Let f and g be differentiable functions. If g and f are inverses of each other,
g(-4)= 7, and f'(7) = 2, then g'(-4) =
Select one answer
A -2
B -1/2
C 1/2
D 2
Answers
Answer:
C 1/2
Step-by-step explanation:
You have differentiable functions f and g that are inverses of each other with ...
f(7) = -4f'(7) = 2g(-4) = 7and you want to know g'(-4).
SolutionConsider the composition ...
f(g(x)) = x . . . . . . the functions are inverses of each other.
Differentiating with respect to x, we get ...
f'(g(x))·g'(x) = 1
g'(x) = 1/f'(g(x)) . . . . . . divide by the coefficient of g'(x)
For x = -4, this is ...
g'(-4) = 1/f'(g(-4)) = 1/f'(7) . . . . . use the given values
g'(-4) = 1/2
__
Additional comment
In the attachment, you can consider the red line to be the tangent to f(x) at x=7, and the blue line to be tangent to g(x) at x=-4. The slope of the tangent, g'(-4), is 1/2, the reciprocal of the slope at f(7)=-4.
A function and its inverse are reflections of each other in the line y=x. That line is shown as dashed orange, and the points of interest are marked: (7, -4) and its inverse, (-4, 7).
Related Questions
During one month andre used 785 gallons of water at his home. There are approximately 3. 8 liters in 1 gallon. Which measurement is closest to the number of liters andre used during this month?.
Answers
Andre used 2983 gallons of liquid all through this month.
Given;
Andre used 785 gallons of water at his house in a single month. In a gallon, there are roughly 3.8 liters.
To get the measurement that is closest to the number of liters Andre used during this month;
The total gallons of water used in a month = 785 gallons
The quantity of water in a single gallon = 3.8 liters
Therefore, the number of liters Andre used during this month;
U = total gallons of water used in a month * quantity of water in a single gallon
U = 785 * 3.8
U = 2983
Hence, the number of liters Andre used during this month is 2983 gallons.
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Q2.
I am thinking of two numbers.
The first number is x
The second number is 7.5 more than x.
Write down an expression, in terms of x for the second number.
For the two numbers,
the product is double the sum.
Work out the numbers I could be thinking of.
Give both possible pairs of answers.
Answers
Answer:
second number = (x + 7.5)
Since the product of the two numbers is double of their sum,
x(x + 7.5) = 2(x + x + 7.5)
x² + 7.5x = 2(2x + 7.5)
x² + 7.5x = 4x + 15
x² + 7.5x - 4x - 15 = 0
x² + 3.5x - 15 = 0
∴ x = -6 or 2.5
∴ second number
= -6 + 7.5 or 2.5 + 7.5
= 1.5 or 10
∴ The two numbers that I am thinking of are either -6 and 1.5 or 2.5 and 10.
1. Find the y-intercept of the line paing through the point A (3, -2) and B (-1, 3). (5 pt)
Answers
help please and thankyou
Answers
The value of x will be 24.
What is mean by Triangle?
A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
For a given right triangle, the expression is,
⇒ sin (3x - 7) = cos (x + 1)
Now,
Solve for x as;
The expression is,
⇒ sin (3x - 7) = cos (x + 1)
Since, sin x= cos (90 - x)
So, We get;
⇒ sin (3x - 7) = cos (x + 1)
⇒ cos (90 - (3x - 7)) = cos (x + 1)
⇒ 90 - (3x - 7) = (x + 1)
⇒ 90 - 3x + 7 = x + 1
⇒ 97 - 3x = x + 1
⇒ 97 - 1 = x + 3x
⇒ 96 = 4x
⇒ 4x = 96
⇒ x = 96/4
⇒ x = 24
Thus, The value of x will be 24.
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The graph below shows distance over time.
A student is walking to class. The student increases their speed for 20 seconds for 3 meters. The student then walks a constant speed for 5 seconds and then increases their speed the last 3 meters to class.
