Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
Differentiation formula for [tex]\frac{d}{dx}(\frac{u}{v}) = \frac{v\frac{d}{dx} - v\frac{d}{dx}}{v^{2} }[/tex]
Here, u = 2x - 3
v = 2x + 1
[tex]\frac{d}{dx}u[/tex] = 2
[tex]\frac{d}{dx}v[/tex] = 2
[tex]v^{2} = (2x+1)^{2}[/tex]
[tex]= 4x^{2}+4x+1[/tex]
Putting the values,
[tex]\frac{d}{dx}(\frac{2x-3}{2x+1}) = \frac{(2x+1)(2)-(2x-3)(2)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-(4x-6)}{4x^{2}+4x+1}[/tex]
[tex]=\frac{4x+2-4x+6}{4x^{2}+4x+1}[/tex]
[tex]=\frac{8}{4x^{2}+4x+1}[/tex]
Hence, Differentiation of [tex]\frac{2x-3}{2x+1}[/tex] is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .
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Find the measures of all three interior angles and exterior angles. ILL GIVE BRAINLIEST
The interior angles are 43°, 43° and 94°. and exterior angle is 86°
Let the interior angles are ∠A, ∠B and ∠C.
From the question, we have
∠A = (5x-12)°
exterior angle = (8x-2)°
As the sides are equal
∠A =∠B = (5x-12)°
∠C = 180°-(8x-2)°
=182°-8x
Sum of interior angles of a triangle is equals to 180 degree.
∠A + ∠B + ∠C = 180°
(5x-12)°+(5x-12)°+182°-8x = 180°
2x+158° = 180°
x = 11°
Interior angles,
∠A =∠B = (5x-12)°
= (5*11-12)°
=43°
∠C =182°-8x
=182°-8*11
=94°
exterior angle = (8x-2)°
=8*11-2
=86°
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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write an expression quivalent to -3+2/3y-4-1/3y
Answer:
Re-arrange the terms and combine the like terms.
2
3
y
−
1
3
y
−
3
−
4
=
1
3
y
−
7
Step-by-step explanation:
Another problem I need help with
Answer:
x^4 times q^2
Step-by-step explanation:
Answer:
Step-by-step explanation:
this looks tough, but just remember that powers can be rewritten like this
[tex]\sqrt{x^{4} x^{2} q^{4} }[/tex]
then just break up the square root sign, which is another property of square roots
[tex]\sqrt{x^{4} }[/tex]*[tex]\sqrt{x^{2} }[/tex]*[tex]\sqrt{q^{4} }[/tex]
you could break the [tex]x^{4}[/tex] into two [tex]x^{2}[/tex] but I think you can see that it will just be [tex]x^{2}[/tex] once it's pulled out of the square root
[tex]x^{2} *x*q^{2}[/tex]
[tex]x^{3}[/tex]*[tex]q^{2}[/tex]
Does this all make sense?
Which of the following expressions will have a product greater than 4? pls answer with the questions in the pic
Answer:
Answer D
Step-by-step explanation:
Multiply them all out. D is 4.04
Answer: D is correct I took the test without having to see the answer just wanted to help u out:)
Step-by-step explanation:
A package of pens contains one red pen and five black pens. If 20 black pens are purchased, how many red pens are purchased? HURRY!
15 Points If Answered!
Answer: 4 reds
Step-by-step explanation:
Which of the following is true about these similar triangles dilated by scale factor r?
A) AB = rDF
B) AB = rAB
C) AB = rDE
D) AB = rEF
AB = r AB
This is a dilation of similar triangles dilated by scale factor r.
Option B is the correct answer.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
Dilation means the original triangle is resized by the given dilation scale factor.
We multiply the scale factor with the original value.
Here,
AB, DE, and DF are the sides of the triangle.
If a side of the triangle is dilated we must have the same side along with the dilation scale factor r.
Now,
A) AB = r DF
This is not correct.
B) AB = r AB
This is correct.
C) AB = r DE
This is not correct.
D) AB = r EF
This is not correct.
Thus,
AB = r AB
This is a dilation of similar triangles dilated by scale factor r.
Option B is the correct answer.
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A cylinder has a height of 20 yards and a radius of 17 yards. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the cylinder is 18149.2 yards³.
