The value of the reverse permutation is F-¹(3) = 5.
What is defined as the inverse permutation?An inverse permutation is one in which each number as well as the number of the place it occupies are swapped.
(1) (2), for example, are inverse permutations because the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in are and the positions of 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 in are also.It is important to note it never says that "f" is a function; rather, it asserts that the inverse of "f" is a function is if domain of f is restricted.For, the given values in the question;
So, if you remove the last point, (5,3), the inverse is a function because it contains only the points.
F= {(2, 6), (3, 1), (4, 5), and (5,3)}.
Thus, it can be written as;
F: 2 → 3 → 4 → 5
F: 6 → 1 → 5 → 3.
Thus, F-¹(3); 3 → 5.
F-¹(3) = 5.
Therefore, the value of the reverse permutation is F-¹(3) = 5.
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Please help with problem 25, part a and b Algebra 1, In the attachment.
The equation to represent the number of people that can attend the event will be 18500 +/- 1200.
How to calculate the value?Based on the information, equation to represent the number of people that can attend the event will be 18500 +/- 1200.
The maximum number will be:
= 18500 + 1200
= 19700
The minimum number will be:
= 18500 - 1200
= 17300
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Name the property of 8(9 + 0 ) = 8(9)
The property of 8(9 + 0 ) = 8(9) is the identity property of addition.
How to illustrate the information?It should be noted that the identity property of addition states that the sum of 0 and any number will be equal to that number.
In this case, the property of 8(9 + 0 ) = 8(9) is the identity property of addition. This was illustrated as 9 + 0 equals to 9.
Therefore, the property is the identity property of addition.
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If a rectangular garden is 35 ft. by 25 ft., how many feet of fence are needed to enclose it?
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches, what is the width of the rectangle?
Step-by-step explanation:
Let's denote the length of the rectangle to be L and the width to be W.
The first sentence tells us that the length, L, is "4 less than twice the width". "4 less than" implies we subtract 4 from some quantity. What is that quantity? Well that's "twice the width." We can rewrite this sentence in terms of L and W as: L = 2W - 4.
Now we know the length of the rectangle in terms of the width.
The area of a rectangle is given by A = L x W. Using this equation, we can substitute our values for area and length:
A = L x W
96 = (2W - 4) x W
From this we can solve for W and subsequently solve for L using algebra:
96 = (2W - 4) x W
96 = 2W^2 -4W
96 = 2(W^2 - 2W)
48 = W^2 - 2W
W^2 - 2W - 48 = 0
(W - 8)(W + 6) = 0
W = 8 or W = -6
Since W is the side-length of a rectangle, we can disregard the negative solution. Therefore W = 8 ft.
If W = 8, then L = 2W - 4 = 2(8) - 4 = 12 ft.
Lastly, we know the Perimeter of a rectangle is given as P = 2L + 2W. Substituting into this equation we solve for the perimeter:
P = 2L + 2W = 2(12) + 2(8) = 40 ft.
The width of the rectangle will be 38 inches.
What is the perimeter of the rectangle?Let W be the rectangle's width and L its length. The perimeter of the rectangle will be defined as the total length of all of its sides. So the rectangle's perimeter will be
Perimeter of the rectangle = 2(L + W) units
If the length of a rectangle is four less than twice its width and the perimeter is 220 inches.
L = 2W - 4
Then the equation is given as,
P = 2(L + W)
220 = 2W - 4 + W
110 = 3W - 4
3W = 114
W = 38 inches
The width of the rectangle will be 38 inches.
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Sonya has two rectangular gardens. The larger garden is four times as wide and five times as long as the smaller one. If the area of the smaller one is x, what is the difference in size between the two gardens?
A. 20x
B. 19x
C. 9x
D. 1x
E. None of the above
The required difference in the size between the two garden is 20x. Option A is correct.
Given that,
Sonya has two rectangular gardens. The larger garden is four times as wide and five times as long as the smaller one. If the area of the smaller one is x, what is the difference in size between the two gardens is to be determined.
The rectangle is 4 sided geometric shape whose opposites sides are equal in length and all angles are about 90°.
Here,
length and width of the small rectangular garden is l and b
Let the are of the small garden be x = lw
Now according to the question
Length of the larger garden = 5l
And the width of the larger garden = 4w
Now the area of the larger garden = 5l * 4w
= 20lw
= 20x
Thus, the required difference in the size between the two gardens is 20x. Option A is correct.
