the first derivative of the given function is:
f'(x) = (2x²- 12x - 2)/( 2x² - 2)²
How to find the derivative?
The quotient rule says that, if f(x) = g(x)/h(x), then:
f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²
In this case we know that:
g(x) = x² + x - 2
h(x) = 2x² - 2
The derivatives are:
g'(x) = 2x + 1
h'(x) = 4x
Replacing that we get:
f'(x) = ( g'(x)*h(x) - g(x)*h'(x) )/h(x)²
= ( (2x + 1)*(2x² - 2) - ( x² + x - 2)*(4x) )/( 2x² - 2)²
Expanding the denominator we get:
f'(x) = ( 4x³ - 4x + 2x² - 2 - 4x³ + 4x² - 8x)/( 2x² - 2)²
f'(x) = (2x²- 12x - 2)/( 2x² - 2)²
That is the first derivative of the given function.
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A store has clearance items that have been marked down by 60% they are having a sale advertising an additional 30% off clearance items. What percent of the original price do you end up paying?
Someone help with this too pls
Answer:
the answer is 18 months==1 year 6 months
THIS IS IMPORTANT
Where can you find the pulse that is closest to your head?
elbow
wrist
neck
foot
Answer:
Neck
Step-by-step explanation:
Which one is closest to your head?
T-T
If the big, green rectangle represents 1 whole, then what part of the whole is the shaded, gold
rectangle?
14
2 3
4
5
State your answer as a fraction.
6
The fraction that represents the part of a whole, which is shaded gold is 3/7.
What is fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole.
Given is a big green rectangle divided into seven equal segments. From the image, it can be seen that 3 segments out of the seven are colored with gold. Therefore, we can write that -
Number of segments colored = n[c] = 3
Total segments = n[T] = 7
We know that a fraction defines a part of a whole. The green Rectangle is one whole, therefore it can be concluded that -
1 whole = 7 segments = n[T].
Number of segments colored = n[c] = 3.
Therefore, we can say that the fraction that represents the part of a whole, which is shaded gold is given by -
n[c] / n[T] = 3 / 7
Therefore, the fraction that represents the part of a whole, which is shaded gold is 3/7.
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[The given question is not complete. Please refer to the image attached for complete question]
-x-6=-14 how to solve x
Answer:
x=8
Step-by-step explanation:
-x-6=-14
-x=6-14
x=14-6
x=8
pls answer if wrong i ban you
The coordinates of L are: (8,-4)
Here, triangle is rotated 270° counterclockwise. So the rule that we have to apply here is
(x, y) → (y, -x)
Based on the rule given in step 1, we have to find the vertices of the rotated figure.
(x, y) → (y, -x)
L(4,8) → L'(8.-4)
M(4,3) → M'(3,-4)
N(8,8) → N'(8,-8)
Vertices of the rotated figure are:
L'(8.-4) M'(3,-4) N'(8,-8)
Hence we get the desired result.
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Real number root for V-49
Step-by-step explanation:
there is no real number solution for the square root of a negative number.
a sqare root multiplied by itself had to deliver exactly the number inside the square root.
so for sqrt(-49), what can be the answer ?
which number multiplied by itself gives -49 ?
it any negative number at that.
because
a × a = a²
and
-a × -a = a² but definitely not -a².
we get a negative number only, when we multiply a positive number with a negative number or vice versa.
the only solution is complex or imaginary (based on the imaginary number i):
i² = -1
i = sqrt(-1)
so, sqrt(-49) = sqrt(49 × -1) = 7×sqrt(-1) = 7i
but again, no real solution.
Someone help with this too pls
The answer is 18 months as per the asked question and visible graph
Step-by-step explanation:
Find $900 and follow the horizontal line until it touches the red tilted line
As soon as it touches the red line, go down vertically and find where the line leads you and voila, it leads you to 18 months!
Point A is located at (2,-2) on the coordinate plane. Point A is reflected over the Y-
axis to create point A'. Point A' is then reflected over the x-axis to create point A".
What ordered pair describes the location of A"?
Answer: A''=(-2, 2)
Step-by-step explanation:
A' = (2, -(-2)) = (2,2) ==> the y-coordinate is negated when A reflects over the y-axis
A''=(-(2), 2) = (-2, 2). ==> the x-coordinate is negated when A reflects over the x-axis
A''=(-2, 2)
*Please help*
Xavier bought a new boat for $24,000 in the year 2009. He knows that the value of the boat has depreciated linearly. If the value of the boat in 2010 was $18,500, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.
Answer:
5500 is correct Answer.
Please mark me as brainlist answer.
if this is solved you will be awarded a high mark prove the following formula 1 + sec²=cot²
This relationship is not true.
