no question;;;;;;;;;;;;;;;;;;;;;;
Given that f(x) = x^4 +5,g (x) is the inverse of f (x), and g (6) = 1 find g' (6).
Select one answer
A 4
B 1/4
C 9
D 1/9
Answer:
B 1/4
Step-by-step explanation:
f(x) = y = x⁴ + 5
the inverse function is
y - 5 = x⁴
x = 4th root(y - 5)
now we rename y and x to make it a regular function definition :
g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)
because g(6) = 1 (positive), we have
g(x) = (x - 5)^(1/4)
and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.
g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)
because (x - 5)' = 1
g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =
= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4
please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.
3) Determine the numbers of solutions for 4x + 8 = 12x.
A) No Solutions
B) One Solution
C) Infinite Solutions
A farmer has 180 bushels of wheat to sell at her roadside stand.She sells an average of 14 5/8 bushels each day.Represent the total change in the number of bushels she has for sale after 5 days.
Answer:
Answer:The total change in the number of bushels she has for sale after 5 days is 83.125 bushelsStep-by-step explanation:The given parameters are;The initial number pf bushels the farmer has = 120 bushelsThe amount of bushels of wheat the farmer sells each day = 16⁵/₈ = 16.625 The number of bushels sold after 5 days = 16.625 × 5 = 83.125 bushelsThe total change in the number of bushels she has for sale after 5 days = The number of bushels sold after 5 daysThe total change in the number of bushels she has for sale after 5 days = 83.125 bushels.
Step-by-step explanation:
Find the quotient. Write fractions in simplest form. 1 4/9 divide by -2/9=
Answer: 0.865 to (1dp)
Step-by-step explanation:
In order to solve this equation for x, what expression must be multiplied by each
term?
4/x-1 - 1/ x^2-1= 6/x-1
answers:
A. (x^2-1)
B. (x+1)
C. (x-1)
D. this equation can be solved as is.
E. (x+3/2)
The common factor for the rational expression presented in this problem is given as follows:
A. (x²-1).
How to obtain the greatest common factor of the expression?The rational expression in this problem is given as follows:
4/(x - 1) - 1/(x² - 1) = 6/(x - 1).
It is called a rational expression as it has the variable x in the denominator.
The common factor, which is the expression that multiplies each term, is obtained considering all the terms that are present in the denominators.
The denominators to each term of the expression are listed as follows:
x - 1.x² - 1 = (x - 1)(x + 1) -> subtraction of perfect squares.x - 1.Hence the two terms present in the denominators of the expression are:
(x - 1)(x + 1) = x² - 1 -> subtraction of perfect squares.
Hence option A gives the correct term.
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What do you have to do to
determine which function increases faster when
looking at a table and a graph of two different
functions PLS SOMEONE HELP
To determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].
Rate of Change:
A rate of change describes how an output quantity changes relative to the change in the input quantity. The units on a rate of change are “output units per input units.”
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
[tex]\frac{\triangle y}{\triangle x} = \frac{f(x_{2})-f(x_{1}) }{x_{2}-x_{1}}[/tex]
How to determine:
Given the value of a function at different points, calculate the average rate of change of a function for the interval between two values [tex]x_{1}[/tex] and [tex]x_{2}[/tex].
Calculate the difference [tex]y_{2}-y_{1} = \triangle y[/tex]Calculate the difference [tex]x_{2}-x_{1} = \triangle x[/tex]Find the ratio [tex]\frac{\triangle y}{\triangle x}[/tex]Hence the answer is to determine which function increases faster, we have to find the ratio = [tex]\frac{\triangle y}{\triangle x}[/tex].
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Refer to the table shown below to answer the following question.
Answer: It does not appear to show a function because the numbers are not multiples of each other
Step-by-step explanation: Hope this helps :-)
1. Which of the following numbers has factors that
include the smallest factor (other than 1) of 111?
A. 15
B. 22
C. 28
D. 40
The smallest factor (other than 1) of 111 would be 15.