Which of these situations could be represented by this graph?
Answers
A situation which could be represented by this graph is: A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
What is a graph?In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate and y-coordinate respectively such as time (min) and distance (km).
In this scenario, the time (in minutes) was plotted on the x-axis of the graph while the distance covered (in kilometers) was plotted on the y-axis of the graph.
By critically observing the graph (see attachment), we can reasonably and logically deduce that the first student walked a distance of 1.5 kilometer to his or her friend’s house in 20 minutes, then, they both walked at a constant speed for 5 seconds before increasing their speed, covering another distance of 1.5 kilometer to their school within 40 minutes (60 - 20 minutes).
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Complete Question:
The graph below shows distance over time. Which of these situations could be represented by this graph?
answer choices
A student walks 1.5 km to a friend’s house in 40 minutes. The two students then walk another 1.5 km to school in 20 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 40 minutes.
A student walks 1.5 km to a friend’s house in 30 minutes. The two students then walk another 1.5 km to school in 30 minutes.
A student walks 1.5 km to a friend’s house in 20 minutes. The two students then walk another 1.5 km to school in 60 minutes.
Find the equation of the line passing through the given point and parallel to the given line.
( 1, 9 ), y = 4x + 2
( 5 , 2 ), y = -2x + 7
Answers
The line equation passing through the given points and parallel to the given lines are:
Line 1: y=-4x+13...(i)
Line 2: y=2x-12...(ii)
Line 1
The first line is passing through point (1,9) and parallel to the y=4x+2 line.
Since line 1 would be parallel to line y=4x+2, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=4x+2 has:
ay = bx + c, m= -b/a
y=4x+2, m=-4
We could use the line equation formula, where:
y-y1 = m (x-x1)
we use the given point (1,9) and the slope value (m=-4) to get the line equation passing through the point:
y-9 = -4(x-1)
y-9=-4x+4
y=-4x+13...(i)
Line 2
The first line is passing through point (5,2) and parallel to the y=-2x+7 line.
Since line 2 would be parallel to line y=-2x+7, hence both lines would have the same value of slope (m).
Using the standard formula of line equation, we could identify that line y=-2x+7 has:
ay = bx + c, m= -b/a
y=-2x+7, m=-2
We could use the line equation formula, where:
y-y2 = m (x-x2)
we use the given point (5,2) and the slope value (m=2) to get the line equation passing through the point:
y-2 = 2(x-5)
y-2 = 2x-10
y=2x-12...(ii)
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Jon needs to buy a backpack and several folders for school. If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each. Write and solve an inequality to find the number of folders Jan would need to buy for the Supply Guys to be the cheaper option
Answers
Considering the definition of an inequality, the number of folders Jan would need to buy for the Supply Guys to be the cheaper option is more than 18.
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality is true.
Inequality in this caseIn this case, you know that:
If she shops at smart supply, the backpack will cost $45 and folders cost $0.45 each. If she shops at supply Guys, the backpack will cost $50.40 and folders cost 0.15 each.The Supply Guys is the cheaper option.Being "x" the number of folders, the inequality that expresses the previous relationship is
45 + 0.45x > 50.40 + 0.15x
Solving:
0.45x - 0.15x > 50.40 -45
0.30x> 5.4
x> 5.4÷ 0.3
x> 18
Finally, the number of folders Jan would need to buy is more than 18.
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mario tiene una cinta de 6 m y su amiga beatriz tiene una cinta de 8 m ¿cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz?
Answers
La cinta de Mario tiene una longitud que es 0.75 veces la longitud de la cinta de Beatriz.
¿Como se comparan las longitudes?
Sabemos que la longitud de la cinta de Mario tiene una longitud de 6 metros, mientras que su amiga Beatriz tiene una cinta de longitud de 8 metros.
