Answer:
f⁻¹(x) = 3/2x +9
Step-by-step explanation:
You want the inverse of the function f(x) = 2/3x -6.
Inverse functionThe inverse function can be found by solving for y:
x = f(y)
Here, that is ...
x = 2/3y -6
x +6 = 2/3y . . . . . . . . . . . . . . add 6
y = 3/2(x +6) = 3/2x +9 . . . . multiply by 3/2
The inverse function is f⁻¹(x) = 3/2x +9.
__
Additional comment
Sometimes the division symbol ÷ is used to mean "divided by everything after this symbol." If that is the intended meaning, the function should be written as f(x) = 2/(3x -6) or f(x) = 2÷(3x -6).
We have interpreted the symbol according to the order of operations, which tells us that 2÷3x-6 means ((2÷3)·x)-6.
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Kendra and Haley are each saving money. Kendra starts with $100 in his savings
account and adds $5 per week. Haley starts with $10 in her savings account and adds
$20 each week. After how many weeks will Haley have at least the same amount of
money as Kendra?
OX26
Ox>6
O x 216
Ox< 16
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
Kendra and Haley are each saving money. Kendra starts with $100 in his savings account and adds $5 per week. Haley starts with $10 in her savings account and adds $20 each week. After how many weeks will Haley have at least the same amount of money as Kendra?
Kendra and Haley are each saving money.
Kendra starts with $100 in his savings
account and adds $5 per week.
After 6 week 6* 5 = 30
Total amount in After 6 week in Kendra savings
account = $100 + $30
= $130
Haley starts with $10 in her savings account and
adds $20 each week.
After 6 week 6* 20 =120
Total amount in After 6 week in Haley savings
account = $10 + $120
= $130
That means after 6 weeks will Haley have at least the same amount of
money as Kendra
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f(x)=(x^2-x)/(x+1)
pls show work
Answer:
x - 2 + 2/(x + 1)
Step-by-step explanation:
These are really hard to type out and get the spacing right, so see the attached printout from a website that does carefully show steps in a polynomial division problem.
The website is:
https://www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=x%5E2-x&denom=x%2B1
Shauna says that 2x2 + x - 12 is the same as (x+4)(x-3). Is
she correct? Are the two expressions equal? Explain your
answer.
Answer:
Shauna is incorrect, because (x + 4)(x - 3) is NOT equivalent to 2x² + x - 12
Step-by-step explanation:
Check if she is correct by expanding (x + 4)(x - 3), with FOIL:
(x + 4)(x - 3)
x² - 3x + 4x - 12
x² + x - 12
So, Shauna is incorrect, because the two expressions are not equal.
(x + 4)(x - 3) is equivalent to x² + x - 12, NOT 2x² + x - 12.
Answer:
No she's wrongTwo equations are unequal.Explained belowStep-by-step explanation:
[tex] \sf \rightarrowtail \: (x + 4)(x - 3) \\ \sf \rightarrowtail \: x(x - 3) + 4(x - 3) \\ \sf \rightarrowtail \: {x}^{2} - 3x + 4x - 12 \\ \sf \rightarrowtail \: {x}^{2} + x - 12 \cancel{ = } {2x}^{2} + x - 12[/tex]
The temperature is -3 degrees celcius and 6:00 and rises 12 degress celcius by midday what is the temperature at midday
Answer:
9°C
Step-by-step explanation:
Given that :
Temperature at 6:00 = - 3°C
The change in temperature by midday = temperature rise of 12°C
The temperature at midday is :
Temperature at 6:00 + change in temperature
-3°C + 12°C
= 9°C
A cylinder has a height of 14 millimeters. Its volume is 17,584 cubic millimeters. What is the radius of the cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
help me
Answer:
V = πr2h (Volume of a cylinder is the area of a circle times its height). V = 8167.14. π = 3.14. h = 9.
Step-by-step explanation:
Kias mom is having triplets. Each baby could either be male or female. Which outcome would be included in the compound event "more than one female"
Answer:
The outcomes that have more than 1 female are -
MFF, FMF, FFM, FFF
Step-by-step explanation:
Given - Kias mom is having triplets. Each baby could either be male or female.