[tex]1 + \sec^2(x) = 1 + (1 - \tan^2(x)) = 2 - \tan^2(x)[/tex]
and
[tex]\cot^2(x) = \dfrac1{\tan^2(x)}[/tex]
Rewrite the equation in terms of only tangent.
[tex]2 - \tan^2(x) = \dfrac1{\tan^2(x)} \iff \tan^4(x) - 2\tan^2(x) + 1 = 0[/tex]
Factorize the left side.
[tex]\left(\tan^2(x) - 1\right)^2 = 0[/tex]
Solve for [tex]\tan(x)[/tex].
[tex]\tan^2(x) - 1 = 0[/tex]
[tex]\tan^2(x) = 1[/tex]
[tex]\tan(x) = \pm 1[/tex]
[tex]x = \pm\tan^{-1}(1) + n\pi = \pm\dfrac\pi4 + n\pi[/tex]
where [tex]n[/tex] is an integer. That is, the equation only holds for certain values of [tex]x[/tex], as opposed to all [tex]x[/tex], so it's not an identity.
solve for u.
(u-7) (u - 13)=0
Answer:
u = 7 OR u = 13
Step-by-step explanation:
Using the zero property of multiplication, you know you have to make either u-7 or u-13 equal to zero. You get the two solutions from these two cases, where you make either of the equations equal to 0:
u - 7 = 0
Add 7 to both sides
u = 7
u - 13 = 0
Add 13 to both sides
u = 13
FINAL ANSWER: u = 7 OR u = 13
Makayla and Nathan both leave the library at the Same time, but in opposite directions. If Nathan travels 8 mph faster than makayla and after 6 hours they are 192 miles apart, how fast is each traveling?
The speed of Makayla and Nathan are 12 mph and 20 mph respectively.
What is relation between speed and time?A moving body's speed is the distance it travels in one unit of time. If the distance is in kilometers and the time is in hours, the speed is in kilometers per hour. If the distance is expressed in meters and the time is measured in seconds, the speed is measured in meters per second.Let the speed of Makayla is 'x' mph.
and the speed of Nathan is 'y' mph.
The total distance travelled by both is 129 miles.
The time taken by each is 6 hours, same for both.
Speed = distance / time
Distance = speed × time
Makayla's covered distance = xt
Nathan's covered distance = yt
Total distance = xt + yt
xt + yt = 192
As, Nathan travels 8 mph faster than makayla.
The,
y = x + 8, t = 6 hours substitute;
xt + (x+ 8)t = 192
2x + 8 = 192/6
On simplification;
x = 12 mph (Makayla's speed)
Y = x + 8
y = 12 + 8
y = 20 mph (Nathan's speed)
Therefore, the speed of Makayla and Nathan are x = 12 mph and y = 20 mph respective;y.
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Challenge The temperatures at sunrise and sunset
are shown in the table. What was the temperature
change on each day? On which day did the
temperature change the most?
Day 1
Day 2
Daily Temperatures
Temperature at Temperature at
Sunrise (°C) Sunset (°C)
- 13.94
- 9.12
18.37
28.17
What was the temperature change on Day 1?
°C
(Simplify your answer. Type an integer or decimal rounded to the nearest hundredth as needed.)
1. The temperature change on each day is as follows:
Day 1 = 32.31°CDay 2 = 37.29°C2. The temperature change on Day 1 was 32.31°C.
3. The temperature changed the most on Day 2.
What is a temperature change?A temperature change is a process whereby the degree of hotness or coldness varies from one time to another.
In this instance, the temperature changes can be computed by subtracting the temperature at Sunrise from the temperature at Sunset in degrees Centigrade or degrees Fahrenheit, as the case may be.
Data and Calculations:Daily Temperatures
Temperature at Temperature at Temperature
Sunrise (°C) Sunset (°C) Change
Day 1 - 13.94 18.37 32.31°C
Day 2 - 9.12 28.17 37.29°C
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An appliance store decreases the price of a 19-In television set 29% to a sale price of $442.69. What was the original price?
Answer:
$623.50
Step-by-step explanation:
(100 - 29)% = 71%
71% = 71 / 100 = 0.71
Original price:
442.69 / 0.71 = 623.50
Hope this helps
Laura is completing a 15-week exercise program where she increases the amount of time she works out by the same amount. She exercised 20 minutes per day the third week, 50 minutes per day the ninth week, and 60 minutes per day the eleventh week.
What is the function that represents the sequence?
The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.
It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.
Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.
Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.
Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.
Thus, An = A + [(n-1)*d]
A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)
A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)
A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)
Solving equation (1) and (2), we get d = 5 and A = 10.
Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.
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Please solve for meeee
Answer: 58 degrees
Step-by-step explanation:
a+b=90 ==> angles a and b are on a right angle which measures 90 degrees.
