Which statement describes the inverse of m(x) = x2 – 17x?
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
Use long division to write the fraction -6/8 as a decimal.
[tex] \frac{ - 6}{8} = - \frac{3}{4} = - 0.75[/tex]
Can someone please help me
Answer: (b) 7.8 degrees
Step-by-step explanation: You need to pay attention to the number -8.4. It says the temperature changed by +2.7 degrees an hour for 6 HOURS. Therefore, your equation would be -8.4 + (2.7 * 6).
You have to solve whats in the parenthesis first, so your equation would end up being -8.4 + 16.2 making your answer 7.8 degrees.
Jake has a 1 in 5 chance of winning the egg and spoon race.
What is the probability that he will not win the race?
4/5
subtract 1/5 from 5/5.
Answer:
4/5
Step-by-step explanation:
if he has a 1/5 of winning, the left over chances he has has to be towards losing because we already know his chance of winning, and there is no in between, so the left over is 4/5
plz help me with this qustion
Answer:
c
Step-by-step explanation:
a.) 7+7=14 and 19-5=14 ✓
b.) 9+9=18 and 11+7=18 ✓
c.) 19 and 13+5=18 ✗
d.) 20-12=8 and 4+4+8 ✓
solve for x: -8+22=13x-5-12x
Answer:
x = 19
Step-by-step explanation:
-8 + 22 = 13x - 5 - 12x
switch sides
13x - 5 - 12x = -8 + 22
group like terms
13x - 12x = -8 + 22 + 5
simplify:
x = 19
Translate the following into a verbal expression 3(4-x)+7
Answer:
3 times 4 minus a number, plus 7
3(4 - x) + 7
Round to the nearest thousandth: 4.3218 →
Answer:
4.322
Step-by-step explanation:
You would round up because of 8.
Hope this helps!! :D
Answer:
4.322
Since 8 is greater than 5, you round upwards.
“If it is July then it is summer, and it is not July therefore it is not summer” Is this reasoning valid? Why or why not?
Answer:
No
Step-by-step explanation:
Summer starts in June and ends in August, so this is not valid.
Bam
Football player caught the ball and made a gain of 8 yards on the first play. On the next play the team lost 12 yards. How many years do they need to gain on the next play to get back their original position?
. Bartholomew Jackson is paid $10.56 an hour to knit dog sweaters. He gets paid 1.5 times his normal wages for overtime (over 40 hours per week). If he works 55.5 hours in one week, how much money does he earn
Answer:
$667.92
Step-by-step explanation:
Use the equation (p*1.5)*o=t
the variable p is equal to his hourly pay.
the variable o is equal to hours worked overtime.
the variable t is equal to the total amount of money they will make.
As for the 1.5, this is the way overtime is always calculated, at 1.5 times the rate of your hourly wage.
Back to the question:
the variable p is replaced by his hourly pay, $10.56.
the variable o is replaced by the amount of hours he worked overtime. Now, this part is a bit trickier because the question is designed to confuse you. If his overtime only counts if he works over 40 hours a week, then you need to subtract the 40 from his total amount of hours worked. You should get 15.5 because 55.5-40=15.5. Thus, variable o=15.5.
Lastly, you have to calculate it.
Plug in the variables to get:
($10.56*1.5)*15.5= $245.52
DON'T STOP HERE!!!
Since the question asks for how much he has earned for the week, you have to add this onto his normal salary. This part is easy, just multiply the 40 hours by his pay. So,
40*$10.56= $422.40.
Finally, add the overtime ($245.52) to his normal pay ($422.40).
$422.40+$245.52= $667.92
Jaiden is ordering 2.615, 2.65, 2.7, and 2.623 from least to greatest. Here are his steps: (1) Compare and order 2.7 and 2.65 because they have the fewest digits. (2) Compare each digit of the numbers 2.615 and 2.623. * The units digits are equal. * The tenths digits are equal. * 1 < 2 in the hundredths place so 2.615 < 2.623. (3) Combine the two lists into one: 2.7, 2.65, 2.615, 2.623. Which statement describes Jaiden’s error?
Hurry pleaseeee
Answer: D
Jaiden should have added zeroes to the ends of the shorter decimals to get 2.615 etc
Step-by-step explanation:
The numbers that have the same unit value but different digits in the decimal place can be ordered using place value.
The statement that describes Jaden's error is; Jaiden should have added
zeros to each of the shorter decimals to get 2.615, 2.650, 2.700, and 2.623,
then he should have compared them using place values.
Reasons:
The steps are;
(1) Comparing the digits to select the ones with the least amount of digits
(2) Comparing the digits in the place values of the numbers that equal number of digits
(3) Combining the list of the above comparison into one
Required:
To select the statement that describes Jaiden's error.