Option (A) is correct.
What is the smallest factor of a number other than 1?
A number can have a maximum of one factor, and only one has that many factors. Every other number has more than one factor.
Prime numbers have two factors, for example, 2,3,5,7,11...,2729...,2927, 9999959999, and so on. Prime numbers have only one factor the number itself.
The factors of 111 are 1, 3, 37, and 111.
for option (A), the factors of 15 are 1, 3, 5, and 15.
for option (B), the factors of 22 are 1, 2, 11, and 22.
for option (C), the factors of 28 are 1, 2, 4, 7, 14, and 28.
for option (D), the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
So if you observe all the options, the smallest factor (other than 1) of 111 would be 15.
Hence, the smallest factor (other than 1) of 111 would be 15.
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i need help asap show your work
Answer:
G. 12
Step-by-step explanation:
Step 1: Use PEMDAS to start solving
Start solving by following the following:P: ParenthesesE: ExponentsM: Multiplication [or]D: DivisionA: Addition [or]S: Subtraction*Note: After solving any exponents, you solve from left to right. Also, when solving from left to right multiplication or division can be solve; it depends on which one occurs first. The same goes for addition and subtraction; if subtraction occurs before addition, then you subtract first.Step 2: Solve the problem
*Note: Absolute value is considered the same as parentheses.[tex]5-|7-9|+3^{2}[/tex][tex]5-|-2|+3^{2}[/tex]*Note: Absolute value is the distance a number is from zero, so it is always positive.[tex]5-2+3^{2}[/tex][tex]5-2+9[/tex][tex]3+9[/tex][tex]=12[/tex]Find the logarithm of 5.238 with solution
The logarithm of 5.238 with solution is 0.71916549409.
= log(5.238)
= log(5238/1000)
= log(5238) - log(1000)
= 3.71916549409 - log([tex]10^{3}[/tex])
= 3.71916549409 - 3log10
= 3.71916549409 - 3
= 0.71916549409.
Therefore the logarithm of 5.238 with solution is 0.71916549409.
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automotive homework i dont get it
The speed of the output shaft is 182 rpm.
Given:
Gear index i = 0.33
Input speed = 60 rpm.
Let output shaft speed is x.
we know that:
gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]
i = 60/x
0.33 = 60/x
x = 60/0.33
= 60/033/100
= 60*100/33
= 6000/33
= 181.818 ≈ 182 rpm.
Therefore The speed of the output shaft is 182 rpm.
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Given the definitions of f(x) and g(x) below, find the value of (gof)(-2).
f(x) = 3x² – 3x – 7
-
g(x) = -3x - 10
Answer:
(g.f)(-2) = -44
Step-by-step explanation:
Given:
f(x) = 3x² - 3x - 7
g(x) = -3x - 10
[tex] \rm \implies(g.f)( - 2) = [3 {( - 2)}^{2} - 3( - 2) - 7][ - 3( - 2) - 10] \\ \\ \rm \implies(g.f)( - 2) = [3 (4) + 6 - 7][ 6 - 10] \\ \\ \rm \implies(g.f)( - 2) =(12 - 1)( - 4) \\ \\ \rm \implies(g.f)( - 2) =11 \times ( - 4) \\ \\ \rm \implies(g.f)( - 2) = - 44[/tex]
What is the product of 3x(x2 + 4)?
x2 + 3x + 4
3x3 + 4
3x3 + 12x
3x2 + 12x
answer is c 3x3 + 12x
a=4,n=8,7=2,x=10
do anybody know
what the answer
is;l
Answer: The answer to this question would either be 8 or it would be 7.
with explanation if possible.
part c and d
The coordinates to the intercepts of the functions are given as follows:
c - i) Point P: P(-4,0).
c - ii) Point Q: Q(0,2).
d - i) Point P: P(-3,0).
d - ii) Point Q: Q(0,9).
What is the x-intercept of a function?The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.
For item c, the function is:
2y = x + 4.
