The amount of time it will take both of them is 5.5 days, if Ann and Ben work together
How to determine the amount of time it will take both of them?The given parameters are
Ann = 10 days
Ben = 12 days
Represent the number of days it takes both of them with T
So, we have the following equation
1/T = 1/Ann + 1/Ben
Substitute the known values in the above equation, so, we have the following representation
1/T = 1/10 + 1/12
So, we have
1/T = (12 + 10)/120
1/T = 22/120
Take the reciprocal of both sides
T = 120/22
Evaluate
T = 5.5
Hence, it will take them 5.5 days
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Twenty members of a health club who jog were asked how many miles they jog per week. The responses are to the right. Construct a stem-and-leaf display. For single digit data, use a stem of 0. 14 26 8 14 14 22 26 25 4 34 44 34 6 18 24 17 11 6 19 17
The steam-leaf display is shown as follows
How do stem and leaf displays work?A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf. The number's final digit is not part of the stem. The number's leaf will always be one digit.
What are the advantages of stem and leaf display?Pencil and paper can be used to quickly create the plot. The plot can be used to determine the values of each individual data point. Since the stem is not repeated across multiple data points, the data is organized compactly.
The stem-and-leaf display for the given data is shown below followed by a detailed explanation.
0|358
1|25179476
2|73823
3|44
4|0
Note that it is often customary to organize the "leaf" values from lowest to highest as follows:
0|3578
1|12456779
2|23378
3|44
4|0
Each row's initial number is referred to as the stem, and the group of numbers that come after it as the leaves. The tenth position of the numerals is indicated by the stem. Therefore, a stem of 0 indicates a single-digit number, a stem of 1 indicates a number between 10 and 19, and so on. The leaves identify the numerals' unit position. If the number is 28, for instance, the stem and leaf are each two.
The data for stem 0 contains four one-digit numbers, which are 3, 5, 8 and 7 in appearance order. Therefore, the stem 0's leaves are 3, 5, 8, and 7.
Eight values between 10 and 19 may be found in the data for stem 1, and they are 12, 15, 11, 17, 19, 14, and 16 in that sequence. Therefore, 2, 5, 1, 7, 9, 4, and 6 make up the stem 1's leaves.
Five values between 20 and 29 may be found in the data for stem 2, and they are 27, 23, 28, 22, and 23 in that sequence. As a result, the stem 2's leaves are 7, 3, 8, and 3.
For stem 3, the data contain two integers between 30 and 39 that, in the order of appearance, are 34 and 34. The leaves for the stem 3 are therefore formed by 4 and 4.
For stem 4, the data only contains the number 40, which falls within the range of 40 to 49. Consequently, 4 creates the leaf for stem 2.
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What is the name of subtraction facts that equal 10?
Back to Ten Facts -When subtracting two integers when the digit in the ones place is the same and the larger number has a 1 in the tens place, the result is 10 (for example, 15-5=10, 13-3=10, 12-2=10, etc.).
Subtraction:
Subtraction symbolizes the process of removing elements from a collection. The negative sign represents subtraction. If, for example, four of the nine oranges that are stacked together (as in the figure above) are then relocated to a basket, the stack will now only contain five oranges as opposed to nine. Thus, 5 is equal to 9 less 4 and is the difference between 9 and 4. In addition to natural numbers, other kinds of numbers can also be subtracted. The symbol for subtraction is the letter "-." The difference, the minuend, and the subtrahend are the three numerical components that make up the subtraction operation.
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ASAP
Determine the value for x in the equation x over 6 and 4 tenths equals 3 and 6 tenths.
23.04
19.2
10.0
2.8
The value of variable x is 19.20.
How to solve equations ?Let's find the value of variable x in the equation.
A variable is a number represented with letters in an equation.
Therefore,
x / 6 + 4 / 10 = 3 + 6 / 10
Therefore, let's find the variable x.