Para saber cuantas veces es la longitud de la cinta de mario comparada con la longitud de la cinta de beatriz, tenemos que tomar el cociente entre ambas longitudes, obtendremos:
6m/8m = 0.75
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Which method and additional information would prove δonp and δmnl similar by the aa similarity postulate? segments om and lp intersect at point n; triangles are formed by points lnm and onp; line k intersects with both triangles at point n. use a rigid transformation to prove that ∠opn ≅ ∠mln. use rigid and nonrigid transformations to prove segment pn over segment mn = segment ln over segment on. use a rigid transformation to prove that ∠npo ≅ ∠lnm. use rigid and nonrigid transformations to prove segment ln over segment on = segment pn over segment mn.
Answers
The correct option for the method and additional information that would prove triangle ONP and triangle MNL similar by AA similarity postulate is
option B.
B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
Angle Angle AA similarity postulate states that two triangles are similar if : two angles in one of the triangles are congruent (equal) to two angles in the other triangle.
The reason for arriving at the above selection is as follows:
The known parameter in triangle ΔONP and ΔMNL are;Lines MO and LP intersect at vertex point N.The angles on opposite side of the point N (either side of the X shape formed by the two lines) which are ∠ONP and ∠LNM are vertically opposite angles or opposite angles.According to vertically opposite angles theorem ∠ONP and ∠LNM, which are vertically opposite angles are congruent, and we can write.
∠ONP ≅ ∠LNM
The required parameters are:
To find the additional information that would prove ΔONP and ΔMNL by
AA (Angle-Angle) similarity postulate.
Given from the drawing,
One (vertex) angle in one triangle is congruent to one (vertex) angle in the other triangle, that is ∠ONP ≅ ∠LNM, it is required to prove that one other angle in triangle ΔONP is congruent to a corresponding angle in triangle ΔMNL.
Prove that:
either ∠NPO or ∠NOP in ΔONP are congruent to ∠NLM or ∠NML respectively in ΔMNL by performing rigid transformations (transformations that does not change shape) on either ΔONP or ΔMNL including:
Rotating triangle ΔONP by 180° with origin at point N, to form the image ΔO'N'P'.
Translating the vertex point P' in the image ΔO'N'P', to the location of the point L in ΔMNL, and verify that the segments LN and LM in ΔMNL coincide with the segments P'N' and P'O' respectively of triangle ΔO'N'P'.
Therefore, the correct option is option B. Use rigid transformation to prove that angle NPO is congruent to angle NLM.
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Answer:
b
Step-by-step explanation:
HELP ME PLEASE, I NEED TO FINISH THIS MATH PROBLEM!
Anna is working two summer jobs, making $9 per hour washing cars and $12 per hour landscaping. Last week Anna worked a total of 7 hours and earned a total of $78. Determine the number of hours Anna worked washing cars last week and the number of hours she worked landscaping last week.
ANSWER: ANNA WORKED _____ HOURS WASHING CARS AND ______ HOURS LANDSCAPING.
Answers
Answer: anna worked 4.33repeating hours washing cars and 3.25 hours landscaping
Step-by-step explanation:
i personally used a guess and check method.
i multiplied 9(hourly wage for washing cars) and 4.33repeating(number of hours) = 39
i multiplied 12(hourly wage landscaping) and 3.25(number of hours) = 39
39 + 39 = $78
The tens digit of a two-digit number is twice the ones digit. Its reversed number is 36 less than the original number.
Answers
From the calculation, the original number is obtained as 84.
What is the original number?We know that we are told in the question that in the question, we are required to obtain the number and that is what we are going to do below.
Let the tens digit be T and let the units digit be U
We can then write
10U+T = 10T+U-36
Since the reversed number is 36 less than the original number.
Then;
9U = 9T -36
Dividing both sides of the equation by 9
U = T -4
U=2U-4
U=4
T = 8
It then follows that the original number is 84.