To find - Which outcome would be included in the compound event "more than one female"
Solution -
The sample space outcomes are -
{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF}
Now,
The outcomes that have more than 1 female are -
MFF, FMF, FFM, FFF
Which set only contains numbers that make the inequality true?
x + 19 < 28
A. {3, 4, 5, 6}
B. {7, 8, 9, 10}
C. {10, 11, 12, 13}
D. {12, 13, 14, 15}
Answer:
A
Step-by-step explanation:
3 + 19 = 22
4 + 19 = 23
5 + 19 = 24
6 + 19 = 25
All sums are less than 28
Answer:
A)
Step-by-step explanation:
x < 9
all numbers less than 9 make the inequality true
Given the function f(x) = | -2x + 4 |. Complete the table.
x f(x)
6 Blank 1
-1 Blank 2
Blank 3
4
Blank 4
14
The table representing the given absolute function should be completed as follows;
x f(x)
6 8
-1 6
4 4
9 14
How to complete the table of this absolute function?Based on the information provided, we have the following absolute function:
f(x) = |-2x + 4|
When x = 6, the value of the absolute function is given by;
f(6) = |-2(6) + 4|
f(6) = |-12 + 4|
f(6) = |-8|
f(6) = 8
When x = -1, the value of the absolute function is given by;
f(-1) = |-2(-1) + 4|
f(-1) = |2 + 4|
f(-1) = |6|
f(-1) = -6.
When the value of the absolute function y = 4 is given by;
4 = |-2x + 4|
±4 = -2x + 4
2x = 4 ± 4
2x = 8
x = 4 or 0.
When the value of the absolute function y = 14 is given by;
14 = |-2x + 4|
±14 = -2x + 4
2x = 4 ± 14
2x = 18
x = 9 or 5.
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A certain map shows two roads. Road A is 1 1/5 miles long but is 1 4/5 inches on the map. What is the unit rate for inches per mile on the map. If road B is 2 miles long, how long is road B on the map ?
The length of the map would be 3 inches.
What is the unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units.
Given here: length of the road as 6/5 miles and on the map 9/5 inches and thus 1 mile = 1.5 inches and therefore the length of the 2 mile road on the map is 2×1.5=3 inches
Hence, The length of the map would be 3 inches.
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if the perimeter of the rectangle was known to be 90 in what would the value of x be in order for this to be true
Answer:
x = 30 in
Step-by-step explanation:
length of rectangle is (2/3)x + 10; width is (1/3)x + 5;
perimeter is 90 in; find x:
P = 90 in = 2(2/3)x + 2(10) + 2(1/3)x + 2(5), or
90 in = (6/3)x + 30 in
Solving for x, we get (2)x = 60 in, or x = 30 in
Davis earns a 4% commission for all furniture he sells. If David receives $7509 in commission this year , what is the dollar amount of his sales?
Answer:
187,725
Step-by-step explanation:
7,509/.04=187,725
A 2.2 GB game is being downloaded onto your laptop. when you have downloaded half a gigabyte you notice that your computer has been downloading at a rate of .01GB/min.
Answer:
it takes 110 minutes
Step-by-step explanation:
Answer:
it takes approximately 110 minutes
please help thxssssssssssssssssssssssssssss
Answer:
The visiting team took more shots than the home team.
Step-by-step explanation:
Solve this system of equation by elimination. 2x-5y=8 3x+5y=-13
Answer:
x=-1, y=-2. (-1, -2).
Step-by-step explanation:
2x-5y=8
3x+5y=-13
----------------
5x=-5
x=-5/5
x=-1
2(-1)-5y=8
-2-5y=8
5y=-2-8
5y=-10
y=-10/5
y=-2
On a soccer team, 40% of the goals are
scored by the star player on the team. If 70 goals
are scored all season, then how many are scored
by the rest of the team?
[tex]40 \div 100 \times 70 \\ 4 \times 7 = 28 \\ 70 - 28 = 42[/tex]
Step-by-step explanation:
First find 40% of 70, which is 28
Then subtract the 28 from 70 to find the goals scored by the rest of the team
How do you simplify 3 Way ratios?
To simplify 3 ratios, divide each part of the ratio with the same amount and keep diving numbers in the ratio until they are as small as possible but they remain as whole numbers.
To simplify or reduce a fraction, first, we need to find a common factor between the ratio numbers. When we have multiple ratio numbers, we must find a common factor between all of them.
The greatest factor between all the ratio numbers (greatest common factor) will be utilised to divide or reduce the ratios down to their lowest form.