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Make a conjecture about the sum of the measures of the interior angles of a triangle.
The Conjecture is : "the sum of the measures of the interior angles of a triangle is 180° ".
What are interior angles?The interior angle of any triangle is defined as the angle which is inside the triangle. In the other words if the triangle has the point within the angle it is in the interior of the angle. A triangle has three internal angles. The interior angles are always less than 180.
Triangle Angle-Sum TheoremAccording to triangle Angle Sum theorem, the measurement of the sum of all interior angles of a triangle is always equals to 180°. That means, For a given triangle say ΔABC if ∠A, ∠B and ∠C are the interior angles then their sum i.e. ∠A + ∠B + ∠C = 180°.
Thus according to this we can make the conjecture about the sum of measures of the interior angles of a triangle.
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In order to design an appropriate touchscreen for a computer, the manufacturer has to consider the average size of the fingers and hands that will be touching the screen. One lab found that the average width of the index ( or pointing ) finger for adults is from 1.6 cm to 2 cm wide.
1. All the measurements on this page are inclusive. Explain what that means for the inequality symbols you will use.
2. Write the average width as an inequality using centimeters.
3. One centimeter = 0.39 inches. Write the average width as an inequality using inches.
The range of the average width of the index finger which is between 1.6 centimeters and 2 centimeters gives;
1. The symbols to use for the inequality are ≤ and ≥
2. The average width expressed as an inequality is; 1.6 ≤ w ≤ 2
3. The inequality for the average width in inches is 0.624 ≤ w ≤ 0.78
How can the inclusive range be expressed as an inequality?1. With regards to working with number ranges or intervals, the term inclusive means that the endpoints of the (closed) interval are included in the range.
The inequality symbol to be used in an inclusive interval are ≤ and ≥ (the symbols < and > are used for an exclusive measurements)
2. The minimum width = 1.6 centimeters
Maximum width = 2 centimeters
The average width in centimeters, w, written as an inequality is therefore;
1.6 ≤ w ≤ 23. The given conversion factor is 1 cm. = 0.39 inches.
Therefore;
1.6 cm = 1.6 × 0.39 in. = 0.624 in.
2 cm = 2 × 0.39 in. = 0.78 in.
The inequality for the average width in inches is therefore;
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4 is subtracted from the product of 5 and a number.
Answer:
5x-4
Step-by-step explanation:
Product of a number, x , and 5 = 5x
subtract 4 5x -4
Alexandra and her children went into a bakery where they sell cupcakes for 3.25 each and donuts for 1.25 each. Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether. If x represents the number of cupcakes purchased and y represents the number of donuts purchased, write and solve a system of inequalities graphically and determine one possible solution.
explanation up top:) that's the explanation I hope you understand
The number of maximum cupcakes and cookies sold is 6 and 5 respectively.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
Alexandra sell cupcakes for 3.25 each and donuts for 1.25 each.
let x be the number of cupcakes purchased and y be the number of donuts purchased.
Now, Alexandra has 25 to spend and must buy a minimum of 11 cupcakes and donuts altogether.
So, x+ y ≥11
and, 3.25x + 1.25y ≤ 25.
Thus, x= 5.625 and y= 5.375
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Q2 The length of a roll of ribbon is 30 metres, correct to the nearest half-metre. A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll. Work out the maximum possible length of ribbon left on the roll.
The maximum possible length of ribbon left on the roll is 24.5 m.
Find bounds, Roll
30 → nearest half metre.
0.5 ÷ 2 = 0.25
LB = 30 – 0.25 = 29.75
GB = 30 + 0.25 = 30.25
Piece
5.8 → nearest 10cm or 0.1m
(10÷100=0.1)
0.1÷2 = 0.05
LB = 5.8 – 0.05 = 5.75
GB = 5.8 + 0.05 = 5.85
Max length left = GB roll – LB piece
=30.25 – 5.75
=24.5m
The metric system's default unit of measurement for length. 100 centimeters equal to 1 metre. A meter is a common metric unit that is around 3 feet, 3 inches long. It measures 100 times more than a Centimetre, or 0.01 meters, in size. 1000 meters make up one kilometre.
Hence, the maximum possible length of ribbon left on the roll is 24.5 m.