What is the volume?It is important to note that the volume of a cylinder is calculated as:
Volume = πr²h
Radius = 17
Height = 20
Therefore, the volume will be:
Volume = πr²h
Volume = 3.14 × 17² × 20
Volume = 18149.2
The volume is 18149.2 yards³.
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Suppose that you draw two cards from a well-shuffled deck of 52 playing cards without replacement. What is the probability that the second card is an ace, given that the first card is an ace?.
Probability that the second card is an ace, given that the first card is an ace is 1/ 221
Without replacement means drawing the card first but not putting back to the deck and then drawing again.
Total number of cards in a deck = 52
Number of an ace in whole deck = 4
let event of getting an ace in first draw be A
and event of getting an ace in second draw be B
P(A) = 4 / 52 = 1 /13
drawing without replacement
P(B) = 3 / 51 = 1 / 17
Probability that second card is an ace given that first card is an ace is
P(A).P(B) =
1/13 × 1/ 17 = 1 / 221
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A kicker licked a football 60 yards deep into the end zone the hang time on the ball was 8.5 seconds. What is the average speed of the ball
The speed of the football in the air is 7.1 yards per second
How to determine the speed of the ball in the air?From the question, the given parameters are:
Distance = 60 yards
Time to cover this distance = 8,5 seconds
The speed of the football in the air is calculated as
Speed = Distance/Time to cover this distance
Substitute the known values in the above equation
So, we have the following equation
Speed = 60/8.5
Evaluating the quotient in the above equation, we have
Speed = 7.1
Hence, the ball's speed in air is 7.1 yards per second
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The volume of a cone with height h and radius r can be found using the formula V
Find the volume of a cone with radius 9 feet and height 6 feet.
ft3
1
Tr²h
Answer:
508.94
Step-by-step explanation:
V = 1/3pi(r^2)(h)
plug in the values of r and h
V = 1/3(pi)(9^2)(6)
simplify
V = 508. 9380099
Round to nearest hundredth
V = 508.94
A certain species of bird was introduced in a certain county 25 years ago. Biologists observe that the population doubles every 10 years, and now the population is 21,000. What was the initial size of the bird population?
The initial bird population density is 3713.
Given info;
A certain county received a new species of bird 25 years ago. According to biologists, the population doubles every ten years and is currently 21,000 people.
To get the initial size of the bird population;
We use the formula,
[tex]P(t)=Po* 2^\frac{t}{10}[/tex]
Where Po is the initial population and t is the time in years.
[tex]21000= P(25)=Po*2^\frac{25}{10}[/tex]
[tex]21000= Po*2^\frac{5}{2}[/tex]
[tex]21000= 4\sqrt{2}*Po[/tex]
[tex]Po = 21000/4\sqrt{2}[/tex]
[tex]Po = 3712.31\\Po = 3713[/tex]
Hence, the initial size of the bird population is 3713.
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40 is what percent of 54?
Answer: The answer will be 74.07 percent.
According to the question, let the number be x
Then, x*54/100 = 40
x = 40 × 100 / 54
x = 74.07 (approx)
Can I get some help please?
Answer:
66
Step-by-step explanation:
The angle 108 is equal to the angle 42 plus the vertical angle to x
108-42 = 66 this is the measurement for the vertical angle to x. Vertical angles are congruent so angle x is 66
An article costs Rs 750. all prices are reduced by 40 % in a sale.
find its sale price.
Answer:
Rs. 450
Step-by-step explanation:
Selling Price ----- 750
Reduced by 40% therefore 40/100 x 750
=300
750-300= 450
Answer:
$450
Step-by-step explanation:
40 percent *750 =
(40:100)*750 =
(40*750):100 =
30000:100 = 300
750-300=$450
graph the system of inequalities y+5<2x and 2y≥-2x+6
Using graphing calculator, the solution to the inequality is attached
Graph of InequalityAn inequality can be represented graphically as a region on one side of a line. Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line.
If the inequality is strict ( < or > ), graph a dashed line. If the inequality is not strict ( ≤ or ≥ ), graph a solid line.
Using a graphing calculator;
Kindly find the attached graph as solution to the inequality
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Water i draining from a conical tank at the rate of 2 m3/min. The tank i 16 meter high and the top radiu i 4 meter. How fat i the water level falling when the water’ level i 12 meter high?
