if h(x)=x+2/x-2, then dy/dx=? A. x-2 B. -5/2 C. 1/(x-2)². D. none
Answers
1/(x-2)². The correct option is C
What is quotient rule ?The quotient rule is a formula used in calculus to find the derivative of a function that is the quotient of two other functions. Specifically, it gives the formula for finding the derivative of a function of the form f(x) = g(x) / h(x), where g(x) and h(x) are both functions of x.
We can use the quotient rule to find the derivative of h(x):
h(x) = (x+2)/(x-2)
h'(x) = [ (x-2)(1) - (x+2)(1) ] / (x-2)^2 (apply quotient rule)
Simplifying the numerator, we get:
h'(x) = [ x-2 - x-2 ] / (x-2)^2
h'(x) = -4 / (x-2)^2
Therefore, the answer is (C) 1/(x-2)².
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Related Questions
Fill 4x4 squares with 1-16 so that the sum of each row and column is a prime number
Answers
Help me out with this one guys
(10 points)
Answers
p is all real number
r has no solution
everybody go to the chrome web store and report Securly lets get it baned
Answers
Answer:
Ok will do so.
Step-by-step explanation:
Later tell me why you want to get it banned but ima report it.
A line passes through the point (10,-8) and has a slope of -1/2. Write an equation in slope-intercept form for this line
Answers
y - 9 = -8x - 32
y = -8x - 23
A person's blood pressure (in millimeters of mercury) while resting is given by the function (1) = 23 sin (2xt) + 100, where t is time in seconds. Find his blood pressure after 1 second
Answers
Does tha 1 in the equation represent the second
Step-by-step explanation:
Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Which measurement is closest to the side length of this canvas in inches? 8 in. 9 in. 19 in. 39 in. say the number and tell me why you got it.
Answers
Answer:
9 inStep-by-step explanation:
Since the square canvas was completely covered using 77.8 in.² of fabric without any overlap, to get the side length of the canvas, we will use the formula for calculating the area of a square.
Area of a square = Length * Length
A = L*L
A = L²
Given the Area of the area of the square canvas as 77.8 in², on substituting this values into the formula to get L we have;
77.8 = L²
Take the square root of both sides
√77.8 = √L²
L = √77.8
L = 8.82 in
L ≈ 9inches
The length 8.82in gotten was approximated to 9in because the first value after the decimal point is greater that 4 and once we have such case 1 will be added to the value before the decimal point i.e 8 to make it 9.
Hence measurement that is closest to the side length of this canvas in inches is 9inches.
What is the y-intercept of y = 5
Answers
Answer:
(0,5)
Step-by-step explanation:
We know that x will equal 0
because y=5 is a horizontal line running through 5 on the y axis, we know that the y intercept will be (0,5)
Brainliest to whoever gets this correct , Describe the end behavior of the following function:
Answers
Answer:
graph starts high and ends high
Expand binomial using binomial expansion (x-y)^3
Answers
The expression is,
\((x-y)^3\)Expanding the expression we get,
\((x-y)^3=(x-y)(x-y)^2\ldots.(1)\)We have,
\((x-y)^2=x^2-2xy+y^2\ldots..(2)\)Substituting equation 2 in equation 1, we get,
\(\begin{gathered} (x-y)^3=(x-y)(x^2-2xy+y^2) \\ \text{ =}x(x^2-2xy+y^2)-y(x^2-2xy+y^2) \\ \text{ =}x^3-2x^2y+xy^2-yx^2+2xy^2-y^3 \\ \text{ =x}^3-y^3+3xy^2-3x^2y \end{gathered}\)Yesterday, Jack drove 20 miles in his car. Today, Jack drove 15 miles in his car. What is the percent decrease of the time spend driving the car?
Answers
The percentage change will be 25%.
What is the percentage?According to its definition, a percentage is any number relative to 100. It is shown with the sign %. "Out of 100" is what the percentage means. Consider dividing any quantity or item into 100 identical bits.