10x + 24 / 60 = 30 + 6 / 10
10x + 24 / 60 = 36 / 10
60 × 36 = 10(10x + 24)
2160 = 100x + 240
2160 - 240 = 100x
1920 = 100x
divide both sides by 100
x = 1920 / 100
x = 19.20
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The formula to calculate the gravitational force between two objects is F
GM1 M2
where M₁ and M2 are the masses of the objects, G is the gravitational constant and
r is the distance between the objects. Solve for M₂ in terms of Fg, G, M₁ and r.
Solving M2 in terms of Fg, G, M1 and r yields,
[tex]M2 = F {r}^{2} /GM1[/tex]
What does gravitational force between two objects mean?
An object with mass attracts another object with mass this attractive force that exists between all objects is known as gravitational force. It is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects.
Given,
The formula to calculate the gravitational force between two objects is F,
[tex]F=G M1 M2/ {r}^{2} [/tex]
where M₁ and M2 are the masses of the objects, G is the gravitational constant and
r is the distance between the objects.
Solving the equation for G2 we get,
[tex]F {r}^{2} =G M1 M2[/tex]
[tex]F {r}^{2}/G M1=M2[/tex]
[tex]M2 = F {r}^{2} /GM1[/tex]
This means, if there are two objects having mass M1 and M2 then M2 is directly proportional to the gravitational force between the two objects and the square of the distance between them, and it is indirectly proportional to M1.
Hence,
Solving M2 in terms of Fg, G, M1 and r yields,
[tex]M2 = F {r}^{2} /GM1[/tex]
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what is the center of a circle whose equation is x2 y2 12x 2y 12 0
The center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
What are circles?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
A circle is a closed shape that can be created by following a moving point in a plane while maintaining a constant distance from another point.
The Greek word kirks, which means hoop or ring, is whence the word circle gets its form.
So, we have the equation: x²+y²-12x-2y+12=0
Compared to the circle's basic equation:
2 + y² + 2gx + 2fy + c = 0
2g = -12, 2f = -2, c = 12
g = -6, f = -1
Centre = (-g, -f)= (6, 1)
Now, fill in the square:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1
(x - 6)² + (y - 1)² = 25
(x - 6)² + (y -1)² = 52
When compared to the equation for a circle with the centers at (h, k) and radius "r," Centre = (h, k) = (6,1).
Therefore, the center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
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Correct question:
What is the center of a circle whose equation is x²+y²-12x-2y+12=0?
Answer:
6,1
Step-by-step explanation:
trust me
7. Choose the graph below that best represents the equation: x-y = -2
Answer: B
Step-by-step explanation:
First, we will turn this equation into slope-intercept form as it is easier to view in terms of a graph.
Given:
x - y = 2
Add y and subtract 2 from both sides of the equation:
y = x - 2
We can see that this equation has a y-intercept of -2, so it must intercept the graph at (0, -2). The answer option that meets these requirements is B.
Answer: it is graph A
Step-by-step explanation:
It is pretty easy to tell when x-y= -2
Let's say x is 0 then we have left is -y=-2
So y= 2
And we have [0,2] so graph A is correct
Functions are in the world all around us. You have used functions to model phenomena and to make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or even with the same function. A composition of functions is useful when a change in one function will create a change in another function, which, in turn, affects a third function. For example, suppose that humans build a housing development on land that was previously used as a corn field. This change in land usage causes the number of birds in the area to decrease, which causes the number of mosquitos to increase. You could model the increase in the number of mosquitoes as a function of the number of birds in the area, which is a function of the number of humans that live on that land.
You can also use the composition of functions to show that one function is the inverse of another function. Recall that the graphs of inverse functions are reflections of each other over the line. Think about these ideas as you read through the scenario below.
Last night it started raining as Hiba was closing up the store where she works. By 3 am, the roof of the store developed a small hole and water began to leak onto the sales floor. The water created a circular puddle on the floor. At any time, t, in minutes, the radius of the puddle increases by 0.1 cm. The rain continued through the night, but stopped by the time the morning shift arrived at the store at 7 am.
When the employees arrived at work, the leak and water puddle were discovered. The employees cleaned up the water puddle and placed a tall circular bucket underneath the leak, which was still slowly dripping. The capacity of the bucket can be expressed as. By 10 am, the amount of water in the bucket is.
Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.
What is composition function ?The procedure known as "function composition" in mathematics takes two functions, f and g, and creates a function, h = g f, such that h(x) = g(f(x)). The combination of two functions to create a third function is known as function composition. Simply using the first function's output as the input for the second function is how it works.The function g is applied in this operation on the outcome of applying the function f to x. In other words, a function that maps x in domain X to g(f(x)) in codomain Z is produced by composing the functions f: X Y and g: Y Z. It makes sense that z would be a function of x if z were a function of y and y was a function of x. The resulting composite function is designated as (g f )(x) = g(f(x)) for all x in X, and is written as g f: X Z. [nb 1]Find the attachment of answer
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What is the solution to this system of linear equations 2x 3y 3?
The solution to this system of linear equations is x = 3 & y = -1.
Given linear equations are
2x + 3y = 3 ---- 1
7x - 3y = 24 ---- 2
By dividing both the equations, we get
9x = 27
x = 27/9
x = 3
Now substituting x = 3 in the equation 1, we get
2(3) + 3y = 3
6 + 3y = 3
3y = 3 - 6
y = -3/3
y = -1
Hence the answer is the solution to this system of linear equations is x = 3 & y = -1.
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What is linear inequality examples?
The linear inequality examples are as follows,
What is linear inequality?
Any two real numbers or two algebraic expressions associated with the symbol ‘<’, ‘>’, ‘≤’ or ‘≥’ form a linear inequality. For example, 9<11, 18>17 are examples of numerical inequalities and x+7>y, y<10-x, x ≥ y > 11 are examples of algebraic inequalities.
The examples of linear inequalities in two variables are:
3x < 2y + 5
8y – 9x > 10
9x ≥ 10/y
x + y ≤ 0
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Find the volume of a right cone that has height of 13.8m and a base with a circumference of 15.8m.
The volume of the cone is 91.05[tex]m^{3}[/tex]
What is a cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex. We can also define the cone as a pyramid which has a circular cross-section, unlike pyramid which has a triangular cross-section.
circumference of the base of a cone is same as circumference of a circle which is 2[tex]\pi[/tex]r
15.8 = 2[tex]\pi[/tex]r
make r subject of equation
r = [tex]\frac{15.8}{2\pi }[/tex]
r = 2.51m
Volume of a cone = 1/3 x [tex]\pi[/tex][tex]r^{2}h[/tex], but h =13.8m
volume = 1/3 x 3.142 x [tex](2.51)^{2}[/tex] x 13.8 which is 91.05[tex]m^{3}[/tex]
In conclusion the volume of the cone is 91.05[tex]m^{3}[/tex]
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What are the 2 characteristics of a regular polygon?
Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.
Given that,
We have to find what are the 2 characteristics of a regular polygon.
We know that,
What are the characters of a regular polygon?Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.
Regular triangles and quadrilaterals are given unique names, such as squares and equilateral triangles.
Therefore, Any polygon that is equilateral and equiangular is a regular polygon. In other words, the sides or edges and interior angles of a regular polygon are both congruent.
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What is a graph answer?
Answer:
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Hope this helps!
Rewrite as equivalent rational expressions with denominator (5u+5)(u−9)(u+5): 9/5u^2−40u−45,2u/5u^2+30u+25
The equivalent rational expression of the given expression, 9/5u² - 40u - 45, is 9/(5u + 5)(u - 9)
The equivalent rational expression of the given expression, 2u/5u² + 30u + 25 , is 2u/(5u + 5)(u + 5)
Writing equivalent expressionsFrom the question, we are to rewrite the given expressions as equivalent rational expressions.
The given expressions are:
9/5u² - 40u - 45 and 2u/5u² + 30u + 25
Writing an equivalent expression for 9/5u² - 40u - 45
Factorize the denominator
5u² - 40u - 45
5u² - 45u + 5u - 45
5u(u - 9) + 5(u - 9)
(5u + 5)(u - 9)
Thus,
The equivalent expression is 9/(5u + 5)(u - 9)
Writing an equivalent expression for 2u/5u² +30u + 25
Factorize the denominator
5u² +30u + 25
5u² +25u + 5u + 25
5u(u + 5) + 5(u + 5)
(5u + 5)(u + 5)
Thus,
The equivalent expression is 2u/(5u + 5)(u + 5)
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What are 5 types of inequalities?
