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
given a right-angled triangle with perimeter 18. The sum of the squares of the three side lengths is 128. What is the area of the triangle ?
Answers
Answer:
9units²
Step-by-step explanation:
A triangle has 3 sides. Let the length of the three sides be a, b, c.
If the perimeter of the triangle is 18, then;
P = a+b+c
a+b+c = 18... 1
If the sum of the squares of the three side lengths is 128, this means;
a²+b²+c² = 128... 2
Since the triangle is also right angled, according to Pythagoras theorem;
c² = a²+b²... 3 (taking c as the hypotenuse)
Substitute equation 3 into 2;
(a²+b²)+c² = 128
c²+c² = 128
2c² = 128
c² = 128/2
c² = 64
c = √64
c = 8
Substituting c = 8 into 1
a+b+c = 18
a+b+8=18
a+b = 10 ...... 3
Substituting c = 8 into 2
a²+b²+c² = 128
a²+b²+8² = 128
a²+b²+64 = 128
a²+b²= 64..... 4
Solve equation 3 and 4 simultaneously;
a+b = 10
a²+b²= 64
From 4; a = 10-b
Substitute a = 10-b into 4;
(10-b)²+b² = 64
100-20b+b²+b² = 64
2b²-20b+100-64 = 0
2b²-20b+36 = 0
Divide through by 2:
b²-10b+18 = 0
b = 10±√10²-4(18)/2
b = 10±√100-72/2
b =( 10±√28)/2
b =(10±√4×7)/2
b = (10±2√7)/2
b = 5±√7
Hence b = 5+√7
If a+ b = 10
a+(5+√7 ) = 10
a = 10-(5+√7)
a = 10-5-√7
a = 5-√7
Area of the triangle A = 1/2 ab
A = 1/2 × (5+√7) × (5-√7)
A = 1/2 × (25-5√7+5√7-7)
A = 1/2 × (25-7)
A = 1/2 × 18
A = 9
Hence the are of the triangle is 9units²
The rectangle has a length of -2x + 10 and a width of 10. a) Find the area of the rectangle and simplify.
Answers
Answer:
Area = -20x + 100Perimeter = -4x + 40Step-by-step explanation:
Given rectangle with
Length l = - 2x + 10 Width w = 10To find
AreaPerimeterSolution
A = lwA = (-2x + 10)*10 = -20x + 100P = 2(l +w) P = 2( -2x + 10 + 10) = 2( -2x + 20) = -4x + 40A diver descends 90 feet in 5 minutes. What is the
diver's change in depth per minute?
Answers
Answer:
18 feet/min
Step-by-step explanation:
Divide 90/5 to find the diver's change in depth per minute 18 feet per minute is the answerwhayt is the value 4x0.36
Answers
In a scale drawing of a painting, 1 centimeter represents 6 Inches.
Scale
1 cm: 6 in
Answer the following.
(a) In the scale drawing, the length of the painting is 7
centimeters. What is the length of the real painting?
(I) inches
X
(b) The height of the real painting is 24 inches. What is the
height of the painting in the scale drawing?
I centimeters
Answers
Given: KM bisects JKL
Prove: m MKL= 1/2m JKL
please explain
Answers
Start with out given statement:
Line KM bisects <JKL and the reason for that is because it's given.
For statement 2, we know that m<JKM = m<MKL
because of the definition of an angle bisector.
For statement 3, we can use the angle addition
postulate to get m<JKM + m<MKL = m<JKL.
For statement 4, we use substitution from
the info in statement 2 to get m<MKL + m<MKL = m<JKL.
For statement 5, we simplify to get 2(m < KML) = m<JKL.
For statement 5, we use the division property of equality.
All the reasons are underlined.
