The inverse function is [tex]\( f^{-1}(x) = \frac{x + 7}{4} \)[/tex].
To find the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex], we follow these steps:
1. Replace [tex]\( f(x) \) with \( y \): \( y = 4x - 7 \)[/tex].
2. Swap[tex]\( x \) and \( y \): \( x = 4y - 7 \)[/tex].
3. Solve this equation for [tex]\( y \)[/tex].
So, let's solve for [tex]\( y \)[/tex]:
[tex]\[ x = 4y - 7 \][/tex]
Add 7 to both sides:
[tex]\[ x + 7 = 4y \][/tex]
Divide both sides by 4:
[tex]\[ \frac{x + 7}{4} = y \][/tex]
Thus, the inverse function of [tex]\( f(x) = 4x - 7 \)[/tex] is:
[tex]\[ f^{-1}(x) = \frac{x + 7}{4} \][/tex]
The function p(x)=8x-10 shows the profit, in dollars, for selling x books.
p(10) is the profit, in dollars, from selling 10 books. Replace every copy of x with 10 and simplify
p(x) = 8x-10
p(10) = 8*10-10 .... every x is replaced with 10
p(10) = 80-10
p(10) = 70
So the profit is $70
For the function p(x) = 8x - 10, the profit for selling 20 books is $150.
Explanation:
In the problem, the function p(x) = 8x - 10 represents the profit, in dollars, for selling 'x' books. When it's stated that p(20) = 150, it means that by substituting the value of 'x' as 20 in the function, we get the value as 150. In terms of the problem, it means that the profit for selling 20 books is $150.
Let's break down the problem step by step.
1. You're given the function p(x) = 8x - 10, which represents the profit, in dollars, for selling x books. In this equation, p(x) is the profit, and \(x\) is the number of books sold.
2. You're asked to evaluate the function at x = 20, which means you want to find p(20). To do this, substitute x = 20 into the function and calculate the result.
p(20) = 8(20) - 10
3. Perform the calculation:
p(20) = 160 - 10
4. Complete the subtraction:
p(20) = 150
So, p(20) = 150, which means that the profit for selling 20 books is $150. This is the interpretation of the statement "p(20) = 150" in terms of the problem.
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The probable question can be: The function p(x) = 8x - 10 shows the profit, in dollars, for selling x books.
p(10) = 70
p(20) = 150
What does p(20) = 150 mean in terms of the problem?
It costs $150 to make 20 books.
It costs $20 to make 150 books.
The profit for selling 150 books is $20.
The profit for selling 20 books is $150.
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A polygon has an interior sum of 3060 degrees how many sides must the polygon have?
whats the equivalent of this equation? help please
[tex]9^{\frac{1}{8} }[/tex]x
note that [tex]\sqrt[4]{9}[/tex] = [tex]9^{\frac{1}{4} }[/tex]
and all raised to the power [tex]\frac{1}{2}[/tex] x
multiply [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{2}[/tex] x = [tex]\frac{1}{8}[/tex] x
-12-a=6y+12
solve the equation
Answer:
a = -1Step-by-step explanation:
[tex]-12-a=4a-7\qquad|\text{add 12 to both sides}\\\\-a=4a+5\qquad|\text{subtract 4a from both sides}\\\\-5a=5\qquad|\text{divide both sides by -5}\\\\\boxed{a=-1}[/tex]
help now I don't know !!!
Additive inverse: the additive inverse of a number a is the number that when added to a yields zero.It's also known as the opposite sign change and negation. For a real number it reverses its sign: the opposite to a positive number is negative and the opposite to a negative number is positive
Integer:Any number that is positive negative or nuetral, intergers cannot have decimals or fractions
Negative number: A number that is below zero. For example, -1 or -2 2/3
Positive number: A number that is above 0. For example, 1 or 2 2/3. You can also write a positive number with a + sign infront of it. For example, +1 or +2
good luck
Susanna spends a total 0f 47 minutes on her project. How many more minutes than Susanna does Abby spend working? Draw a number line to model the problem, and write an equation to solve.
a - 47 = more time spent
In this mathematical problem, Abby's time is represented as x and the difference in time between Abby's and Susanna's work can be modeled by the equation x-47=y, where y is the extra time Abby spends. A number line can be used to visualize this problem, but without knowing Abby's time, we cannot determine y.
Explanation:The subject of this problem is mathematics and it discusses time spent by two individuals on their project. We know that Susanna spends 47 minutes on her project. However, we do not know how much time Abby spends on her project. We could represent the time Abby spends on her project as x.