Answer:
7.07 cm/min
Step-by-step explanation:
You want the rate of change of water level in a conical tank 16 m high with radius 4 m when the level is 12 m and the water is draining at 2 m³/min.
Surface areaThe level of water in the tank is 12/16 = 3/4 of the height of the tank, so the radius of its surface is (3/4)(4 m) = 3 m. The surface area is ...
A = πr²
A = π(3 m)² = 9π m² ≈ 28.3 m²
Level changeThe rate of change of level is the rate of change of volume divided by the surface area:
V'/A = (-2 m³/min)/(9π m²) = -2/(9π) m/min ≈ -0.07074 m/min
The water level is falling at about 7.07 cm/min.
Graph JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis.
JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis is J'(-1, 0), K'(-5, -3), L'(-7, 1).
In the given question we have to graph JKL with vertices J(1, 3), K(5, 0), and L(7, 4) and its image after the glide reflection with a translation along <0,-3> and areflection in the y-axis.
The given vertices are J(1, 3), K(5, 0), and L(7, 4).
Firstly translation along (0,-3).
So translation is (x,y)→(x,y-3)
J'=(1, 3-3)=(1, 0)
K'=(5, 0-3)=(5, -3)
L'=(7, 4-3)=(7, 1)
We have to find the reflection in the y-axis so (x,y)→(-x,y).
Now the points are J'(-1, 0), K'(-5, -3), L'(-7, 1).
The graph of the glide reflection with a translation along <0,-3> and a reflection in the y-axis is given below.
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If you select two different women at random, what’s the probability that:
A. At least one experienced IPV?
B. At least one did not experience IPV?
The probability of selecting at least one experienced IPV is 0.598 and at least one did not experience IPV is 0.866.
In the given question we have to find the probability of selecting at least one experienced IPV and at least one did not experience IPV
From the given table
Probability of experiencing IPV
P(Experienced IPV) = 366 / 1000 = 0.366
Probability of not experiencing IPV
Q(Not-experienced IPV) = 634 / 1000 = 0.634
Now when n samples are chosen from the population, the binomial probabilty distribution follows (P + Q)^n.
Here, n = 2,
So, (p +q)^2 = p^2 + 2pq + q^2
p^2 = Both experienced IPV
2pq = One has experienced IPV and other hasn’t
q^2 = None have experienced IPV.
A. Finding the probability of at least one experienced IPV.
P(At least one has experienced IPV) = P^2 + 2PQ
= (0.366)^2 + 2(0.366)(0.634)
=0.1339+0.4641
= 0.598
B. Finding the probability of at least one did not experienced IPV.
Q(At least one did not experienced IPV) = Q^2 + 2PQ
= (0.634)^2 + 2(0.366)(0.634)
=0.4019+0.4641
= 0.866
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Find the equation of the line that passes through (-1,-3) and is perpendicular to 2 y = x − 3 . Leave your answer in the form y = m x + c
Answer:
y=-1(-3)+2
Step-by-step explanation:
on my test
Identify the graph of the rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.
The equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
It is given that:
The rational function with an x-intercept at (–4, 0) and (4, 0), a vertical asymptote at x = 2, and an oblique asymptote at y = x + 2.
The rational function has x-2 in the denominator.
The denominator cannot be zero.
The rational function will be:
[tex]y=\dfrac{\left(x^{2}-16\right)}{x-2}[/tex]
Thus, the equation for the rational function will be f(x) = (x² - 16)/(x - 2) and the denominator cannot be zero.
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Answer:
its a
Step-by-step explanation:
The width of a rectangle is 4 units less than the length. The area of the rectangle is 32 units. What is the width, in units, of the rectangle?
The width and length of the rectangle will be 4 units and 8 units, respectively.
What is the area of the rectangle?Let W be the rectangle's width and L its length.
The area of the rectangle is the multiplication of the two different sides of the rectangle. Then the rectangle's area will be
Area of the rectangle = L × W square units
The width of a square shape is 4 units less than the length. The region of the square shape is 32 square units. Then the equations are given below.