A line with a slope of 1/7 passes through the points seven and one what is it equation in slope intercept form
Answers
Answer:
y=1/7x
Step-by-step explanation:
Plug into Point slope form:
y - 1= 1/7( x -7)
y -1 = 1/7 x -1
y -1 +1 = 1/7x -1 +1
y= 1/7x
You have taken up gardening for relaxation and have decided to fence in your new
rectangular shaped masterpiece. The length of the garden is 4 meters and 34 meters
of fencing is required to completely enclose it. What is the width of the garden?
Answers
Answer:
13 meters
Step-by-step explanation:
Adjacent sides form half the perimeter, so the sum of the unknown side and the given side is 34/2 = 17 meters.
4 meters + width = 17 meters
width = 13 meters . . . . . subtract 4 meters
In which expression should the exponents be multiplied? (4 points)
Answers
can someone help me? help
Answers
Answer:
Step-by-step explanation:
Remove the brackets
3x*x^2 - 5x*3x + 3x*1 - 2x^2+3x -7
Combine
3x^3 - 15x^2 + 3x - 2x^2 + 3x - 7
3x^3 17x^2 +6x - 7
Alfred and his 4 friends bought 13 1/4 pounds of gummy bears at $1.20 pound . If the cost is divided between alfred and his four friends what would each person pay
Answers
to find the total cost, just multiply 13.25 by $1.20 to get $15.90. to find the cost per person, just divide $15.90 by 5, which results in each person paying $3.18
The volume of a pyramid, V, is calculated using the formula V = 1/3 AH, where A is the area of the base and H is the height of the pyramid.
Rearrange the formula to solve for the base area (A)
Answers
Answer:
A= 3V/H
Step-by-step explanation:
V=1/3 AH
multiply 3 on both sides
3V=AH
divide both sides by H
3V/H=A
a decimal number in which a digit or group of digits
repeats without end
Answers
Answer:
that is called a repeating decimal.
Step-by-step explanation:
You want to buy a new hat that costs $9.20 on the price tag. How much
will you pay at the register if there is an 8.5% tax? Round to the nearest
cent. *
Answers
Answer:
$9.98 :)
Step-by-step explanation:
just multiply the tax (0.085) by the price ($9.20) then add the initial price ($9.20) to that.
A local church has a rectangular fellowship room that it will expand by increasing the
length by 20 feet to form a larger rectangle. If the current dimensions of the room
are unknown, write an algebraic expression for the perimeter of the new room.
Answers
Answer:
perimeter of new room = 2[(l+20)*b]
Step-by-step explanation:
Which of the following is an equation of the line with slope 2 that passes through the point (-1,-4)
Show complete working format
Answers
Answer:
y = 2x - 2
Step-by-step explanation:
Slope-Intercept Form: y = mx + b
Step 1: Define
Slope m = 2
Random point (-1, -4)
y = 2x + b
Step 2: Find b
-4 = 2(-1) + b
-4 = -2 + b
-2 = b
Step 3: Rewrite linear equation
y = 2x - 2
3х^2–36 = — 84
can someone help me with this one
Answers
Answer:
No real solution.
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
At the fair, Terrell has 47 ride tickets. Each ride on the Ferris wheel costs 6 tickets. After
riding the Ferris wheel as many times as possible, how many tickets will Terrell have left?
Answers
Answer:
Terrell has 5 tickets left.
Step-by-step explanation:
Convert 10 mL/sec to L/min
Answers
Step-by-step explanation:
1000 mL = 1 L
10 mL = 1/1000 × 10 = 0.01 L/sec
60 sec = 1 min
1 sec = 1/60 min
0.01 L/sec
= 0.01 L × 60
= 0.6 L/min
10 mL/sec = 0.6 L/min
How do I rewrite a quadratic into graphing form
Answers
Step-by-step explanation:
Standard form of a quadratic is f(x) = ax² + bx + c.
To convert to vertex form, the simplest method is to find the x-coordinate of the vertex using h = -b/(2a).
Then, plug back into the equation to find the y-coordinate of the vertex. k = f(h).
