 = 5.2x - 1.2
thus, linear expression is equivalent.
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150 14 Solve for x. Round to the nearest tenth. 63.5 54.1 3.6 74.9
The given triangle is a right angled triangle having the follwoing sides;
Hypotenuse = x (longest side)
Opposite = 14 (side facing the given acute angle)
Theta = 15 degrees
Using the SOH trigonometry identity;
sin 15 = opposite/hypotenuse
sin15 = 14/x
x = 14/sin15
x = 14/0.2588
x = 54.09
x is approximately equal to 54.1. Option B is coorect
8b^2 + 56b + 48 = 0
Solve for X
Answer:
b= -1, -6
Step-by-step explanation:
divide by common factor
then use x=- b+- sqrt b^2-4ac/2a
separate the equations and solve them
What is the number sentence for "4 and N together make9"?
Given:
The number sentence for 4 and n
Required:
We have to find the given sentence
Explanation:
4 and N, simply means you mixed them up, you sum them up
your result is 9, 4+N=9
Required solution :
4+N=9
In a race, Kara ran eight- eighteenths of a kilometer and cycled sixteen-eighteenths of a kilometer. Estimate how many kilometers the race was in all.
a) 1/2 kilometer
b) 1 kilometer
c) 1 1/2 kilometers
d) 2 kilometers
Number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
Given that, Kara ran 8/18 of a kilometer and cycled 16/18 of a kilometer.
What is addition of two fractions?To add two fractions, with different denominators, we need to rationalise the denominators by taking out the LCM and make the denominator same. Then add the numerators of the fractions, keeping the denominator common.
Now, total distance in race
8/18 + 16/18
= (8+16)/18
= 24/18
= 4/3
= [tex]1\frac{1}{3}[/tex] kilometers
Therefore, number of kilometers the race was in all is [tex]1\frac{1}{3}[/tex] kilometers.
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Find the measure of each angle in the diagram
When and where does the story The circuit take place?
Answer:
Mexico to the United States in 1947
Step-by-step explanation:
PLEASE HELP ME ASAP :,)
Answer:
154 feet squared
Step-by-step explanation:
1. Divide 14 by 2
2. Use the equation pie times radius squared
3. Answer is 153 foot squared
Rain fell at a rate of .25 inches per hour. Before the rain began, 6 inches had already fallen that month. At this rate, how much total rain will have fallen after 4 hours?
Answer:
y=.25x+6
Step-by-step explanation:
Find the values of Y and X
f(x)= x-6/2
g(x)=√x-4
Express the function gf in the form gf(x) = ...
Give your answer as simply as possible.
The function is given below
What is a function?
The value of a function f at an element x of its domain is indicated by f(x); the numerical value resulting from the function evaluation at a given input value is expressed by substituting x with this value; for example, the value of f at x = 4 is denoted by f(x) (4). When the function is not named and is represented by an expression E, the function's value at, say, x = 4 can be expressed by E|x=4. In science, engineering, and the bulk of the mathematical disciplines, functions are commonly used. Functions are claimed to be "the central objects of research" in most branches of mathematics.
The given function is
f(x) = x - 6/2
The function in gf is
g{f(x)} = √(x - 6/2) - 4
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The value of the required composite function is [tex]g(f(x))=\sqrt{x-\frac{6}{2} } -4[/tex].
What is a composite function?
When the result of one function is utilized as the input for another, a composite function is created.
Given that:
[tex]f(x)=x-\frac{6}{2}[/tex] and [tex]g(x)=\sqrt{x}-4[/tex]
To find the composite function [tex]g(f(x))[/tex], it is required to use the output of the first function as the input of the second function. It means that replace [tex]x[/tex] by [tex]f(x)[/tex] in the second function as:
[tex]g(x)=\sqrt{x}-4\\g(f(x))=\sqrt{f(x)}-4[/tex]
Now, substitute the value of [tex]f(x)[/tex] on the right side of the above equation as:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
Hence, the required answer is:
[tex]g(f(x))=\sqrt{x-\frac{6}{2}}-4[/tex]
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A ball is thrown directly upward from a height of 7 ft with an initial velocity of 28 ft/sec. The function s(t)= -16t+28t+7 gives the height of the ball, in feet, t seconds after it has been thrown. Determine the time at which the ball reaches the maximum height and find the maximum height.
Answer:
Brainliest Answer?
( 7 / 8 ) seconds
( 77 / 4 ) feet
Step-by-step explanation:
The question is a bit confusing but I will do it both ways. I will assume that you made a mistake copying over the function because the graph s( t ) is linear. Linear functions have a maximum value of infinity because it is an odd-degree polynomial.
AlgebraAssume that s( t ) = - 16t² + 28t + 7;
The equation forms an upside-down parabola which means it has a maximum value.
Complete the square to get the axis of symmetry and the maximum value of the parabola or use my very cool formula. The variables h and k represent the axis and max respectively.
Formulaax² + bx + c = a( x - h )² + k;
ax² + bx + c = a( x - ( - b / 2a ) )² + c - ( b² / 4a );
Completing the Squareax² + bx + c;
Take a as a factor.
a( x² + ( b / a )x + ( c / a ) );
Add and subtract the square of ( 1 / 2 ) of ( b / a ). This is called completing the square because it forms a perfect square trinomial.
a( x² + ( b / a )x + ( b / 2a )² - ( b / 2a )² + ( c / a ) );
Factorise the trinomial.
a( ( x + ( b / 2a ) )² - ( b / 2a )² + ( c / a ) );
Use the distributive property of multiplication.
a( x + ( b / 2a )² + a( ( c / a ) - ( b / 2a )² );
a( x + ( b / 2a )² + a( ( c / a ) - ( b² / 4a² ) );
Simplify the fractions.
a( x + ( b / 2a )² + c - ( b² / 4a );
SolutionSubstitute the values.
- 16( t - ( - 28 / 2( - 16 ) )² + 7 - ( ( 28 )² / 4( - 16 ) );
Time is the x-axis so we need to solve for the axis of symmetry.
h = ( - 28 / 2( - 16 ) );
h = ( - 28 / - 32 );
Simplify the fraction.
h = ( 7 / 8 );
Maximum height is the parabola's y of the vertex.
k = 7 - ( ( 28 )² / 4( - 16 ) );
k = 7 - ( ( 28 )( 28 ) / - 64 );
k = 7 - ( 784 / - 64 );
k = 7 - ( - 49 / 4 );
k = ( 28 / 4 ) + ( 49 / 4 );
k = 77 / 4;