Hence the x-intercept is obtained as follows:
x + 4 = 0
x = -4.
Then the coordinates of point P are:
P(-4,0).
For item d, the function is:
y = 3x + 9
Hence the x-intercept is obtained as follows:
3x + 9 = 0
3x = -9
x = -3.
Then the coordinates of point P are:
P(-3,0).
What is the y-intercept of a function?The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.
For item c, the function is:
2y = x + 4.
Hence the y-intercept is:
2y = 4
y = 2.
The coordinates of Q are:
Q(0,2).
For item d, the function is:
y = 3x + 9.
Hence the y-intercept is:
y = 3(0) + 9 = 9.
The coordinates of Q are:
Q(0,9).
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…………………………………………/,,/,,..,,.,…….
Answer:
…………………………………………/,,/,,..,,.,…….
Step-by-step explanation:
Answer:.
Step-by-step explanation: .
The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of a type I error is 0.022.
Given,
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.
The null hypothesis is given as "the individual does not have the disease".
We have to find the probability of type l error if the new blood test is used;
Here,
A: The individual does not have the disease
B: The individual does have the disease
We know that,
Type I Error is rejecting the true null hypothesis
Then, probability;
P (Type I Error) = P(Positive reaction to an individual who does not have the disease) = 0.022
That is,
The probability of a type I error is 0.022.
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what is the probability of getting heads twice in a row at some point during three coin flips? assume it is a fair coin where heads and tails are equally likely.
The probability of getting heads twice in a row at some point during three coin flips is 1/8.
Given info;
Assume that a fair coin has an equal chance of coming up heads or tails.
What is the likelihood that three coin flips will result in two consecutive heads at any point?
There is a three-coin flip. The potential results are;
(HHH) (HHT) (HTH) (HTT) (HTT) (THH) (THT) (TTH) (TTT)
1 is the number of successful results.
Probability is calculated as follows: Probability = Number of favorable Results / Total Number of Results = 1/8
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Help please, I don't understand this. And Im being timed
Answer:
3rd choice
No, it is NOT a linear function because the variable x is in the denominator. x will be multiplied by y.
um so like hii,, not school related or anyrhing but ill just like to ask anyone if they know the reason why ur phone (samsung) like randomly delted ur music and photos. yah and ill like to know how u could resolve that from happening again
Answer: Can you check the "Recently Deleted" folder? You may find this in the "My Files" app. If this does not work, and you can confirm you have no backups whatsoever, then your photos are as good as gone. This has happened to Android devices in the past (or Samsung devices mostly) where all their media would just disappear. As far as I know, all Samsung themselves say is to restart your phone to try your luck. An app crashing or some form of corrupt media may have caused your photos to go missing. There may, however, still be a small chance that the photos are there, somewhere on your phone, you just can't find them. I advise checking the storage in "Device Care" and see if the Gallery app is using much storage. If it is, I would connect it to a PC and look through the files again.
Step-by-step explanation:
Please help me with this and also remember your answer has to be step by step
The two figures above are congruent. Find the measure of the angle that isn't labeled on either figure.
The measure of the angle that isn't labeled are:
∠B = 100
∠K = 100
∠L = 41
∠M = 86
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
Two congruent figures.
Each figure's total sum of the angles must be 360.
The figures are congruent so the corresponding angles must be equal.
From the first figure we get,
∠A = 133 ( Corresponding angles )
∠A + ∠B + ∠C + ∠D = 360
133 + ∠B + 41 + 86 = 360
∠B = 360 - 260
∠B = 100
Now,
∠k = ∠B = 100
∠L = ∠C = 41
∠M = ∠D = 86
Thus,
The measure of the angle that isn't labeled are:
∠B = 100
∠K = 100
∠L = 41
∠M = 86
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A school of 38 teachers has 15 married women. If 6 of the teachers are couples, how many of the teachers are neither married nor have their spouses not in the school?.
Answer:
17
Step by step explanation
15-6=21
38-21=17
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 9)(0,9) and (3, 576)(3,576).