To visualize the situation, we can draw a number line. Place a point at 47 which represents Susanna's time. Then place another point at x which represents Abby's time.
The difference in time between Susanna and Abby can be represented by the equation x - 47 = y, where y is the number of extra minutes Abby spends working on her project.
Without any additional information on how much time Abby spent on her work, it's impossible to give a specific answer.
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Evaluate the expression for the given values of the variables.
4a+7b+3a-2b+2a ;
a=-5 & b=3
a) 17
b) -5
c) -20
d) -30
The answer is D or -30
The value of the expression for the given values of the variables is -30.
The given expression is 4a+7b+3a-2b+2a, the values of the variables a=-5 and b=3.
We need to evaluate the expression for the given values of the variables.
How to find the value of the expression?To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number. To evaluate an expression, we substitute the given number for the variable in the expression and then simplify the expression using the order of operations.
Now, put a=-5 and b=3 in the given expression and simplify.
That is, 4a+7b+3a-2b+2a=4(-5)+7(3)+3(-5)-2(3)+2(-5)
=-20+21-15-6-10
=-30
Therefore, the value of the expression for the given values of the variables is -30.
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What is the complement of a single die being rolled to a number greater than 2
a single die being rolled to a number less or equal to 2
Final answer:
The complement of rolling a number greater than 2 on a single six-sided die is rolling a 2 or less, which has a probability of 1/3.
Explanation:
In the context of a single six-sided die roll, the complement of rolling a number greater than 2 would be rolling a number that is 2 or less, which in this case includes rolling a 1 or a 2. Each face of a fair six-sided die has an equal chance of landing face up, giving us a probability of 1/6 for landing on a specific number. Since there are two outcomes that are 2 or less (1 and 2), we simply add their probabilities to get the complement. Thus, the complement of rolling a number greater than 2 is:
P(rolling a 1 or 2) = P(rolling a 1) + P(rolling a 2)
= 1/6 + 1/6
= 1/3.
Therefore, there is a 1/3 chance of rolling a number that is 2 or less when rolling a single fair six-sided die.
I need help with these last two please?
is feet a type of surface area
It would have to be feet squared, it couldn't just be feet.
please answer quickly thanks :) good morning btw
1. 1/9
2. 0
3. -9
4. -1
Reasoning: To get the opposite of a number just add a negative sign or take it away. This can be done to all numbers other than 0
Let p: x < −3 Let q: x > 3 What is represented by p ∨ q? x < −3 and x > 3 x > 3 or x < −3 If x < −3, then x > 3 x < −3 if and only if x > 3
[tex]\vee=or\\\\therefore\\\\p:x < -3\ ; q:x > 3\\\\p\vee q\to x < -3\ or\ x > 3[/tex]
[tex]\wedge=and\\\\\Rightarrow=if\ ...,\ then\ ...\\\\\Leftrightarrow=if\ and\ only\ if[/tex]
Answer:
the one with or just got it right
Step-by-step explanation:
Witch expression is equivalent to g-^m ➗ g^n?
A. g-^m + ^n
B. g-^m • n
C. g-^m -^n
D.g-^m ➗ ^n
Answer,
C.g-^m -^n
Hope this helps :-)
A landscaper has 34 ton of mulch. She puts 116 ton of mulch on each flower bed.
How many flower beds does she put mulch on?
Enter your answer in the box.
The Answer Is 12
yes the answer is 12
hope it helps
What is 2 1/6 - 3 4/9?
Ella owns 15% of Fitz Incorporated. The rest of the shares are owned equally by the remaining 5 shareholders. What percent of the corporation does each of the other shareholders own?
Answer:
17%
Step-by-step explanation:
The total corporation shares is 100%If Ella owns 15% of Fitz,the remaining shares is 100-15=85%If there are 5 shareholders and they all own equal shares,the percentage for each shareholder will be;85/5=17% eachFinal answer:
Ella owns 15% of Fitz Incorporated, and the remaining 85% is shared equally among 5 other shareholders. Thus, each of these shareholders owns an equal share of 17% of the corporation.
Explanation:
The question asks about corporate stock and how it relates to the percentage of ownership in a corporation. Ella owns 15% of Fitz Incorporated, and the remaining 85% is owned equally by 5 other shareholders. To find the percentage each of these shareholders owns, we divide the remaining percentage by the number of shareholders.
The calculation would be:
Subtract the percentage owned by Ella from the total, which is 100% - 15% = 85%.
