Answers
Answer:
The correct option is;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
Step-by-step explanation:
The given information is that m(x) = x² - 17·x
The above equation can be written in the form;
y = x² - 17·x
Therefore;
0 = x² - 17·x - y
From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;
[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]
By comparison to the equation,0 = x² - 17·x - y, we have;
a = 1, b = -17, and c = -y
Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;
[tex]x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}[/tex]
Which can be simplified as follows;
[tex]x = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2} \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}[/tex]
And further simplified as follows;
[tex]x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}[/tex]
Interchanging x and y in the function of the inverse, m⁻¹(x), we have;
[tex]m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]
We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;
m'(x) = 2·x - 17 = 0
x = 17/2
Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;
m''(x) = 2 > 0, therefore, the point is a minimum point on the graph
Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;
[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex] to increase m⁻¹(x) above the minimum.
Answer:
b
Step-by-step explanation:
edge 2021
Related Questions
two decimals that are equivalent to (4 × 10) + ( 7 × 1/100)
Answers
Answer:
0.07 ibelive hope this helps
Step-by-step explanation:
Find the surface area of each solid to the nearest tenth if necessary
Answers
The sum of three consecutive numbers is 198. Find the numbers.
(Show Your Work)
Answers
first number = x
second number = x + 1
third number = x + 2
x + x + 1 + x + 2 = 198
3x + 3 = 198
3x = 195
x = 65
the numbers are 65, 66, and 67
can someone pleaseee help me with explaination
2-3a / 4 >5
THE DASH IS FOR DIVISION SO 2- 3a OVER 4
Answers
Answer:
a < -4
I apologise if it is wrong.
Consider this Venn diagram of the prime factors of 210 and 330. Which is the least common multiple of these two numbers?
Answers
Bob, Joe, Pete, Tom, Dic and Tim share s sandwiches. How many sandwiches does each boy get?
Answers
Answer:
s divided by 6
Step-by-step explanation:
there's 6 ppl and there's s sandwiches
0.77 in scientific notation
Answers
Answer:
7.7 x 10 ^-0.1
Step-by-step explanation:
you move the decimal till it is behind the the first number. making it a whole number.
hope this helps
Find all numbers such that 18 plus 4 times the number is less than 30.
Answers
Answer:
The numbers are 2,1,0,-1,-2,..............etcStep-by-step explanation:
This is actually a word problem
step one:
let the maximum number be x
18+4x<30
4x<30-18
4x<12
divide both sides by 4 we have
4x<12
x<3
step two:
From this analysis, we can see that all possible numbers are real numbers less than 3 that is 2,1,0,-1,-2,..............etc
Which of the following statements is false?
2 ≥ 8
2 ≤ 8
8 ≤ 8
2 < 8
Answers
Answer:
the top one
Step-by-step explanation:
The answer is A. 2 ≥ 8
Match each equation to the situation it represents.
Situation
Equation
Kate buys 10 tickets to
a show. She also pays a $5 parking fee. She spent $35 to see the
show.
5x + 10 = 35
Ram has 35 gel pens. He gives an equal number of pens to each of his 5 friends and has
10 pens left for himself.
10x + 5 = 35
Yin spends 10 hours on homework this week. She spends 5 hours on science homework
and then answers 35 math problems.
353 +5 = 10
pls help someone
Answers
Answer:
See below.
Step-by-step explanation:
******************************************************************************
Kate buys 10 tickets to a show. She also pays a $5 parking fee. She spent $35 to see the show.
Each ticket costs x.
10 tickets cost 10x.
Parking is $5.
Total is $35
10x + 5 = 35
******************************************************************************
Ram has 35 gel pens. He gives an equal number of pens to each of his 5 friends and has 10 pens left for himself.
The number of pens he gives each friend is x.
The total number he gives is 5x.
He started with 35 pens ands ended up with 10 pens.
35 - 5x = 10
5x + 10 = 35
******************************************************************************
Yin spends 10 hours on homework this week. She spends 5 hours on science homework and then answers 35 math problems.
Total time spent on homework is 10 hours.
Science homework is 5 hours.
She spends x time on each of the 35 problems, so the total time spent of the 35 problems is 35x.
35x + 5 = 10
This table represents a proportional relationship. Use the table to identify the constant of proportionality between the ratio of the number of laps to the number of swimmers. A 2-column table with 4 rows. Column 1 is labeled Number of Swimmers with entries 20, 18, 14, 9. Column 2 is labeled Number of Laps with entries 240, 216, 168, 108.
Answers
Answer:
12
Step-by-step explanation:
Answer:
a
Step-by-step explanation:
What does the symbol "kg" represent in the metric system?
1,000 grams
100 liters
10 meters
1 degree Celsius
Answers
Answer:
1000 grams
Step-by-step explanation:
The symbol "kg" represents 1,000 grams in the metric system.