32+b=90
b=58 degrees
5. Tad needs to measure where the free-
throw line should be in front of his
basketball goal. He knows his feet are
1 1/8 feet long and the free-throw line
should be 15 feet from the backboard.
How many toe-to-toe steps does Tad
need to take to mark off 15 feet?
10.i
A basketball court has symmetry; one half of the court is a mirror image of the other. The entire basketball court ( is 94 feet by 50 feet. On each half-court, painted lines show the free throw lane and circle, as well as the three-point arc, whose distance from the basket varies based on the level of hoops being played.
The borders of the court have their own commonsense names:
Along the length of the court, the borders are the sidelines.
Along the ends, the borders are the endlines, or baselines.
Separating both halves of the court is a midcourt line.
In the very center of the midcourt line is the center circle (12 feet in diameter), where the center toss takes place to begin the game.
The free throw lane is the hub of the action in each half-court. This rectangle is 12 feet wide — 16 feet at the men's pro level. Its length, as measured from the basket to the free throw line, is 15 feet at all levels. An offensive player may not stand inside the lane for more than three seconds unless he or one of his teammates is shooting the ball. After a shot is taken, the count starts over again. A defensive player may remain inside the lane for as long as he desires.
A player fouled by another player sometimes receives free throws, also known as foul shots. She takes these shots (they aren't really "throws") from the free throw line at the end of the lane — 15 feet from the basket. The shots are "free" because a defender does not guard the shooter .The remaining players line up alongside the free throw lane (or behind the shooter) and cannot interfere with the shot. They line up in order, on either side of the lane, of defense-offense-defense-offense. (Up to four players may stand on one side of the lane.) If a player opts not to take a spot (say, for example, the second defensive spot), then a player from the opposing team is permitted to step into that spot. The fans behind the basket usually scream, jump up and down, and wave their hands to try to distract an opposing team's shooter during free throws.
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Foundational Concepts Unit Test
22. What is the simplified form of the following expression? (1 point)
11[(92-52)+2248]
0224.5
0242
051.3
0110
The simplified form of the following expression is 51.3.
Given,
11(9²-5²)/(2²+8)
= 11(81-25)/(4+8)
= 11(56)/(12)
= 51.3
Expressions are simplified when they are rewritten in a concise manner and without any similar phrases. When simplifying an expression, we combine all similar terms and, if necessary, solve all of the supplied brackets, leaving just the, unlike words that cannot be further reduced.
Combining like terms together and leaving unlike terms alone is the fundamental principle for simplifying phrases. The following is a list of some of the guidelines for simplifying expressions:
Add the coefficients of two or more similar terms together, then include the common variable in the equation.
In the phrase a (b + c) = ab + ac, open the brackets using the distributive property.
Change the sign of all the phrases placed inside that bracket if there is a negative sign right outside the parenthesis to make things simpler.
Simply remove the bracket and put the words as they are, keeping the terms' original signs if there is a "plus" or other positive sign outside of it.
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Tanisha mowed five lawns last week she mowed each one and 712 hour she wrote the same ones this week in 5/12 hour using her lawnmower how many times longer was tanisha’s Time to mow all the lawns last week and this week express your answer as an improper fraction
Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.
Here, we are given that Tanisha mowed 5 lawns last week in 7/ 12 hours each.
Thus, the total time taken by her to mow 5 lawns = 5(7/12)
= 35/ 12 hours
Now, this week she mows the five lawns in 5/12 hours each
Thus, the total time taken by her = 5(5/12)
= 25/12 hours
Therefore, the difference between the time taken by her last week and this week will be-
35/ 12 - 25/ 12
= (35 - 25)/ 12
= 10/ 12
= 5/6
Thus, Tanisha takes 5/6 hours longer to mow all the lawns last week than this week.
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At Elmo's, an old-fashioned barber shop in Melbourne, Florida, 66% of all customers get a haircut, 49% get a shave, and 40% get both.
a) What is the probability that a randomly selected person doesn't get a shave and doesn't get a haircut? Your answer should have at least 3 decimal places.
b) What is the probability that a randomly selected person gets a shave, given that they get a haircut? Your answer should have at least 3 decimal places.
The probability that a randomly selected person doesn't get a shave and doesn't get a haircut is 0.250.
The probability that a randomly selected person gets a shave, given that they get a haircut is 0.606.
What is the probability?The probability that a person selected at random would not get a shave or a haircut can be found as:
= 1 - (Prob. of haircut + Prob. of shave - Prob. of both)
= 1 - (0.66 + 0.49 - .40)
= 0.250
The probability that a random person would get a shave given they have gotten a haircut is:
= Probability of both / Probability of getting a haircut
= 0.40 / 0.66
= 0.606
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What is the y intercept of the line
Answer:
2 is the y-int.