Using these estimates, we can calculate the per cent decrease in the time spent driving as follows:
The initial time spent driving was 0.5 hours.
The final time spent driving was 0.375 hours.
The decrease in time spent driving was 0.5 - 0.375 = 0.125 hours.
The per cent decrease in time spent driving is,
P = (0.125/0.5) x 100%
P = 25%.
Therefore, we can estimate that the per cent decrease in the time Jack spent driving his car is 25%.
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Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
Answers
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Answers
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
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im falling asleep at the kitchen table bc i have not slept in 3 days and i cant go to bed until its 8 or 9 and its 5:56pm ughhh
Answers
Answer:
I hope u can sleep more
Step-by-step explanation:
Answer:
ohhhhhhh
Step-by-step explanation:
yea that sucks but why can't you go to bed until 8-9?????
USE A MODEL Olivia and her brother William had a bicycle race. Olivia rode at a speed
of 20 feet per second, while William rode at a speed of 15 feet per second. Olivia gave
William a 150-foot head start and the race ended in a tie.
How far away was the finish line from where Olivia started
Answers
Answer:
Step-by-step explanation:
The distance from where Olivia started to the finish line is 600 foot
How determine how far away was the finish line from where Olivia started?
A model function is a way of describing a real-life system or situation using mathematical concepts and language
If Olivia rode at a speed of 20 feet per second, while William rode at a speed of 15 feet per second. Olivia gave William a 150-foot head start.
We can write write a linear model function for both Olivia and William as follows:
Olivia: y = 20x
William: y = 15x + 150
where y is the distance and x is the time taken to reach finish line
Since the race ended in a tie (i.e. draw), we can equate the two functions:
20x = 15x + 150
20x -15x = 150
5x = 150
x = 150/5
x = 30 seconds
Thus, the distance from the finish line to where Olivia started can be determined by substituting x = 30 into y = 20x. That is:
y = 20(30) = 600 foot
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This Venn diagram shows the pizza topping preferences for 9 students. Petal Owen LIKES PEPPERONI Joe Kalie Noah Let event A = Student likes pepperoni. Let event B = Student likes olives. What elements are in A and B? Maria Zack A. (Bo, Petal, Owen} B. (Bo, Petal, Owen, Julia) C. (Joe, Kalie, Noah, Maria, Zack, Julia) D. {Maria, Zack} OLIVES Julia
Answers
Answer:
Option D
Step-by-step explanation:
We have to find out the students who like both pepperoni and olives.
The part, which is in dark green, is the collection of students who like pepperoni and olive.
So, it is Maria and Zack
will give brainliest but it Has to be correct.
Measure the thumbtack to the nearest inch.
6/8 inches
7/8 inches
3/8 inches
5/8 inches
Answers
Answer: 6/8 inch
Step-by-step explanation:
0.25(60) + 0.10x = 0.15(60 + x)
Answers
Answer: X = 120
Step-by-step explanation:
lol:
V = (−∞,∞)
X = 120
What is the ratio of the leg opposite the angle to the leg adjacent to the
angle.
Answers
Answer:
tangent (angle) or tan (angle)
Step-by-step explanation:
tangent (angle) = the leg opposite the angle / the leg adjacent to the angle
A circle has a radius of 30 cm and a central angle that measures 312 degrees. Find the length of the arc defined by this central angle
Answers
The length of the arc defined by the central angle of 312 degrees is 26π cm.
The formula for the arc length of a circle is given by:
L = (θ/360) × 2πr
where L is the length of the arc, θ is the central angle in degrees, and r is the radius of the circle.
Substituting the given values, we get:
L = (312/360) × 2π(30)
L = (26/30) × π × 30
L = 26π cm
Therefore, the length of the arc defined by the central angle of 312 degrees is 26π cm.
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8) A car wash had to make their soap last 9 days. If they only have one-ninth of a gallon of soap, how much should they use each day so it lasts 9 days?