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find the annual salary of a person who is paid $835.50 per week
Answers
Answer:
43446
Step-by-step explanation:
52 weeks in an year
835.5 × 52 = 43446
A bookstore had 150 copies of a magazine. Yesterday the bookstore sold 2/5 of these copies. How many copies were sold yesterday
Answers
Answer:
Hi
Step-by-step explanation:
so the question is asking what is 2/5 of 150
if 150 is able to evenly be split up into 5 even parts we can the add two of those parts to get our answer.
does 150 split up into 5 even parts??
hmmm you probably are thinking, 15 does divide by 5 evenly into 3 parts, so we now know that 150 also splits up into 5 even parts of 30 :)
2 time 30 = 60
so there is how to figure out the answer and , the answer 60 :)
Rewrite in simplest terms: (-10x+2)+(-9x+8)
Answers
The simplest form of the given expression is -19x + 10.
The process or product of making something less complicated and thus easier to do or understand is called simplification. Replace 'of' with 'Multiplication' and '/' with 'Division.' Always perform operations in the order specified by 'BODMAS.' Division and multiplication are both given equal weight (Starting from left) Subtraction and addition have the same.
Given that
(-10x+2) + (-9x+8)
We have to simplify the given expression
= -10x + 2 - 9x + 8
= (-10x - 9x) + (2 + 8)
= -19x + 10
Therefore the simplest form of the given expression is -19x + 10
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Riley found a receipt for a pair of jeans for $142.95, tax included. If the sales tax rate was 6%, what was the list price of the jeans? Round your answer to the nearest cent.
Answers
Answer:
$134.86
Step-by-step explanation:
Let the original price before tax be x.
A whole amount is 100% of the amount, so x is 100% of the original price without tax.
The tax rate is 6%, so the tax on x is 6% of x. Add 6% of x to 100% of x, and you have 106% of x. The item plus tax cost 106% of x.
106% of x = $142.95
106/100 × x = 142.95
1.06x = 142.95
x = 142.95/1.06
x = $134.86
Answer: $134.86
PLEASE HELP!
Simplify the expression to a + bi form:
√25 + √-81 + √25 - √-16
Answers
Answer:
10 + 5i
Step-by-step explanation:
[tex] \rm \implies \sqrt{25} + \sqrt{ - 81} + \sqrt{25} - \sqrt{ - 16} \\ \\ \rm \implies 5 + 9i + 5 - 4i \\ \\ \rm \implies 10 + 5i[/tex]
3.6 x 10^7 + 2.1 x 10.7=
a) 14
b) 5.7
c) 3.6
d) none of these
Answers
The value of the exponent 3.6 x 10^7 + 2.1 x 10.^7 is D. None of the above.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value of 3.6 x 10^7 + 2.1 x 10^7 will be:
= 3.6 x 10^7 + 2.1 x 10.^7
= 5.7 × 10^7
Therefore, the correct option is D.
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find the perimeter and area
Answers
Answer:
perimeter = 22 km and area = 18 km^2
Step-by-step explanation:
First I found and labeled the missing lengths. For the one at the top of the shape, I added 1 + 2 + 3 to get the length, since those are what make up the length.
Afterwards I just added up all the side lengths to get the perimeter. 2+6+2+3+2+3+1=22, so the perimeter is 22 km.
To find the area, I split the shape into two, labeled 1 and 2. (Check the image attached) To find the area you multiply length by width, so i did that for shapes 1 and 2. For shape 1, I did 2 x 6 and got 12, and for shape 2 I did 3 x 2 to get 6. To get the total area of the entire shape, add these two areas. 12 + 6 = 18, so the total area is 18 km^2. (km squared)
let me know if anything is confusing :-))
area is 18km squared
What is the sum of (3x + 4) + (9x – 10)?
Answers
12x-6
Step by step explanation:
So in this question you’re going to want to combine the like terms. This means that you add 3x and 9x, since they both have the same variable, and you add 4 to -10. Once you combine the terms, you should get 12x-6, and that’s your final answer. Hope that helps!