Finally, the leading coefficient is the same as the standard form, a.
f(x) = a(x − h)² + k
Another method is to complete the square.
helphelphelphelphelp
Answers
Answer:
Point A
Step-by-step explanation:
A scale drawing of a school bus has a scale of 1 inch to 10 feet. If the length of the school bus is 2 1/2 inches on the drawing, what is the actual length of the bus?
Answers
Answer: 25 feet
Step-by-step explanation:
Answer:
25 feet
Step-by-step explanation:
10 times 2 is 20 and half of 10 is 5 so 20 and 5 = 25
Write the word phrase for the equation 7x + 10 = 14 divided by x
Answers
Step-by-step explanation
ten plus x multiplied by seven is equal to fourteen divided by X
-1 7/8 + -6 Help, please.
Answers
8. Why is it NOT useful to view science as a set of facts?
Answers
(assuming this isn't actually for math?) but one reason is bc science shouldn't be always taken as fact. science can be wrong.
Explanation:
not all but many scientists are skeptical and won't accept anything without proof, and even when things are accepted as right they can still be wrong later. example: humans once believed the planets revolved around the earth and that the earth was flat (even, some people still believe the earth is flat today....) but both those things are generally unaccepted today.
science shouldn't be viewed as fact always, because accepting everything as fact will lead to misassumptions and false information. it's like we should never take things for granted
This is my honest opinion
Science is not just facts. Science, to me, is full of theories and hypotheses that can be proved wrong. Yes, a majority of it is actually factual, but in the future it may or may not be true.
I hope it helps.
38503.45 in standard form
Answers
Hey there!
ANSWER:[tex]38503.45[/tex]EXPLANATION:38503.45 in standard form.
The decimal 38503.45 is already in standard form. Try multiplying [tex]38503.45[/tex] by [tex]10^0[/tex].
[tex]38503.45*10^0=38503.45\\38503.45(ANSWER)[/tex]
The answer is the same as the decimal. That is because it was already in the standard form.
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]
The number of fungi on a culture has increased from 800 spores to 1,600 spores in 1 hour. What is the growth factor for
this fungus?
0.1
1
2
10
Answers
Angle A and angle B are complementary angles. If m angle A = (x + 8) and m
angle B = (8x + 1)", then find the measure of angle A.
Answers
17
Explanation:
(x + 8) + (8x + 1) = 90
Combine like terms to get:
9x + 9 = 90
Subtract 9 on both sides:
9x = 81
Divide by 9:
x = 9
Plug in 9 for x in
9 + 8 = ?
9 + 8 = 17
A football team loses 8 yards on each of 4 consecutive plays. Find the total change in yards from where the team started. pls help fgkogijriojg
Answers
Answer:-32
Step-by-step explanation:
You times the two numbers and add a negative sign in front of it
8 would be a negative in this situation and 4 would be a positive. So the problem would look like this:
-8 x 4 = ?
For this particular problem, we would do 8 x 4 which would equal 32. Then we would try to find which one has the greater absolute value.
Absolute Value:
4 = 4
-8 = |8|
Since -8 has the greater absolute value, the answer would be negative.
The Answer: -32
Randy is four times as old as Kenneth and Randy is 36 years older than Kenneth
i) How old is Kenneth?
ii) How old is Randy?
Answers
Answer:
Kenneth: 12 years old
Randy: 48 years old
Step-by-step explanation:
For this problem, we can use system of equations to solve. Let's use r for Randy and k for Kenneth.
Equation 1
r=4k
This equation comes from the first part, where Randy is four times as old as Kenneth.
Equation 2
r=36+k
This equation comes from the second part, where Randy is 36 years older than Kenneth.
Since we have r=, we can use substitution method.
4k=36+k [subtract both sides by k]
3k=36 [divide both sides by 3]
k=12
Now that we have found k, we can plug that into any equation to find r.
r=4(12) [multiply]
r=48
Now, we know that Randy is 48 years old and Kenneth is 12 years old.