Answers
Answer:
9/81
Step-by-step explanation:
Because 1/9 is all they have so they need to reduce usage by nine so divide by nine It probably wrong tho srry :(
Answer:
2/81
Step-by-step explanation:
it says that 1/9 gallon has to be used over 9 days, so you would divide 1/9 by 9, which is basically multiplying 1/9 and 1/9, because you flip the second fraction around when dividing. 1/9 x 1/9 is 2/81, and it is already in simplest form, therefore the answer is 2/81 of a gallon. hope this helped
a) b) QUESTION I Use a protractor to measure the size of angle 9 and a ruler to measure the length of AB and BC in each case. (a) A 8 B What do you notice? (b) Complete the statements: The line drawn from the centre of a circle will be The line drawn from the centre of a circle O the chord. 0 B A to the chord.
Answers
(a) When measuring angle 9 and the lengths of AB and BC, one observation is required.
(b) The line drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord, while the line drawn from the center of a circle to an endpoint of a chord bisects the chord.
a) In the given diagram, we have angle AOB (angle 9) and line segments AB and BC.
To measure angle 9, we use a protractor. We align the baseline of the protractor with the line segment OA, ensuring that the center point of the protractor coincides with the vertex O. Then, we read the degree measurement where the line segment OB intersects the protractor. Let's assume the measurement of angle 9 is x degrees.
To measure the length of line segments AB and BC, we use a ruler. We align the ruler with the line segments and read the length in units (e.g., centimeters or inches).
b) The statements to complete are:
(i) The line drawn from the center of a circle to the midpoint of a chord will be perpendicular to the chord.
(ii) The line drawn from the center of a circle to the endpoint of a chord will bisect the chord.
In a circle, the center of the circle lies on the perpendicular bisector of any chord. This means that if we draw a line from the center of the circle to the midpoint of a chord, it will be perpendicular to the chord (statement i). Similarly, if we draw a line from the center of the circle to one of the endpoints of the chord, it will bisect the chord into two equal parts (statement ii).
These properties hold true for any chord in a circle, and they are based on the geometric properties of circles and perpendicular bisectors.
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The sum of two numbers is 21. The second number is six times the first number. Work out the two numbers. Write your answer on one line
Answers
Answer:
Step-by-step explanation:
a +B=21 B=6a a+6a=21 7a=21 a=21:7 a=3 b=6x3 b=18
If x=1 in the equation below, what does y equal? 3x+2y=9
Answers
Answer:
y=3
Step-by-step explanation:
3x+2y=9
Let x =1
3*1+2y=9
3 +2y = 9
Subtract 3 from each side
3-3+2y=9-3
2y = 6
Divide each side by 2
2y/2 = 6/2
y =3
Chevy and 167 mile bicycle trip to build up stamina for a triathlon competition unfortunately his bicycle chain broke so he finished a trip walking the whole trip took six hours if Jim walks at a rate of 4 mph and rides at 30 mph find the amount of time he spend
on the bicycle
Answers
The amount of time Chevy spent on the bicycle is 5.5hours or 5 hours 30 minutes.
Given that:-
Total distance = 167 miles
Speed of bicycle = 30mph
Speed of Chevy walking = 4 mph
Total journey time = 6 hours
We have to find the amount of time Chevy spent on the bicycle.
Let the time spent on bicycle be x hours and,
Let the time spent on walking be y hours
Hence, we can write,
30x + 4y = 167 ... (1)
Also,
x + y = 6 ... (2)
Multiplying (2) by 4, we get,
4x + 4y = 24 ...(3)
(1) - (3), Using elimination method, we get
(30x - 4x) + (4y - 4y) = 167 - 24
26x + 0 = 143
x = 143/26 = 11/2 =5.5 hours = 5 hours 30 minutes.
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These shapes are similar.
Find X.
5
X
5
30
24
30
Answers
The value of x is 4.
To determine the value of x, we can use the concept of similarity between shapes.
Similar shapes have corresponding sides that are proportional to each other.