For example reduce the ratio 225: 125: 25
The first step is to determine a common factor between all of the ratio numbers. In this example, we can see that all of the numbers end in either 5 or 0. This means that each number should have 5 as a factor.
If numbers are large and we are not sure of the greatest common factor between them all, we can reduce by a common factor and then reduce again.
Now divide each number by 5 and see what we get.
225/5: 125/5: 25/5
45: 25: 5
When we divide each one by 5 again, we can see that each number again ends in 5 or 0 which means that 5 is still a factor of each number.
Now divide each number by 5 again and get a final ratio of 9: 5: 5.
45/5: 25/5: 5/5
9: 5: 1
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2. Gravetter/Wallnau/Forzano, Essentials - Chapter 4 - End-of-chapter question 2
What is the range for the following set of scores? (You may have more than one answer. )
6, 12, 9, 17, 11, 4, 14
The range for the following set of scores: 6, 12, 9, 17, 11, 4, and 14 is 13.
In statistics, the range is a measure of dispersion that describes the difference between the largest and smallest values in a dataset. The range is used to describe the spread of a dataset and can be a simple way to identify outliers or unusually large or small values. It is a simple measure of statistical dispersion and is most useful for interval and ratio data.
It is calculated by subtracting the minimum value from the maximum value among the data set.
range = maximum value - minimum value
Plug in the necessary values and solve for the range.
range = 17 - 4
range = 13
Therefore, the range for the following set of scores is 13.
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if a:b is 2:5 and b:c is 3:4, find a:b:c
Answer:
just keep in mind am not sure if the answer 6:15:20
Step-by-step explanation:
now we have ab= 2 : 5
and bc= 3 : 4
so b is the common one between them so multiply both of the b together which will give u 15 so now we have b = 15
to get a multiply 2 by 3 to get 6 so a = 6
to get c multiply 4 by 5 to get 20 so c = 20
now I hope that its correct and that u understood
What does the expression 5n represents The quotient of 5n and a number The product of 5and a number The sum of 5 and a number The difference of 5 and a number
Answer: The product of 5 and a number
Step-by-step explanation:
The expression 5n represents the product of 5 and a number. For example, let the number be 8. Therefore, the value of the expression will be:
= 5n
= 5 × 8
= 40
The sum of 5 and a number will be:
= 5 + n
The difference of 5 and a number will be:
= 5 - n
Task #2: Jack makes $32 when he sells 4 pumpkins. How many pumpkins will he have to sell to make $48? If Jack finds that he has $120 at the end of the day, how many pumpkins did he sell?
Answer:
1. 6
2. 15
Step-by-step explanation:
4 pumpkins: $32
=> 1 pumpkin = 32 : 4 = $8
- He will have to sell 48 : 8 = 6 pumpkins to make $48
- He sold: 120 : 8 = 15 pumpkins that day
What are my financial goals? What major purchases should I save for?
It depends on your personal financial situation and goals. Generally, it is important to save for major purchases such as a house, car, and vacations, as well as setting aside money for retirement. Additionally, you may want to consider investing in stocks, bonds, or mutual funds to achieve your long-term financial goals.
Find the volume of the cone. Round your answer to the nearest tenth.
Answer: 56.6
Step-by-step explanation:
You find the volume by V=1/3hπr² , it becomes 56.55 . you round that to the nearest ten then it leads you to 56.6
A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs. Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages
The proportion and percentage is as follows;
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
What is the difference between proportions and percentages?A percentage represents a ratio or fraction with a denominator that is always 100 as opposed to a proportion, which asserts the equivalent of two ratios or fractions.
Given
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & & \\ 5-6 & 50 & & \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
To estimate the total frequency:
Total = sum f
Total = 29 + 53 + 50 + 22 + 1
Total = 155
The proportion (p) exists calculated by:
[tex]$p = \frac{f}{\text { Total }}[/tex]
The percentage (P) exists calculated by:
P = p × 100 %
For interval 7 - 8, we have:
p = 53 / 155 = 0.34
P = 0.34 × 100 % = 34 %
For interval 5 - 6, we have:
p = 50 / 155 = 0.32
P = 0.32 × 100 % = 32 %
So, the complete table is:
[tex]$\begin{array}{cccc}\text { Score Interval } & f & \text { Proportion } & \text { Percentage } \\ 9-10 & 29 & 0.19 & 19 \% \\ 7-8 & 53 & 0.34 & 34 \% \\ 5-6 & 50 & 0.32 & 32 \% \\ 3-4 & 22 & 0.14 & 14 \% \\ 1-2 & 1 & 0.01 & 1 \%\end{array}$[/tex]
The complete question is:
A statistics content developer at Aplia wanted to know whether study skills are related to memory quality. She invited student volunteers to perform an online memory task. The students saw a list of 60 words and were then asked to recognize a list of five brand new words that are related to words that were on the original list. Students were also asked to provide their GPAs.