W = L - 4 ...1
L × W = 32 ...2
From equations 1 and 2, then we have
L × (L - 4) = 32
L² - 4L = 32
L² - 4L - 32 = 0
L² - 8L + 4L - 32 = 0
L(L - 8) + 4(L - 8) = 0
(L - 8)(L + 4) = 0
L = 8, -4
Then the width of the rectangle is given as,
W = 8 - 4
W = 4 units
The width and length of the rectangular shape will be 4 units and 8 units, separately.
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Fiona's fashion store is world renowned for its buttoned uniforms. A collection of 363636 shirts and 424242 jackets contains 842842842 buttons. A collection of 666 shirts and 777 jackets contains 137137137 buttons. Each shirt has the same number of buttons, and each jacket has the same number of buttons. How many buttons are there in a fiona's fashion shirt, and how many buttons are there in a jacket?.
The value of an integer or any letter associated with a variable is known as its coefficient. In the expression 2x + 3y, for instance, the variable x has a coefficient of 2 and the variable y has a coefficient of 3.
There are 842 buttons in 36 shirts and 42 jackets if the number of buttons in each is equal to x.
Additionally, the collection of six shirts and seven jackets has 137 buttons.
It can be expressed using the following equations:
36 x + 42 y = 842 ------(1);
6 x + 7 y = 137 ------(2);
6 x + 36 x + 42 y = 822 ------(3).
Although the constant term on one side of equation is different, the x and y coefficients are the same in both of these equations. This indicates that neither equation has a solution.
I.e →a1/a2=b1/b2≠c1/c2
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Your rate of pay is 9.45 per hour if you workers 5 hours for 3 days and 7 hours for 2 days what is your gross pay before deductions
Answer: 274.05 dollars
Step-by-step explanation:
9.45 x 5 x 3 = 141.75
9.45 x 7 x 2 = 132.3
141.75 + 132.3 = 274.05
Brainliest by any chance?
[tex]x^{2} =81[/tex]
Answer:
x = ± 9
Step-by-step explanation:
x² = 81 ( take square root of both sides )
x = ± [tex]\sqrt{81}[/tex] = ± 9
[tex]{ \red{ \boxed{ \pink{ \sf{x = 9}}}}}[/tex]
Step-by-step explanation:
Here, the question is,
[tex]{ \green{ \sf{ {x}^{2} = 81}}}[/tex]
Apply square root on both the sides then,
[tex]{ \green{ \sf{ \cancel { \sqrt{x} }^{ \cancel2}}}} \: = { \green{ \sf{ \sqrt{81}}}} [/tex]
Now,
[tex]{ \green{ \sf{x = \sqrt{81}}}} [/tex]
We got √81 as answer but what is the perfect square number of 81? That is 9. Same number when multiplied twice to get the resultant number makes a perfect square number. i.e. 9×9 = 81. So, the answer is
[tex]{ \green{ \boxed{ \red{ \tt{x = 9}}}}}[/tex]
PLEASE HELP! QUICK!
It costs $15 to become a member at Workout World Gym and then $30 per month for a membership.
A. What is the total cost (start-up fee and monthly charger) to be a member of Workout World Gym for 2 months? Show your work.
B. What is the total cost for x months? (Please show how you got it)
C. Graph the cost of the membership over a period of 2 years, using months as the units of time. Be suet to label your axes and scale them by labeling each grid line with a number.
D. Is there a proportional relationship between time and costs of the gym membership plan? Explain how you know.
Answer:
A) $75
B) y = 30x + 15
C) (24, 735) **graph below
D) Yes, there is a proportional relationship
Step-by-step explanation:
We can represent this relationship with an equation.
y = 30x + 15
where x would represent the months and y would be the total cost. The 15 would be the initial fee, which only occurs once.
A) Using the relationship [tex]y = 30x + 15[/tex], we can substitute 2 for x, since that would represent the months.
[tex]y = 30x + 15\\y = 30(2) + 15\\y = 75[/tex]
It would be 75 dollars.
B) The total cost for x months would just be the relationship
[tex]y = 30x + 15[/tex]
C) 2 years would represent 24 months. The screen shot below would represent the relationship. The y axis would be the total cost in dollars and the x axis would be the months. (24, 735)
D) Yes, there is a proportional relationship because as the time (months) progress or increases so does the price (dollars). The graph is linear too, which means it increases.
Which graph shows y= 1/2 [x]?
The third graphical representation is that of the function y = 1/2[x] .