What is a metric system?A system of measurements is called the metric system. It is employed in calculations and research across the globe. Here are some instances of measurements made with the metric system:
The unit used to measure lengths and distances is the meter. In daily life, we use this unit to measure things like the length of a piece of clothing, the distance from school to home, etc.
You may have noticed that the bag of your favorite food has a weight listed on it. 250 grams of potato chips, The unit of weight used here is the gram.
We know 1 kilogram is equal to 1×1000 grams.
Therefore, The symbol "kg" represents 1,000 grams in the metric system.
Similarly to convert gram to kg we have to divide by 100.
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What is the scientific notation for 6.782 x 10-4
Answers
Answer:
that is already in scientific notation
Step-by-step explanation:
if you are asking for what's the actual number, then it's 0.000678
Solve the following problem. My bank account balance was $7676 and i withdrew amounts of $1369, $2618, and $937. What is my balance now?!??!
Answers
$6307 - $2618 = $3689
$3689 - $937 = $2752
There is $2,752 left in the bank account.
A craft store sells boxes of two different varieties of colored pencils. The table shows the number of boxes sold last month. What is the total dollar amount of colored pencils sold?
Answers
Answer:
So the answer is 108.75
Step-by-step explanation:
15 * $4.25 = 63.75
12* $3.75 = 45
63.75 + 45 = 108.75.
Answer:108.75
The total dollar amount of coloured pencils sold is $108.75.
Given that, a craft store sells boxes of two different varieties of coloured pencils. The table shows the number of boxes sold last month.
We need to find what is the total dollar amount of coloured pencils sold.
What is the tally table?A tally table is a table that represents the occurrence of an event in a way that calculates it becomes easy.
Now, the cost of each pencil is $4.25.
Then the cost of 15 pencils=15×4.25=$63.75
The cost of each pencil is $3.75.
Then the cost of 12 pencils=12×3.75=$45
Total=63.75+45=$108.75
Therefore, the total dollar amount of coloured pencils sold is $108.75.
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can someone please help me .
Answers
S, U, N are collinear. Select the point that satisfies the definition of betweenness if NU + US = NS.
Answers
The order S, U, N shows U is in the middle. We can read this in reverse to get N, U, S.
Notice how the letter "U"s are adjacent in NU and US to get NU+US.
The more time that I spend reading, the more pages I have read. Which variable is independent?
Answers
Answer:
The more time i spend reading
Step-by-step explanation:
The variable which causes a change to the variable which we intend to measure in an experiment is the independent variable, Hence, the independent variable is the amount of time spent reading.
The Independent variable in an experiment is also called the explanatory variable, which is used to tweak the value obtained for the dependent or measured variable.
In the scenario described, the measured variable is the number of book pages read which is determined by the number of time spent reading (independent variable.)
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What value of x is in the solution set of 9(2x+1) <9x-18?
Answers
Answer:
x = 0
Step-by-step explanation:
9(2x+1) < 9x - 18
Distribute the 9 through
18x + 9 < 9x - 18
Get like terms on the same sides
9x < -27
Divide both sides by the value in front of the x
x < -3
Hope this helps! :)
Which of these sets of ordered pairs below does not represent a function?
{(1, 1) (2, 2) (3, 3) (4,4) (5,5)}
{(2, 1) (4, 2) (6, 3) (8, 1) (10, 2)}
{(0, 0) (2, 3) (3,6) (2.9) (6, 12}}
{(1,5) (2, 4) (3, 3) (4,2) (5, 1)]
Answers
Answer:
0,0
Step-by-step explanation:
The function set is empty
The ordered pair in options B and D does not represents the function.
The sets of ordered pairs {(1, 1) (2, 2) (3, 3) (4,4) (5,5)}, {(2, 1) (4, 2) (6, 3) (8, 1) (10, 2)}, {(0, 0) (2, 3) (3,6) (2.9) (6, 12)} and {(1,5) (2, 4) (3, 3) (4,2) (5, 1)}.
What is function?A function is defined as a relation between a set of inputs having one output each.
For the given ordered pairs graphs are plotted below.
A) The ordered pair {(1, 1) (2, 2) (3, 3) (4,4) (5,5)} represents the linear function.
B) The ordered pair {(2, 1) (4, 2) (6, 3) (8, 1) (10, 2)} does not represents the function.
C) The ordered pair {(0, 0) (2, 3) (3, 6) (2, 9) (6, 12)} does not represents the function.
D) The ordered pair {(1,5) (2, 4) (3, 3) (4,2) (5, 1)} represents the linear function.
Therefore, the ordered pair in options B and D does not represents the function.
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What is an equivalent fraction for 0.625
Answers
Answer:
5/8
Step-by-step explanation:
The answer is 5/8 because 1/8 is equivalent to 0.125, so just multiply 0.125 with 5. Then, you will get 0.625 as you answer.
Hope this helps!
Convert 1.76km into cm
Answers
Answer:
176000cm
Step-by-step explanation:
1.76km * 1000m / 1km * 100cm / 1m = 176000cm
Answer:
176000
Step-by-step explanation:
To convert km to cm, we need to multiply the number by 100000, which results in your answer.