Given the dimensions of the first shape as 5, x, and 5, and the dimensions of the second shape as 30, 24, and 30, we can set up the following proportion:
5/x = 30/24
To solve for x, we can cross-multiply:
30 · x = 5 · 24
30x = 120
Dividing both sides of the equation by 30:
x = 120 / 30
x = 4
Therefore, the value of x is 4.
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help me 10 pnts thanks so much
Answers
The expression 3.2^2 - 1 and 10 - 0.33 * 2 should be joined by less than to form an inequality
What is inequality?Inequality refers to a way of representing relationships between variables at the left hand side of equation to the variables to the right hand side of an equation.
The signs used in inequality are of 4 types namely
less thangreater thanless than or equal togreater than or equal toThe given expression is solved as follows
3.2^2 - 1
= 10.24 - 1
= 9.24
10 - 0.33 * 2
= 10 - 0.66
= 9.34
The two expressions can be joined as below
9.24 < 9.34
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Sophia cuts two pieces of ribbon for a craft project. The first ribbon is 7.74 cm long. The second ribbon is 9.281 cm long.
What is the total length of the two ribbons if she lines them up end to end?
Answers
Answer:
17.021 CM
Step-by-step explanation:
7.74 +9.281 = 17.021
Answer:
17.021 CM
Step-by-step explanation:
Carson is g years old Haley is 2 yrs younger then Carson. find the sum of their ages in terms of g
Answers
Answer:
2g-2
.....................
Answer
2g -2
Step-by-step explanation:
Carson is =gHarley = 2-gThe difference of two numbers is 14. The sum of those numbers is 32,
Write a system of equations to represent the scenario.
Answers
Answer:
step explanation: 16+ 16 = 32
please find the p-value
Answers
The statistical analysis of the data using a two-sample t-test indicates;
(a) B. Yes, the Meters On data appears to have higher speeds
A. No, there does not appear to be any outlier
(b) H₀; \(\mu_{on}\) = \(\mu_{off}\)
H₁; \(\mu_{on}\) > \(\mu_{off}\)
The P-value for the test is about 0.037
What is a two-sample t-test?A two-sample t-test is used to determine if there is a difference between the means of two independent groups of data.
(a) The average of the data values are;
Ramp meters on;
\(\mu_{on}\) = (29+47+55+38+32+25+42+47+51+36+55+41+43+25+47)/15 ≈ 40.87
\(\mu_{off}\) = (25+25+43+35+36+31+48+37+19+29+22+40+36+50+40)/15 ≈ 34.4
The higher average value for the speed with the Ramp meters on indicates;
B. Yes, the Meters On data appears to have higher speeds
The five number summary are;
Ramp Meters On
Min = 25, Max = 55, Q₁ = 32, Q₂ = 42, Q₃ = 47
IQR = 47 - 32 = 15
Outlier = 47 + 1.5 × 15 = 69.5
32 - 1.5 × 15 = 9.5
Therefore, there are no outliers for the Ramp Meters On
Ramp Meters Off
Min = 19, Max = 50, Q₁ = 25, Q₂ = 36, Q₃ = 40
IQR = 40 - 25 = 15
Outlier = 40 + 1.5 × 15 = 62.5
25 - 1.5 × 15 = 2.5
Therefore, there are no outliers for the Ramp Meters Off data
(b) The null hypothesis is; H₀; \(\mu_{on}\) = \(\mu_{off}\)
The alternative hypothesis is; H₁; \(\mu_{on}\) > \(\mu_{off}\)
(c) The two sample t-test, can be obtained using the formula;
\(t_{cal} = \frac{(\bar{x}_1 - \bar{x}_2)}{\sqrt{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} ) } }\)
Where; \(\bar{x}_1\) = 40.87
\(\bar{x}_2\) = 34.40
s₁ = 9.91
s₂ = 9.20
n₁ = n₂ = 15
Therefore; \(t_{cal}\) = 1.8516. The degrees of 15 + 15 - 2 = 28, and the one-tailed hypothesis, indicates, using an online tool;
The p-value = 0.037328The p-value is less than 0.05, therefore, the result is significant.
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