Solution:
The place value indicates the multiple of 10 by which the digit is multiplied. The given numbers have the same values in the ones place value, the difference are in the numbers to the right of the decimal point.
The given numbers are;
2.615
2.65
2.7
2.623
The steps to order the numbers from least to greatest;
Add zeros to the shorter decimals such that each number have the same number of digits after the decimal point; 2.615, 2.650, 2.700 2.623Then
Select the number with the lowest ones; Which gives all the numbersThen
From the above list, select the number with the lowest tenth, and move them to the left of the list; Which gives the numbers, 2.615, 2.650, 2.623, 2.700Next
From the above list, select the number with the lowest hundredth, and move them to the left of the list, in increasing order of the hundredth; Which gives the numbers, 2.615, 2.623, 2.650, 2.700The numbers 2.615, 2.623,2.650, 2.700, are in the order from least to
greatest.
Therefore Jaiden's error is that Jaiden should have added zeros to each of
the shorter decimals to get 2.615, 2.650, 2.700, and 2.623, then he should
have compared them using place values.
Learn more here:
https://brainly.com/question/25078902
The possible question options are;
The numbers are listed from greatest to listThe two numbers with the most digits should have been compared firstZeros should have been added to the numbers to get, 2.615, 2.065, 2.007, and 2.623. Then the numbers should be compared using place valueHe should have added zeros to each of the shorter decimals to get 2.615, 2.650, 2.700, and 2.623, then he should have compared them using place values.Jenny invests $8500 for 3 years in a savings account. She gets 2.3% per year compound interest. How much money will Jenny have in her savings account at the end of 3 years? Give your answer correct to the nearest dollar.
Answer:$9,100.09
Step-by-step explanation:
A bicycle tire is 28 inches in diameter. Approximately how far does the bicycle move forward each time the wheel goes around? (Use 22/7 as an approximation for .)? i forgot this sorry someone help please
Answer:
Step-by-step explanation:
28x pi=87.96 in
I need help ASAP PLEASE! WILL GIVE BRAINLIEST
Determine whether this statement is true or false. If the statement is false, give a counterexample.
Statement: All integers are rational numbers.
Answer:
true
Step-by-step explanation:
because no integers are irrational.
The Price of dried mango is $9 for every 3/4 pound.
what is the price per pound of the dried mango?
$_ per lb
Answer:
12
Step-by-step explanation:
9 ÷3 =3 ×4 that is how to do the problem
Plz answer this as soon as possible it’s my hw I have to submit it tomorrow.
Answer:
43
Step-by-step explanation:
-2+3×15
45-2
43 is the answer
the difference of six times a number and 7 is -49.
Answer:
6x - 7 = 6(x + 4)
Step-by-step explanation:
The value of the number (n) is -7.
What is an Algebraic Expressions?When we apply the mathematical operations on constants and variables then we get the mathematical statements, these are known as algebraic expressions.The mathematical operators include, division, addition, multiplication and subtraction.Let a number we want to find be n.
Hence, according to the given condition, the equation will be:
⇒ 6n - 7 = -49
⇒ 6n = -42
Dividing both sides by 6, we get:
⇒ n = -7
Therefore, the number that satisfy the algebraic expression is n = -7.
Learn more about the Algebraic Expressions here: https://brainly.com/question/4348710?referrer=searchResults
#SPJ2
A teacher surveyed all 120 of her students about their lunch and lunch schedule. The teacher asked two questions:
• Do you buy a school lunch or bring lunch from home?
Do you eat during festlunch, second lunch, or third lunch
The results showed the majority of her students eat during second lunch and most students buy a school lunch
Which two way table could be a correct representation of the results?
D
you buy lunch and your teacher asks you how much you brought from home then you divide, simple.
if DF = 15 and DE = 6, find EF if E is between D and F?
Answer:
EF=9
Step-by-step explanation:
DF=15
DE=6 EF=9
Write equation 6+x=15
subtract 6 on both sides
x=9 EF=9
How do I do solving systems by substitution please help
The problem I'm on is x-y=-5 with x+y=1
Please show steps I need an answer before my report card comes in tomorrow
Answer:
I believe the answer is x=-2, and y=3.
Step-by-step explanation:
Given: x-y=-5
Fill in: -2-3=-5
Calculate: -5=5
-------------------------------
Given: x+y=1
Fill in: -2+3=1
Calculate: 1=1
Answer:
x = -2.
y = 3.