Divide this remaining percentage (85%) by the number of other shareholders, which is 5.
85% / 5 = 17% ownership for each of the other shareholders.
So, each of the remaining 5 shareholders owns 17% of the corporation.
Kenya solved the equation below. -6
(x-2)+3x=-3(x+3)+21 What is the solution to Kenya’s equation? –4 12 no solution infinitely many solutions
Answer:
Kenya’s equation has infinitely many solutions
Step-by-step explanation:
we have
[tex]-6(x-2)+3x=-3(x+3)+21[/tex]
Solve for x
Eliminate the parenthesis
[tex]-6x+12+3x=-3x-9+21[/tex]
Group terms that contain the same variable
[tex]-6x+3x+3x=-9+21-12[/tex]
Combine like terms
[tex]0=0[/tex] ---> is true for any value of x
therefore
Kenya’s equation has infinitely many solutions
Answer:
D
Step-by-step explanation:
A student notices in the table below that as the x-value increases by 5, the y-value decreases by 2. Because there is a pattern, the student has determined that, x is proportional to y.
Do you agree with the student’s claim? Why or why not?
___________
X
5x1=5
5x2=10
5x3=15
5x4=20
5x5=25
Y
20-2=18
18-2=16
16-2=14
14-2=12
X Is by 5 and Y is subtracting by 2
Perform the indicated operation.
x3 • x2
I believe it would be x5 considering you must add exponents when you multiply.
Answer:
[tex]x^3\cdot x^2=x^5[/tex]
Step-by-step explanation:
The rule to multiply two powers with the same base consists in adding the exponents. The general form would be:
[tex]x^a\cdot x^b=x^{a+b}[/tex]
For verifying the previous rule, let's say that x=2, a=2 and b=3. The equation would be:
[tex]2^2\cdot 2^3=2^{5}[/tex]
[tex](4)\cdot (8)=2^{5}[/tex]
[tex]32=32[/tex]
We have obtained the result multiplying individually and applying the rule.
Now, for the [tex]x^3\cdot x^2[/tex] exercise, the result would be obtained by adding 3 and 2. It would be:
[tex]x^3\cdot x^2=x^{3+2}=x^5[/tex]
The solution is [tex]x^5[/tex]
a jar contains 2 red and 4 blue marbles. a marble is drawn from the jar. what is the probability that a red marble will be drawn?
2 red / 4 blu
just semplify
1 red / 2 blu
so the probability is
1/2
Answer:
The answer is 50% Hope this helps!
Can someone plz help me find the GCF if number 9 plz
Two enterprising college students decide to start a business. They will make up and deliver helium balloon bouquets for special occasions. It will cost them $39.99 to buy a machine to fill the balloons with helium. They estimate that it will cost them $2.00 to buy the balloons, helium and ribbons needed to make each balloon bouquet. Which of the following expressions could be used to model the total cost for producing b balloon bouquets?
$2.00b + $39.99$37.99b$39.99b + $2.00$41.99bSave
Answer:
Option A.
Step-by-step explanation:
Machine to fill the balloons with helium will cost = $39.99
Cost of the balloons, helium and ribbons for each bouquet = $2.00
If b balloon bouquets are produced then cost of b balloon bouquets = $2b
Total cost for producing b balloon bouquets = cost of machine + cost of material
= $(39.99 + 2b)
Therefore, cost to produce b bouquets will be $2.00b + $39.99
Hence option A is the answer.
I need help remembering the steps to 56=
2(x+2)
The slope of a line is 0. What do you know about the line?
Your answer (C, the line is vertical) is correct
Your line would have to be horizontal. A vertical line yields an undefined slope.
Slope is rise over run. For a horizontal line you would have 0 rise and X amount of run or 0/x. 0 divided by anything = 0
For a vertical line, you would have the opposite, X rise and 0 run or x/0. You cannot divide by 0. It is impossible.
Therefore, your answer is the second option.
what is Fraction equation that equals 10
Hey there,
Here is your answer:
10/1 = 10
I don’t understand this. In class we have been doing these problems with only one transversal, not two.
Answer: Yes it is possible. Angle DCF is also 50 degrees
=================================================
Check out the image attachment below. On that image, I've marked that angle EBA is congruent to angle BAC by the alternate interior angle theorem. Those angles are shown in red. Furthermore, angle BAC is congruent to DCF (corresponding angles) using a green marker. Finally, using the transitive theorem, you can connect the statements in a chain to say that angle EBA is congruent to angle DCF, which is why angle DCF is 50 degrees as well.