What's the answer to 1 1/2 + 3/4
Cyclical Unemployment Rate = 1%
Natural Unemployment Rate = 6%
What is the Actual Unemployment rate?
The Actual Unemployment rate is 7%.
What is unemployment?Unemployment simply means a scenario where those who are willing and able to work can't find suitable jobs.
Cyclical Unemployment Rate = 1%
Natural Unemployment Rate = 6%
The Actual Unemployment rate will be:
= Cyclical Unemployment Rate + Natural Unemployment Rate
= 1% + 6%
= 7%
The unemployment is 7%.
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Graph the linear inequality below.
y ≤ x -5
To see the attachment of graph of linear inequality.
Given,
In the question:
The linear inequality is given as:
y ≤ x -5
To graph the above inequality.
Now, According to the question:
What is linear inequality?
Inequality represents the mathematical expression in which both sides are not equal. If the relationship makes the non-equal comparison between two expressions or two numbers, then it is known as inequality in Math. In this case, the equal sign “=” in the expression is replaced by any of the inequality symbols such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤) or not equal to symbol (≠). The different types of inequalities in Math are polynomial inequality, rational inequality, absolute value inequality.
Hence, To see the attachment of graph of linear inequality.
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Can someone help me please with these problems, please and thank you
1) If 7 donuts cost $6.09, how many donuts would you get for $20.88?
2) $20 is equivalent to 389.10 Mexican pesos. How many dollars would you get for 1500 pesos?
Answer:
1. 3 donuts
2.$76.90
Step-by-step explanation:
assistance I'm stumped it is a very hard question for me answer correct first and be awarded the brainlyest.
Answer:
u = 2
Step 1: Simplify both sides of the equation.
−7u −u +2u +11u = 10
−7u +−u +2u +11u = 10
(−7u +−u +2u +11u) = 10 (Combine Like Terms)
5u = 10
Step 2: Divide both sides by 5.
5u/5 = 10/5
Hope this helped!
X+62+x+9=180 help please
Answer:
x=54.5
Step-by-step explanation:
x+62+x+9=180
2x+71=180
2x+71-71=180-71(subtract 71 from both sides)
2x=109
2x/2=109/2(divide both sides by 2)
x=54.5
Answer:
x=54.5
Step-by-step explanation:
1. Combine like terms
x+62+x+9=180
2x+71=180
You can only combine the x and 62 and 9 in this equation.
2. Subtraction property of equality
2x+71=180
-71 = -71
2x=109
Subtract 71 from both sides to isolate the variable, x.
3. Division property of equality
2x=109
/2 /2
x=54.5
Hope this helps!
Please someone help me with this question my exams in a few days
Answer:
see explanation
Step-by-step explanation:
(i)
using Pythagoras' identity in the right triangle
the square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
(k + x)² = m² + (k - x)² ← expand factors on both sides using FOIL
k² + 2kx + x² = m² + k² - 2kx + x² ( add 2kx to both sides )
k² + 4kx + x² = m² + k² + x² ( subtract k² + x² from both sides )
4kx = m² ( divide both sides by 4k )
x = [tex]\frac{m^2}{4k}[/tex]
----------------------------------------------------------
(ii)
the area A of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = m and h = k - x
A = [tex]\frac{1}{2}[/tex] m (k - x) ← substitute x = [tex]\frac{m^2}{4k}[/tex]
= [tex]\frac{1}{2}[/tex] m ( k - [tex]\frac{m^2}{4k}[/tex] ) ← distribute parenthesis
= [tex]\frac{mk}{2}[/tex] - [tex]\frac{m^3}{8k}[/tex] ← express as a single fraction
= [tex]\frac{4mk^2-m^3}{8k}[/tex] ← factor out m from each term in the numerator
= [tex]\frac{m(4k^2-m^2)}{8k}[/tex] ← factor (4k² - m² ) as a difference of squares
= [tex]\frac{m(2k+m)(2k-m)}{8k}[/tex]