Answer:
[tex]12x -6[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
I need help please!!!
Answers
The slope of a line = y1-y2 / x1-x2
(The 1 and 2 represent the first x and the second x, and the first y and the second y).
5-(-6) / -3-(-10)
5+6 / 7
11/7
how many distinct 5-letter strings can be created using the letters a, b, c, d, e if repetition is allowed, but the letters a appears at most twice?
Answers
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
Given that
form 5-letter distinct strings can be created using the letters a,b,c,d, and e, and repetitions are allowed but the letter a appears at most twice
let's consider that letter a is not there in the string
each letter is repetitive then it is [tex]4^{5}[/tex]
now letter a is considered once
5c1 ×[tex]4^{4}[/tex]
now letter a is repetitive twice
5c2 × [tex]4^{3}[/tex]
[tex]4^{5}[/tex] + 5c1 × [tex]4^{4}[/tex] + 5c2 × [tex]4^{3}[/tex]
1024+ 1280 + 640 = 2944
2944 distinct 5-letter strings can be created using the letters a, b, c, d, and e if repetition is allowed but the letter a appears at most twice
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Expression that equal to p/6+(q+8)
Answers
Answer: (p/6 + q) + 8
Step-by-step explanation:
What is 125 in simplest form?
Answers
Answer:
125 in simplest form is 1/8.
Step-by-step explanation:
If that was a typo and you meant to say 12/5, the answer is 2 2/5.
5 fits inside of 12 two times, with 2 left over.
We can check this by multiplying 5 by 2 (denominator by remainder), and adding 2 (the numerator). With this, we get 12/5, and we know our math is correct.
1/25 is already is simplest form.
0.96 in fracton form
Answers
Answer:
As a fraction in simplest form it SHOULD be 24 over 25.
Step-by-step explanation:
"0.96 as a fraction (simplified form)" MagnetsAndMotors (Dr. B's Other Channel)
Answer:
24/25
Step-by-step explanation:
0.96
By counting the numbers after the decimal point which is two.
so we will write: 96/100, since hundred has to two zero.
Then we will divide 96/100 to it simplest form which is 24/25
643251 to the nearest then thousands
Answers
Answer:
64000
Step-by-step explanation:
When you are rounder you must look at the last number to determine if you are rounding up or down.
How many minutes are in 1 hour and 3/4? How do you solve it as well?
Answers
Answer:
Step-by-step explanation:
105 min
60 min in a hour and then 3/4 of a hour is 45 min.
Total: 105 minutes
1.209, 1.9, 3.76, 1.29 order these numbers from least to greatest
Answers
Answer:
1.209 < 1.29 < 1.9 < 3.76
Step-by-step explanation:
HELP ASAP GIVING BRAINLIEST
Answers
Answer: C
Step-by-step explanation:
A square and rectangle are shown below. The width of the rectangle is the same as
the length
of a side of the square, both represented by .x. The length of the rectangle is one
foot more
than twice its width. The perimeter of the rectangle is 26 feet more
than that of the square.
(a) Write an expression for the length of the rectangle in
terms of.x. Label on the drawing.
x
Answers
Answer:
Step-by-step explanation:
x=26
A bank employee notices an abandoned checking account. The bank charges a monthly fee for the account modeled by the function
A(m)=184-8m, where M is in months and A(m) is in dollars.
What is the domain of the function within the context? Use inequality Notation.
Answers
The domain of the function A(m) = 184 - 8m representing the bank charges on monthly fees is m ≤ 23
How to find the domain of the functionThe equation is linear equation in the slope intercept form as
y = mx + c
where
m = slope = -8
c = intercept = 184
x = input variables = m
y = output variables = A(m)
The domain refers to all possible values of m, generally the equation has no restriction for m however for the problem being discussed y should not be negative. hence we solve for m when y = 0
0 = 184 - 8m
8m = 184
m = 23
The maximum value of m is 23 hence the domain is m ≤ 23
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