The five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol ().
What are some examples of inequality?"A relation is called an inequality if two real numbers or algebraic expressions are related by the symbols ">," "," "," or ""." As an illustration, x>3 (x should be greater than 3) Open Sentence: If there is just one variable in the inequality, it is said to be an open sentence.In mathematics, an inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare two numbers on the number line based on their size. In mathematics, the five inequality symbols are greater than symbol (>), less than symbol (), greater than or equal to symbol (), less than or equal to symbol (), and not equal to symbol (). When solving an inequality, you can: • add the same amount to each side; • subtract the same amount from each side; and • multiply or divide each side by the same positive quantity. If you multiply or divide each side by a negative number, the inequality symbol must be reversed.To learn more about inequality refer to:
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How do you know △ ABC ≅ △ DEF explain?
We know that △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.
According to the question,
We have the following information:
△ ABC ≅ △ DEF
Now, we know that this sign is used to show that the two triangles are congruent.
Now, we also know that in these two triangles, their corresponding sides will be equal. So, all the three sides of one triangle will be corresponding to the same sides in another triangle.
Hence, we know that △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.
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Find the mean,median, and mode(s) of the distance in feet from home plate to the left-field fence at various ball park: 303,279,297,321,310,310,301.
The mean, median and mode of the distance from home plate to the left-field fence is 302.57 ft, 303 ft, 310 ftrespectively.
What is mean?Mean is the sum of all values divided by the total number of values
To calculate the mean of the data given, we use the formula below.
Formula:
Mean = ∑x/∑n......... Equation 1Where:
∑x = 303+276+297+321+310+310+301 = 2118∑n = 7Substitute these values into equation 1
Mean = 2118/7Mean = 302.57 ftAlso, to calculate the median of the distribution, we arrage the data into ascending or decending order.
Ascending order ⇒ 279, 297, 301, 303, 310, 310, 321
Then, the median is the middle term in the distribution
Median = 303 ft,Finally to get the mode, we look for the term in the distribution that has the higest frequency.
Mode = 310 ftHence, the mean, median and mode is 302.57ft, 303 ft, 310 ft respectively
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what is the measure of the base in the triangle below question 7 options 11 45 25 30
The measure of the base BC in the given triangle is (C) 25 units.
What is a triangle?A polygon with three edges and three vertices is called a triangle.
It is one of the fundamental geometric shapes.
The letter ABC stands for a triangle having the vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
If all of the geometry is in the Euclidean plane, then all triangles are encompassed in a single plane, however, in higher-dimensional Euclidean spaces, this is no longer the case.
This article concerns triangles in Euclidean geometry, specifically the Euclidean plane unless otherwise stated.
So, the given triangle is an isosceles triangle with AB = AC.
Then get the value of x as follows:
AB = AC
4x + 1 = 2x + 23
4x - 2x = 23 - 1
2x = 22
x = 22/2
x = 11
Now, substitute x = 11 in 3x - 8 that is BC.
3x - 8
3(11) - 8
33 - 8
25
Therefore, the measure of the base BC in the given triangle is (C) 25 units.
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Correct question:
What is the measure of the base in the triangle below?
a. 11
b. 45
c. 25
d. 30
What is a mixed fraction and how would you explain it?
Mixed Fractions A mixed fraction is a type of fraction in which there is a whole number part and a fractional part. For example, 31, 7, 3, 1, and 7 are all mixed fractions. It is also referred to as a mixed number.
Answer:
Fraction 7/2
Mixed fraction of the above 3 1/2
Step-by-step explanation:
a mixed number is a whole number and. Fraction for an answer
So 3 1/2 is a mixed number 7/2 is the fraction befor reduced to a mixed number
GREETINGS NEED HELP ASAP!