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For a ride on a rental scooter , ahmad paid $3 fee to start the scooter plus 11 cents per minute of the ride. The total bill for Ahmad’s ride was $20.49. For how many minutes did ahmad ride the scooter
Answer:
159 minutes
Step-by-step explanation:
y = .11x + 3
$3 initial fee to start the scooter
$0.11 per minute
y = the total bill price of the scooter ride
x = the total minutes of the ride
plug in what we know : $20.49 for the whole ride
20.49 = 0.11x + 3
SOLVE !! 20.49 - 3 = 0.11x
17.49 = 0.11x
17.49 / 0.11 = x
x = 159 minutes
check answer if you want
20.49 = 0.11 (159) + 3
20.49 = 17.49 + 3
20.49 = 20.49
You can find the equation of a line through two points even if one point is not the y -intercept. Find the slope m of the line passing through the two points.Using either point, substitute for x, y , and m into y=m x+b . Solve for b and rewrite y=m x+b for the values of m and b . Write an equation in slope-intercept form for the line passing through each pair of points.
b. (-4,16) and (3,-5)
16 = -4(-3) + 4 is an equation in slope-intercept form for the line passing through points (-4,16) and (3,-5)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope.
We have been asked to write an equation in slope-intercept form for the line passing through (-4,16) and (3,-5)
First we will find the slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (-4,16) and (3,-5)
⇒ m = [tex]\frac{-5- 16}{3 - (-4)}[/tex]
⇒ m = [tex]\frac{-21}{7}[/tex]
⇒ m = -3
We know that the equation for slope(m) and y - intercept(b) of a line is given by :
y = mx + b
Here lets take equation 16 = -4(-3) + b .Here x and y is substituted with the second two points.
⇒ 16 = -4(-3) + b
⇒ 16 = 12 + b
⇒ b = 16 - 12
⇒ b = 4
The equation in the slope intercept is as follows:-
16 = -4(-3) + 4
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The quotient of a number X and 7
Answer: x / 7
Step-by-step explanation:
"the quotient of" represents division, or /.
"a number" represents a variable, in this case, it's x.
while "7" just means the number 7.
Hope this helps!
Solve for the missing exponent
(4a^3)^2=16a
Step-by-step explanation:
= 16 a^6=16a divide for 16
a^6=a there are only two solutions 1 and 0 cause:
1^6=1 and 0^6=0
The scale on a map is stated as
1: 100 000
On the map, Jennifer estimates that the distance to her destination is 8 cm.
If she is correct in her estimate, how many kilometres is it to her destination?
The required estimate of the destination on the map is 800,000 kilometers.
Given that,
The scale on a map is stated as 1: 100 000 on the map, Jennifer estimates that the distance to her destination is 8 cm. If she is correct in her estimate, how many kilometers is it to her destination is to be determined.
The scale factor is defined as the ratio of modified change in length to the original length.
Here,
1 cm = 100, 000 km
Multiply both sides by 8
8cm = 800,000 kilometers.
Thus, the required estimate of the destination on the map is 800,000 kilometers.
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Determine whether each relation is a function. (1,1),(2,0),(3,1),(4,3),(0,2)
Range - { 1 , 0, 1 , 3 , 2 } is relation is a function.
What is domain and range ?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.Definitions of domain and example?
The domain is the set of x -coordinates, {0,1,2} , and the range is the set of y -coordinates, {7,8,9,10} .
function. (1,1),(2,0),(3,1),(4,3),(0,2)
Domain - { 1,2, 3 , 4 , 0 }
Range - { 1 , 0, 1 , 3 , 2 }
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Can someone explain how I’d solve this?
Answer:
please upload a picture of your question
On a construction crane, the amount of force needed to move objects is directly proportional to the weight of the objects. If 4 Newtons of force is needed to move an object that is 1200 pounds, how much force would be needed to move an object that is 900 pounds?
Based on the fact that the force needed to move object is directly proportional to the weight of the objects, the force needed to move and object that is 900 pounds is 3 newtons of force.
How much force is needed?When things are directly proportional, it means that they increase by a given amount together and also decrease by the same amount.
If 4 Newtons are needed for 1,200 pounds, the newtons needed for 1 pound is:
= 4 / 1,200
= 1/300 newtons
If there are 900 pounds to be moved, the newtons needed are:
= 1/300 x 900
= 3 newtons of force
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State the property that justifies the following statement.