Which of these is not an integer?
6/3
3/6
6/2
Answer:
3/6is not a integer.
Step-by-step explanation:
6/3 integer
6/2 integer
3/6 not a integer
Final answer:
The fraction 3/6 is not an integer because it equals 0.5, which is a fraction and not a whole number.
Explanation:
To determine which of these values is not an integer, we need to perform the division for each fraction:
6/3 = 2, which is an integer3/6 = 0.5, which is not an integer; it is a fraction6/2 = 3, which is an integerTherefore, 3/6 is not an integer because when you divide 3 by 6, you get a fractional number rather than a whole number.
2c - 5 < -21 - 2c pls
2c - 5 < -21 - 2c |add 5 to both sides
2c < -16 - 2c |add 2c to both sides
4c < -16 |divide both sides by 4
c < -4
Edison has a sales job and receives $45,448 as his annual pay plus commission his company pays him commission of 15% on this total sales if he makes sales of $25000 in the first 3 months how much will he be paid for those 3 months
Answer:
Edison will be paid $15,112 for the first three months.
Step-by-step explanation:
We know that Edison receives an annual fixed pay of $45,448. Therefore, his fixed pay for each month will be [tex]\frac{45448}{12}=\$3787.33[/tex]
Therefore, his fixed pay for the 3 months will be [tex]3787.33*3=\$11362[/tex].
Now let us compute the commission that Edison received. For that we will compute the 15% of the total sales for those 3 months. Total sales for the 3 months is $25000. Therefore, his commission would be [tex]0.15*25000=\$3750[/tex]
Therefore, total pay that Edison received during first 3 months would be:
[tex]11362+3750=\$15,112[/tex]
Edison will be paid $48,862 for the first 3 months.
To calculate Edison's total payment for the first 3 months, we need to consider both his annual pay and the commission he earns from his sales.
First, let's calculate the commission Edison earns from his sales. He makes sales of $250,000 in the first 3 months, and the commission rate is 15% of the total sales. The commission can be calculated as:
[tex]\[ \text{Commission} = \text{Total Sales} \times \text{Commission Rate} \] \[ \text{Commission} = \$250,000 \times 0.15 \] \[ \text{Commission} = \$37,500 \][/tex]
Next, we need to calculate Edison's base salary for 3 months. Since his annual pay is $45,448, we divide this by 4 to get the quarterly pay (as there are 4 quarters in a year):
[tex]\[ \text{Quarterly Pay} = \frac{\text{Annual Pay}}{4} \] \[ \text{Quarterly Pay} = \frac{\$45,448}{4} \] \[ \text{Quarterly Pay} = \$11,362 \][/tex]
Now, we add the quarterly pay to the commission to find the total payment for the first 3 months:
[tex]\[ \text{Total Payment for 3 Months} = \text{Quarterly Pay} + \text{Commission} \] \[ \text{Total Payment for 3 Months} = \$11,362 + \$37,500 \] \[ \text{Total Payment for 3 Months} = \$48,862 \][/tex]
A random sample produced the pie chart below. The chart gives percentages of students that under reported, accurately reported, and over reported their heights. If there are 2,500 students at the school, how many of them can you reasonably expect report their height accurately?
A. 500
B. 200
C. 50
D. 20
Answer:
The correct option is A.
Step-by-step explanation:
Total number of students at the school is 2,500.
In the given pi chart Pink, Yellow and Sky Blue color represent the percentage of students that under reported, accurately reported, and over reported their heights respectively.
From the graph we can conclude that the yellow portion is approximately one fifth of whole circle. It means the number of students that accurately reported their height is one fifth of total number of students.
[tex]2500\times \frac{1}{5}=500[/tex]
Therefore the number of students that accurately reported their height is 500. Option A is correct.
Answer:
Option A) 500
Step-by-step explanation:
We are given the following information:
Total number of students = 2500
From pie chart:
[tex]\text{Under Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Accurately Reported }= \displaystyle\frac{1}{5}\times 100\% = 20\%\\\text{Over Reported }= \displaystyle\frac{3}{5}\times 100\% = 60\%[/tex]
We have to find the number of students whose height were accurately reported =
[tex]\text{Number of students whose height were accurately reported }= \\\text{Number of students}\times \text{Percentage of students whose height were accurately reported}\\= 2500\times 20\%\\\\= 2500\times \displaystyle\frac{20}{100} = 2500\times \frac{20}{100} = 500[/tex]
500 students report their height accurately.