Consider the following data set, which was collected from student volunteers in 2009. The table gives the frequency for the number of incorrectly identified related words. Use the dropdown menus to complete the table by filling in the missing values for the proportions and percentages.
Score Interval f Proportion Percentage
9â10 29 0.19 19%
7â8 53
5â6 50
3â4 22 0.14 14%
1â2 1 0.01 1%
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Explain how the Quotient of Powers property was used to simplify this expression. 2 to the fifth power, over 8 = 22
The Quotient of Powers was used to simplify this expression is By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents
We have given that,
2 to the fifth power, over 8 = 22
What is the simplified form of expression?The simplification calculator allows you to take a simple or complex expression and simplify and reduce the expression to it's simplest form or to rewriting the same algebraic expression with no like terms and in a compact manner.
By simplifying 8 to 2^3 to make both powers base two and subtracting the exponents.
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Edwin got 95% of the questions right on a quiz. If there were 20 questions on the quiz, how many questions did he miss??
Answer:
He got a 19 out of 20, great job Edwin ;)
Step-by-step explanation:
Hope this helps :)
Edwin missed 1 question on the quiz.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
If Edwin got 95% of the questions right on a quiz and there were 20 questions in total, we can calculate the number of questions he missed by finding 5% of the total number of questions.
First, let's find 5% of 20:
= 5% of 20
= (5/100) x 20
= 1 x 20 / 100
= 20 / 100
= 0.2
Since we can't have a fraction of a question, we round the decimal up to the nearest whole number.
In this case, 0.2 rounds up to 1.
Therefore, Edwin missed 1 question on the quiz.
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What is the length of the missing leg (in meters)
Answer:
12 meters
Step-by-step explanation:
hdhwhehhehhdhshheheheheueueje
What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?
The equation can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6) \ and\ x=2[/tex]
What is logarithm?A logarithm is a mathematical function that describes the relationship between a number and its exponent. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.
The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.
For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].
The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].
To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:
[tex]log(6^x) = log(6^2)[/tex]
And we can simplify the equation as:
[tex]xlog(6) = 2log(6)[/tex]
So, the value of a is log(6) and the value of x is 2.
Therefore, the equation can be rewritten as:
[tex]ax^4 = (log(6))(2^4)[/tex]
Therefore, [tex]a = log(6)\ and\ x=2[/tex]
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3.5 x 4 + 11 x 2.2 = 38.2 i used a calculator already but i need to show i how got the answer i dont know if i can give the brain thing
Step-by-step explanation: To solve this equation, you'll need to use the order of operations to determine the correct sequence of steps to follow. The order of operations is a set of rules that specifies the order in which calculations should be performed in a math problem. It helps to prevent ambiguity and ensures that all calculations are performed consistently.Here is the order of operations:Perform any calculations inside parentheses or brackets first.Perform all multiplications and divisions, working from left to right.Perform all additions and subtractions, working from left to right.Using this order, we can solve the equation as follows:3.5 x 4 + 11 x 2.2 = 14 + 11 x 2.2
3.5 x 4 + 11 x 2.2 = 14 + 24.2
3.5 x 4 + 11 x 2.2 = 38.2Therefore, the solution to the equation is 38.2.
Using BODMAS,
B-Bracket
O-Of
D-Division
M-Multiplication
A-Addition
S-Subtraction
Multiplication comes first before addition, so
3.5×4=17
+
11×2.2=24.2
17+24.2=41.2
find the zeros of -16x^2 +24+16 and show your work
Step-by-step explanation:
This both answer can be
Draw a tape diagram to represent the following
equation:
3x + 15 = 90
Answer:
25
Step-by-step explanation:
Subtract 15 from both sides then divide by 3.
Answer:
3x + 15 = 90
3x = 90 - 15
3x = 75
x = 25