Step-by-step explanation:
Becuase the line runs through the y-axis at 2.
Is this a function or not. Then state domain and range. WILL GIVE BRAINLEIST
Answer:
Yes
Step-by-step explanation:
It is a function look at the numbers
The percent of 12th graders in a certain state who have ever used cigarettes for each of the years 2000 through 2014 can be modeled by p= -1.773t+60.442, where p is equal to the percent
and t is equal to number of years after 2000. When will the percent be less than 30 %?
The percent will be less than 30% after the year
(Round to the nearest year as needed.)
example Get more help -
The percent will be less than 30% after the year 2017
Let 'p' be the percent of 12th graders in a certain state who have ever used cigarettes for each of the years 2000 through 2014.
Let 't' be the number of years after 2000.
We have to find when the percent is less than 30%.
The function modelling the percent and the number of years through 2000 and 2014 is p= -1.773t+60.442
So first we need to find the number of years corresponding to 30%.
Substitute p = 30 in the above linear equation.
i.e., 30 = -1.773t+60.442
-1.773t = 30 - 60.442 = -30.442
Therefore, t = 30.442/1.773 = 17.17 ≈ 17 years
Since t denotes the number of years after 2000, when t = 17, the year is 2000+17 = 2017
So the percent will be less than 30% after the year 2017
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Find the distance between X(-2,4) and Y(6,1)
Answer:
Exact Distance = [tex]\boldsymbol{\sqrt{73}}[/tex] units
Approximate Distance = 8.544 units
====================================================
Explanation:
I'll relabel the points as A and B, and I'll be using the distance formula.
[tex]A = (x_1,y_1) = (-2,4) \text{ and } B = (x_2, y_2) = (6,1)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-2-6)^2 + (4-1)^2}\\\\d = \sqrt{(-8)^2 + (3)^2}\\\\d = \sqrt{64 + 9}\\\\d = \sqrt{73}\\\\d \approx 8.544\\\\[/tex]
The exact distance is [tex]\sqrt{73}[/tex] units.
The approximate distance is roughly 8.544 units.
Round the approximate value however your teacher instructs.
Which is the value of this expression when m-3 and n=-5
Answer:
1/8
Step-by-step explanation:
(6m^-1n^0)^-3 =
= (6 × 1/3 × (-5)^0)^-3
= (6/3)^-3
= 2^-3
= 1/2^3
= 1/8
A startup sports public relations company is looking to grow. They currently represent 1 client and plan on representing 2 additional clients each year. The following graph can be used to
help determine the number of clients, y, the company will have after x years.
Based on the context, what is the range of the function?
Answer:
Step-by-step explanation: 1x,2y
Expand and simplify (5x - 2)^2
Answer:
The value of x = 2/5
Step-by-step explanation:
=>(5x - 2)²
=> (5x)² + 2² - 2(5x)(2)
=> 25x² -20x +4
=> 25x² -10x -10x +4
=> (5x-2) (5x-2)
=> x = 2/5 or 2/5
Write the first trigonometric function in terms of the second for in the given quadrant. (No theta symbol so used word)
sec(theta), tan(theta); theta in Quadrant IV
sec(theta) =
The expression of [tex] \mathbf{sec( \theta)}[/tex] in terms of [tex]tan( \theta)[/tex] in Quadrant IV is presented as follows;
[tex] sec( \theta) = \sqrt{{tan( \theta)}^{2} + 1} [/tex]
Which trigonometric identity can be used to express the required function?The given trigonometric functions are;
[tex]sec( \theta)[/tex]
[tex]tan( \theta)[/tex]
[tex] {sec( \theta)}^{2} = {tan( \theta)}^{2} + 1[/tex]
In Quadrant IV, the tangent of an angle is -ve, while the secant is +ve
However, the square of -ve is positive;
(-ve)² = +veTherefore;
[tex] \left({tan( \theta)}^{2} + 1 \right) \: is \: positive[/tex]
Which gives;
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Autumn has $.64 worth of pennies and nickels. She has a total of 20 pennies and nickels all together. Determine the number of pennies in the number of nickels that Autumn has.
The number of pennies and nickels are 9 and 11 respectively.
How to find the number of pennies and nickels?Autumn has $.64 worth of pennies and nickels. She has a total of 20 pennies and nickels all together.
Therefore,
let
x = number of pennies
y = number of nickels
Hence,
x + y = 20
0.01x + 0.05y = 0.64
Multiply equation(i) by 0.01
0.01x + 0.01y = 0.2
0.01x + 0.05y = 0.64
0.04y = 0.44
y = 0.44 / 0.04
y = 11
Therefore,
x = 20 - 11
x = 9
Therefore, the number of pennies and nickels are 9 and 11 respectively.
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