Step-by-step explanation:
x-y=-5
x+y=1
From the first equation
x = y - 5
Substitute this in the second equation:
y - 5 + y = 1
2y = 1 + 5 = 6
y = 3.
Substitute this into the second equation:
x + 3 = 1
x = -2.
Can someone help me??
Answer:
C
Step-by-step explanation:
−√57 is -7.54983443 repeating but rounded is -7.5 which is smack dab in the middle of integers (numbers) of -7 and -8.
3 On a coordinate grid, the location of a lighthouse is at L, and the location of a buoy is at B. At noon, a ship is at the midpoint of the segment connecting the buoy and the lighthouse on the grid. Find the coordinates that best represent the ship's position at noon?
Answer:
[tex] (\frac{1}{2}, 2) [/tex]
Step-by-step explanation:
Using the midpoint formula, [tex] M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) [/tex], we can find the coordinates that represents the position of the ship at noon.
Let [tex] L(-4, 7) = (x_1, y_1) [/tex] (given on the coordinate plane)
[tex] B(5, -3) = (x_2, y_2) [/tex] (given also)
Plug in the values into the formula and solve as follows:
[tex] M(\frac{-4 + 5}{2}, \frac{7 +(-3)}{2}) [/tex]
[tex] M(\frac{1}{2}, \frac{7 - 3}{2}) [/tex]
[tex] M(\frac{1}{2}, \frac{4}{2}) [/tex]
[tex] M(\frac{1}{2}, 2) [/tex]
Position of the ship at noon is best represented at [tex] (\frac{1}{2}, 2) [/tex]
a mixture of sugar and cinnamon is made to sell as a cooking product. Sugar costs $0.65/kg, and cinnamon costs $6.50/kg. How many kilograms of each (to the nearest tenth) should be mixed to form 27 kg of a mixed costing $1.30/kg?
Answer:
sss
Step-by-step explanation:
sss
So, what is the pattern? For positive integers a and b: (x^a)^b
Answer: (x^b)^a
Step-by-step explanation:
the inverse of a monomial with an exponent raised to another power will give the same product if you flip the exponents.
Here we have a general rule for exponents.
We will find that:
[tex](x^a)^b = x^{a*b}[/tex]
To get this, we can first check it with some values for the exponents.
a = 2
b = 3
[tex](x^2)^3 = (x^2)*(x^2)*(x^2) = (x*x)*(x*x)*(x*x) = x^6 = x^{2*3}[/tex]
Similarly, we can prove it for two general values of a and b:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a)\\b\ times[/tex]
Now each one of these parentheses has a multiplying by itself a times.
So when we write all the x's, we will see that there are a total of b*a x's
Thus we will have:
[tex](x^a)^b = (x^a)*(x^a)*...*(x^a) = x^{a*b}[/tex]
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A line is an undefined term because it
Can anyone help me please very urgent due tonight being graded need help 2.Joey gets an allowance of $17 per week. He wants to buy a new basketball that costs $43.67. When will Jose be able to buy the basketball if he has already saved $22.22, but also has to pay $13.45 each week for snacks and school supplies? make an equation or inequality and solve. Show your work
HELP ME PLEASE I NEED THIS <3333
Answer:
214°
Step-by-step explanation:
The arc subtending an angle at the centre are equal, that is
arc ED = 90° and
arc DF = 360° - (90 + 146)° = 360° - 236° = 124°
Thus
arc EDF = arc ED + arc DF = 90° + 124° = 214°
6. The amount of time it took four soccer players to run from one goal line to the other is as follows:
Player #1 - 10.4 seconds
Player #2 - 10.1 seconds
Player #3 - 9.9 seconds
Player #4 - 9.4 seconds.
If the data was only accurate to the ones place, which soccer player's time would be different from the others?
A Player #1
B Player #3
C Player #2
D Player #4
Given:
The amount of time it took four soccer players to run from one goal line to the other is:
Player #1 - 10.4 seconds
Player #2 - 10.1 seconds
Player #3 - 9.9 seconds
Player #4 - 9.4 seconds
To find:
Soccer player whose time would be different from the others, if the data was only accurate to the ones place.
Solution:
We need to approximate the time to the ones place.
Player #1 - 10.4 seconds = 10 seconds
Player #2 - 10.1 seconds = 10 seconds
Player #3 - 9.9 seconds = 10 seconds
Player #4 - 9.4 seconds = 9 seconds
Therefore, the time of players 4 is different from others.
Hence, the correct option is D.
Alexa deposit $600 in her checking account. She wrote a check for $600 to pay for a DVD player. Then, she made another deposit of $315. How much money does Alexa have in her bank account?
Answer:
$315
Step-by-step explanation:
600-600=0
0+315=315