Think about wether the diagram shown represents a function. then use the drop down menus to complete the statement about the diagram.
This_____represent a function because the_____ has two different _____
choices for first blank- does or does not
choices for second- x value 7, 11, -5, 2
choices for third- x values or y values
It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.
Given that,
In the picture we have a diagram
We have to find if the diagram is a function or not.
We know that,
What is a function?Mathematical calculus' core component is functions. The unique types of relationships are the functions. When it comes to math, a function is represented as a rule that produces a different result for each input x.
Function is satisfy one-to-one and many-to-one.
So,
In the picture we can see
Input -2 to output 7 it is one-to-one
Input 7 to output 8 and 2 it is one-to-many
Input 11 and 2 1/3 to output 5 it is many-to-one
Therefore, It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.
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Find the equation of the line that satisfies the conditions given in each of the following: 1. Through (3, 2) and (5, 7) 2. Through (-3, 4), m = 2 3. m = -3, b = 5 4. x-intercept = 3, y-intercept
The equations of the line are listed according to slope and intercept below:
y = - (5 / 2) · x - 11 / 2 y = 2 · x + 10 y = - 3 · x + 5 y = 0How to derive the equation of line for each case
According to Euclidean geometry, a line can be constructed by knowing the location of two different points set on Cartesian plane. From analytical geometry we find that lines are represented by an equation of the form:
y = m · x + b
Where:
m - Slopex - Independent variable.y - Dependent variable.b - InterceptThe slope can be found by secant line formula:
m = Δy / Δx
Now we proceed to find the equation of the line for each case:
Case 1 - (x₁, y₁) = (3, 2), (x₂, y₂) = (5, 7)
m = (7 - 2) / (5 - 3)
m = 5 / 2
b = y - m · x
b = 2 - (5 / 2) · 3
b = 2 - 15 / 2
b = - 11 / 2
y = - (5 / 2) · x - 11 / 2
Case 2 - (x, y) = (- 3, 4), m = 2
b = y - m · x
b = 4 - 2 · (- 3)
b = 4 + 6
b = 10
y = 2 · x + 10
Case 3 - m = - 3, b = 5
y = - 3 · x + 5
Case 4 - x-intercept: 3, y-intercept: 0
m · 3 + b = 0
3 · m = - b
m · 0 + b = 0
b = 0
m = 0
y = 0
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s=ut+1 / 2 at²
u=10 a=-2 t=1/2
Work out the value of s.
The value of s in the formula
[tex]s = ut + \frac{1}{2}at^2[/tex] is [tex]\frac{19}{4}[/tex]
What is subject of a formula?
At first, it is important to know about formula
Formula is an equation which consists of variables and numbers and they are connected by mathematical operations.
In a formula, there are many variables present.
Subject of a formula is that variable which can be expressed in terms of other variables present in the formula.
Here, s is the subject of the formula
[tex]s = ut + \frac{1}{2}at^2[/tex]
u = 10, a = -2, t = [tex]\frac{1}{2}[/tex]
s = [tex]10 \times \frac{1}{2} + \frac{1}{2}\times (-2) \times (-\frac{1}{2})^2\\[/tex]
s = [tex]5 - \frac{1}{4}[/tex]
s = [tex]\frac{20 - 1}{4}\\[/tex]
s = [tex]\frac{19}{4}[/tex]
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Write the function for the graph of
g(x)
g(x)=[2x]
g(x)= [x]+2
g(x)= [x-2]
g(x)=[x]-2
The function of the graph is g(x) = [x]+2
What is linear function?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of terms
y = output variable
x = input variable
m = slope
c = y intercept
The c from the graph is +2
m for points (1, 3) and (-3, -1)
= (-1 - 3) / (-3 - 1)
= -4/-4
= 1
substituting to the equation y = mx + c
y = x + 2
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Evaluate 732,178 + 167 - 542,137 =
Answer: 190208
Step-by-step explanation:
Function and function notation
Please help asap
The value of function f(1/2) = 9.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between input variables in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x seems to be the input. A function is typically represented as y = f. (x). In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) as well as their outputs (also referred to as the codomain), where each input does have exactly one output and the output could be linked to its input.