The given function is y = 1/2[x] .
This is called the box function or the greatest integer function.
So for the equation of the line y = 1/2 x the graph passes through origin and through the points (2,1) , (4,2) and many more.
Now for the greatest integer function will take all the values of x greater than 1 up to 2 and round it off to 2.
so the points on the graph will be.
(2,1) , (3,1.5) , (4,2)....
This is clearly seen in the third option.
The integer function that returns an integer closest to the given real number is the largest integer function. also referred to as the step function. The greatest integer function rounds the input to the nearest integer. As a result, the equation to get the greatest integer is rather simple. It has the sign x, where x can represent any value.
The letter "x" denotes the biggest integer function for each real function. Real values are rounded to the nearest integer that is smaller than the input value by the function. Another term for this function is the floor function.
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help pls i dont understand this
Answer:
Basically Mate you gotta make a perpendicular line from the letter your told make a line from and then thats for the 2 pages basically they want you to do the same thing that is done but you do it for the letter.
PLEASE GIVE BRAINLIEST THANK YOU!!!
THROUGH (-3,-1) perp to y=-1/2x+5
ANSWER IT
The equation of the perpendicular line that passes through the point (- 3, - 1) is y = 2 · x + 5.
What is the equation of the line perpendicular to another line?
In this question we must determine the equation of a line that is perpendicular to another line and pass through a given point. Mathematically speaking, lines are represented by the following equation:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableAnd the slopes of two lines perpendicular to each other satisfy the following relationship:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.First, determine the slope of the perpendicular line by means of the slope relationship:
m = - 1 / 2
m' = - 1 / m
m' = - 1 / (- 1 / 2)
m' = 2
Second, find the intercept of the perpendicular line by the equation of the line:
b = y - m · x
b = - 1 - 2 · (- 3)
b = - 1 + 6
b = 5
Third, write the equation of resulting line:
y = 2 · x + 5
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5 Each unit on the grid represents 1 mile. For Tia
to travel from the park to the library, she must
go 3 miles south and 5 miles west. Which
represents the coordinates of the library?
A (0, -8)
B (10,-8)
C (-8, 0)
D (-8, 10)
The coordinates that represents the position of the library is (0, -8)
Each unit on the grid represents 1 mile
Tia is going from park to library
The coordinates of the park = (5, -5)
First she must go 3 miles to the south, Therefore there will be change in the y coordinates and the x coordinates will be same
New coordinate of the Tia's position = (5, -8)
Then she must go 5 miles west, there will be change in the x coordinates and the y coordinates will be same
New coordinates of the Tia's position = (0, -8)
Hence, the coordinates that represents the position of the library is (0, -8)
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9. Higher Order Thinking The length of a postage stamp is
millimeters longer than its width. The perimeter of the
stamp is 124 millimeters.
a. Write the equation that represents the situation.
b. What is the width of the postage stamp?
c. What is the length of the postage stamp?
The equation that represents the situation is 2(x+17/4+x) = 249/2 where x is the width, the width of the postage stamp is 29 millimeters and its length is 33.25 millimeters.
According to the question,
We have the following information:
The length of a postage stamp is [tex]4\frac{1}{4}[/tex] millimeters longer than its width. The perimeter of the stamp is [tex]124\frac{1}{2}[/tex] millimeters.
Now, let's take the width of the stamp to be x millimeters.
Length of the stamp = x + 17/4
(We have the converted the fractions from the mixed fraction.)
Now, we have the following expression because the stamp is in the shape of a rectangle:
2(length+width) = 249/2
a) 2(x+17/4+x) = 249/2
b) 2(2x+17/4) = 249/2
Dividing by 2 on both sides of the equation:
2x+17/4 = 249/2*2
2x+17/4 = 249/4
Subtracting 17/4 from both sides of the equation:
2x = 249/4 - 17/4
2x = 232/4
Dividing by 2 on both sides:
x = 232/(4*2)
x = 116/4
x = 29 millimeters
c) Length of the stamp = 29+17/4
Length = (116+17)/4
Length = 133/4
Length = 33.25 millimeters
Hence, the equation that represents the situation is 2(x+17/4+x) = 249/2 where x is the width, the width of the postage stamp is 29 millimeters and its length is 33.25 millimeters.
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