If 12=2 x+8 and 2x+8=3y, then 12=3y.
The property that justifies the following statement, if 12=2 x+8 and 2x+8=3y, then 12=3y is the transitive property.
Transitive property is one of the properties of equality which states that if there is an equality sign between two values or numbers and one of these numbers is equal to a third numerical value then the other number is also equal to that third numerical value.
Therefore this property can be described as,
if x = y and y = a, then x = a
The transitive property also justifies that if two values x and y are not equal, but y is equal to a, then x cannot be equal to a. That is if x ≠ y, but y = a, then x ≠ a.
So, according to the transitive property, the statement, If 12=2x+8 and 2x+8=3y, then 12=3y is valid.
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can anyone help much appreciated (30 points) image below btw
The sum of the polynomial is equal to -10x^3 + 2x^2 + 7x + 8.
what are polynomials?In mathematics, polynomials refers to an algebraic equation which have more than two terms, the terms are usually same variable but the exponents tends to increase the number of terms.
An algebraic equation with the highest power as two is generally called parabolic equation/ When the power goes above two they are called polynomial.
How to add polynomialsaddition of polynomials is achieved by adding like terms together. the like terms as in the question include similar alphabet and same exponents
( -4x^3 + 10x^2 + 6 ) - ( 6x^3 + 8x^2 - 7x - 2 )
terms with x^3: -4 - 6 = -10
terms with x^2: 10 - 8 = 2
terms with x: 0 - ( - 7 ) = 0 + 7 = 7
constant terms : 6 - ( - 2 ) = 6 + 2 = 8
constant terms refers to terms that does not have x
writing the equation together with their terms gives -10x^3 + 2x^2 + 7x + 8. Hence we can conclude that addition of polynomials involves addition performed considering the terms by adding like term.
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gina wilson unit 3 homework 1
a question with a single correct answer
data that consists of numbers
a question that can have a variety of answers
:: statistical
III
:: numerical
nonstatistical
Answer:
a question with a single correct answer: non statistical
data that consists of numbers: numerical
a question that can have a variety of answers: statistical
Step-by-step explanation:
-
Determine the values of x in the equation x2 = 49.
whoever gets it right gets a crown pls help
Answer:
49/2 or 24 1/2
Step-by-step explanation:
Divide both sides by 2 to get x by itself.
Answer:
x = 7
Step-by-step explanation:
➟ x² = 49
in order to find the value of x will have to take square root of both side
➟ [tex] \sf \sqrt{x} = \sqrt{49} [/tex]
Calculate
➟ [tex] \sf \: x = 7[/tex]
1. (1.2 × 10³) + (8.3 × 10³)
Answer:
9,500
Step-by-step explanation:
first, remove the parentheses
1.2 x 10^3 + 8.3 x 10^3
Collect the like terms
take 1.2x10^3 + 8.3x10^3 and you will get 9.5 x 10^3
Evaluate the power of 10^3 = 1,000
then do 9.5x1000 = 9,500
Which expression best represents a simpler form of 4m+3(m+n) ?
A 7m+3n
B 4m+3mn
C 3m+4n
D 7m²+3n
The expression 7m+3n best represents a simpler form of 4m+3(m+n).
The Simplified Algebraic Expression is defined as the expression that do not have any like terms and also it cannot be simplified further.
For Example : 2x+5y+6x , the simplified form will be 8x+5y as it cannot be simplified further.
In the given question,
=4m+3(m+n)
=4m+3m+3n ...(multiplying 3 with m and n)
Now Combining the like terms ,
We get ;
=7m+3n
Therefore , the expression that best represents a simpler form of 4m+3(m+n) is 7m+3n.
The correct option is (A) 7m+3n.
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A bolt of fabric is a large rectangular strip of fabric. Starr-Lyn designs her own fabric. The design is then produced and placed on a bolt that is 81.5 meters (m) long and 1.32 m wide. Part A: Determine the area in Square meters of a bolt of fabric with Starr- Lyn's design.
The area of the rectangle according to the given length and width is 107.58m².