Hi i just like kinda forgot what that line above the two numbers in 2.21 mean. Can you help me?
Answers
Answer:
It means .21 never ends like 2.2121212121.....
Answer:
it means that what ever is under that line is repeating so it just keeps going ex. 2.212121212121212121212121212121................... and never ends
hope this helps:)
Step-by-step explanation:
Please 20 points like rn 5 mins left on test
Answers
Answer: counterclockwise rotation of 90° and a reflection over y axis
Step-by-step explanation:
Hillary’s summer job at the frozen yogurt shop paid her the amounts shown in the table below in her first three days on the job (she got paid the same hourly rate every day).
Answers
Answer:
P=9.0h
Step-by-step explanation:
Divide the Paid amount by the hours worked and you'll get how much money she gained every hour which is 8.50$ And the question is telling you which of the following equations is GREATER than the amount she got paid per hour. So the answer would be P=9.0h
The required equation represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h. Option D is correct.
Given,
Hillary’s summer job at the frozen yogurt shop paid her the amounts shown in the table below in her first three days on the job (she got paid the same hourly rate every day).
day = 1 2 3
Hours worked(h) = 5 4 6
Amount paid (p) = $42.50 $34 $51
The slope of the line is the tangent angle made by line with horizontal. i.e. m = tanx where x in degrees.
The slope of the data given,
m = 42.5/5
m = 8.5
the slope shows the hourly rate to get paid.
Required expression is
p = 8.5h
From the option, the slope of equations needs to compare greater the slope greater will the hourly rate.
Slope of equation A = 1/8, B =8, C = 8.5 and D = 9.0
hence, only slope D has a greater value by the existing slope of 8.5
Thus, the required equation that represents an hourly pay rate that is greater than Hillary's hourly pay rate p = 9.0h.
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Question is incomplete, correct question has added below.
An object is moving at a speed of 11 yards every 6 months. Express this speed in centimeters per hour. Round your answer to the nearest hundredth.
Answers
Answer:
its c
i took the quiz
Step-by-step explanation:
The speed in centimeters per hour is 0.2328 centimeters per hour.
Given,
An object is moving at a speed of 11 yards every 6 months.
We need to find this speed in centimeters per hour.
How many centimeters in one yard?1 yard = 91.44 centimeters.
We have,
11 yards every 6 months
11 yard = 6 months
1 month = 30 days
1 day = 24 hours
30 days = 30 x 24 hours
30 days = 720 hours
1 month = 720 hours
6 months = 6 x 720 hours
6 months = 4320 hours
11 yards = 4320 hours
1 yard = 91.44 cm
11 x 91.44 cm = 4320 hours
1005.84 cm = 4320 hours
So,
we will find how many cm per hour.
if 1005.84 cm = 4320 hours then,
Dividing both sides by 4320.
1005.84/ 4320 cm = 4320/4320 hours
0.2328 cm = 1 hour
Rounding to the nearest hundredth.
0.23 cm = 1 hour
Thus the speed in centimeters per hour is 0.2328 centimeters per hour.
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Alguém poderia me ajudar nessa questão a print está aí
Answers
I NEED TO KNOW NOW IT'S DUE!!
Last summer, Fred earned 16 dollars per day, and Maria earned 18 dollars per day together, they earned 1780 dollars. If Fred worked 5 more days than Maria, how many days did Maria work?
Answers
x = # of days Maria worked
x + 5 = # of days Fred worded
$16(x + 5) + $18x = $1780
Let's distribute the $16
$16x + $80 + $18x = $1780
Combine like terms
$34x + $80 = $1780
Subtract $80 from both sides.
$34x = $1700
Divide both sides by $34
x = 50 days
Maria worked 50 days
help me please:(((( i’m struggling pretty bad
Answers
3 / (4/9)
First, let's multiply the top and bottom by 9 to get rid of the fraction in the denominator.
27 / 4 is the final answer.
Answer:
31/9
Step-by-step explanation:
3 4/9 as an improper fraction is 31/9.
We get our answer by multiplying the denominator of the mixed numbers by its whole number and adding that answer to its numerator. We get 31, and we put that over the denominator.
3 4/9
9x3=27
27+4=31
31/9
If there are 2.2 pounds in 1 Kilogram, how many pounds are there in x kilograms?
A)2.2x
B)2.2/x
C)x/2.2
D)2.2+c
Answers
Answer:
The answer is A
Step-by-step explanation:
If there are 2.2 in 1 kilogram and you are trying to find out how many are in many kilograms then you multiply.
Hopefully this helps you :)
pls mark brainlest ;)
The expression that represents the pound of weight in x kilogram can be written as 2.2x, where x represents the weight in kilograms.
What is Units conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
As it is given that there are 2.2 pounds in 1 Kilogram. Therefore, the expression that represents the pound of weight in x kilogram can be written as 2.2x, where x represents the weight in kilograms.
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