Given function f(x) = (4+x)/x
put x = 1/2,
f(x) = (4+1/2)/1/2
f(x) = 9/2/1/2
f(1/2) = 9
Now f(3) = (4+3)/3
=7/3
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someone help me tysm
Answer:
6.3[tex]\pi[/tex]
Step-by-step explanation:
6.3[tex]\pi[/tex] is the exact answer.
C= circumference
d = diameter
C = [tex]\pi[/tex]d
C = 6.3[tex]\pi[/tex]
Pi is an irrational number. It never ends or terminates. We will often use 3.14 for an estimate of Pi, but you were asked for an exact answer.
In a clothing store, a shirt that sells for $15 is marked “10% off.” What is the discount? What is the sale price of the shirt?
Answer:
$13.50
Step-by-step explanation:
If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.
If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.
0.9*15 = 13.5
The sale price of the shirt is $13.50
(100)2 in decimal system is written as
The binary number (100[tex])_2[/tex] in decimal system is written as [tex]4_{10}[/tex].
Given:
Binary number = [tex](100)_2[/tex]
Converting Binary to decimal system:
Binary:
In computer applications, where binary numbers are represented by only two symbols or digits, i.e. 0 (zero) and 1(one).
Decimal:
Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.
[tex]100_2 = 1*2^2 + 0*2^1+0*2^0[/tex]
we know that,
[tex]2^0 = 1[/tex]
[tex]2^1 = 2\\2^2 =4[/tex]
substitute these values
[tex]100_2 = 1*4 + 0*2 + 0*1[/tex]
= 4 + 0 + 0
= 4 + 0
= [tex]4_{10}[/tex]
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A Fibonacci-type sequence that has been studied by mathematicians is the Lucas sequence, named after a French mathematician of the nineteenth century. The first ten terms of the Lucas sequence are 1, 3,
4,7, 11, 18, 29, 47, 76,123 what
is the
term of the Lucas
The eleventh term of the Lucas sequence is?
The eleventh term of the Lucas' sequence is 199
How to determine the eleventh term of the sequence?From the question, we have the following parameters that can be used in our computation:
1, 3, 4,7, 11, 18, 29, 47, 76,123
As a general rule of Fibonacci, the current term of a sequence is the sum of the two previous terms
This means that
11th term = 10th term + 9th term
Substitute the known values in the above equation, so, we have the following representation
11th term = 123 + 76
Evaluate the sum
11th term = 199
Hence, the 11th term is 199
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A box is ( 2x-3 ) by ( x+5 )by (3x+1) what is the volume of the box if x=3cm
Answer:
240 cm³
Step-by-step explanation:
Volume = [ 2(3) - 3]( 3 + 5)[ 3(3) + 1 ]
Volume = ( 6 - 3 )( 8 )( 9 + 1)
Volume = ( 3 )( 8 )( 10 )
Volume = 24(10)
Volume = 240 cm³
For each function, select whether it’s inverse is a function or not a function. refer to the attached picture.
Function
y=x⁴
y=x⁹
y=x⁸
y=x¹¹
The inverses of the functions y= x⁹ and y= x¹¹ are functions.
The inverses of the functions y = x⁴ and y= x⁸ are not functions.
How is the functionality of the given functions determined?(a )Consider ,the inverse of the function is a function
(2 ) y= x⁹
The inverse of the function is given by,
x = [tex]\sqrt[9]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
So, this is a function.
(4) y= x¹¹
The inverse of the function is given by,
x = [tex]\sqrt[11]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
Similarly , this is a function.
(b ) Consider ,the inverse of the function is a not a function
(1 )y = x⁴
The inverse of the function is given by,
x = [tex]\sqrt[4]{y}[/tex] (y ≥0)
It is of one- one correspondence,
when y = 4 ,
x = ±√2
Thus, it is not a function.
(3) y= x⁸
The inverse of the function is given by,
x = [tex]\sqrt[8]{y}[/tex]
Likewise , this is not a function.
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