What do we mean by a rectangle?A rectangle is a quadrilateral with four right angles in Euclidean plane geometry. It can also be defined as an equiangular quadrilateral because all of its angles are equal, or a parallelogram with a right angle. A square is a rectangle with four equal-length sides. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D shape, it has two dimensions: length and width.The formula of the area of a rectangle: l × w
Now, substitute the values in the formula:
l × w81.5 × 1.32107.58m²Therefore, the area of the rectangle is 107.58m².
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50 PTS - functional notation (yes or no)
Can someone explain what I have to do for this? Do I just plug them in or what also yes or no for what?? Thanks!
The solution to the functional notations would be either yes or no if the function on the left hand side and right hand side are the same. Hence we would have:
c. No: f ( x ) ≠ f ( -x )
d. Yes: ( - x ) = - f ( x )
What is function notation?Function notation is way of writing functions so that they can easily be understood in the mathematical sense. This method is applied in the question to help read the meaning in the question without much explanations.
Given data
f ( x ) = x^3
f ( -x ) = - x^3
How to solve the function notationsc. No f ( x ) ≠ f ( -x )
f ( x ) = x^3 and f ( -x ) = - x^3
f ( x ) is not equal to f ( -x )
plugging the values for the left hand side of the equation gives
x^3
and plugging the values for the right hand side of the equation gives
- x^3
since the left hand side of the equation is not equal to the right hand side of the equation it means that the both sides of the equation are not equal hence equation sated in c is not correct
f ( x ) ≠ f ( -x ) ( take note of the sign )
d. Yes ( - x ) = - f ( x )
( - x ) is equal to - f ( x )
This represents odd functions where the negative sign persists at the left hand side and the right hand side of the equation. Odd function do appear for functions which have negative signs and have odd exponents too.
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The sum of four consecutive numbers is thirty. Enter the value of the largest number.
ok so the answer is
i might be wrong but
6+7+8+9 = 30
so 9
need help fast !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The correct location of the system of equations are;
Single solution;
y = 11 - 2•x
4•x - y = 7
x + y = 15
2•x - y = 15
No solution;
2•x + y = 7
-4•x = 2•y + 14
x = 12 - 3•y
3•x + 9•y = 24
Infinite solution;
2•x + y = 7
-6•x = 3•y - 21
What are the types of solutions to linear system of equations?The possible system of equations and their solution are presented as follows;
System of equations
y = 11 - 2•x4•x - y = 7Solution;
4•x - y = 7
Therefore;
11 - 2•x = 4•x - 7
6•x = 18
x = 3; Single solution;
System of equations
2•x + y = 7-4•x = 2•y + 14Solution;
2•x + y = 7 gives;
y = 7 -2•x
-4•x = 2•y + 14 gives;
y = -2•x - 7
7 -2•x = -2•x - 7
0 = 14, no solution
System of equations
x = 12 - 3•y3•x + 9•y = 24Solution;
x = 12 - 3•y gives;
3•x + 9•y = 24 gives;
x = (24 - 9•y) ÷ 3 = 8 - 3•y
Which gives;
12 - 3•y = 8 - 3•y
12 = 8 no solutionSystem of equations
2•x + y = 7-6•x = 3•y - 21Solution;
2•x + y = 7 gives;
y = 7 - 2•x
-6•x = 3•y - 21 gives;
3•y = 21 - 6•x
y = 7 - 2•x
7 - 2•x = 7 - 2•x Infinitely many solutions
System of equations
x + y = 152•x - y = 15Solution;
x + y = 15 gives;
y = 15 - x
2•x - y = 15 gives;
y = 2•x - 15
Which gives;
15 - x = 2•x - 15
3•x = 15 + 15 = 30
x = 30 ÷ 3 = 10 Single solution
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i need to know how to solve this please
Step-by-step explanation:
8z^3+z^2+3z-1/z-1 you can use long division to get 8z^2+(9z^2+3z-1)/(z-1). You can keep dividing this equation until you get 8z^2+9z+12+11/z-1.
By using synthetic division, you can divide it into
1 -1. 8 1 3 -1 (a.k.a their coefficients)
Then bring the 8 down three, 1 down two, and 3, down one. Take that and multiply the one by each, and put it down. 8, 1, and 2. Then, do that with -1, to get -1, -2, and 1. So, the answer is 8z^2+9z+12+11+z-1. But since it's division, and there are 4 terms on one side, and 2 terms on the other, you have to divide it so it's 8z^2+9z+12+11/z-1.
Hope this makes sense!
