Answer:
[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]
Step-by-step explanation:
When writing an algebraic fraction as an identity, if its denominator has repeated linear factors, the power of the repeated factor indicates how many times that factor should appear in the partial fractions.
Write out the fraction as an identity:
[tex]\begin{aligned}\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A}{x}+\dfrac{B}{(x+1)}+\dfrac{C}{(x+1)^2}\\\\\implies \dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{A(x+1)^2}{x(x+1)^2}+\dfrac{Bx(x+1)}{x(x+1)^2}+\dfrac{Cx}{x(x+1)^2}\\\\\implies 5x^2+20x+16 & \equiv A(x+1)^2+Bx(x+1)+Cx\end{aligned}[/tex]
Calculate the values of A and C using substitution:
[tex]\begin{aligned}\textsf{When }x=0 \implies 16 & =A(1)+B(0)+C(0) \implies A=16\\\\\textsf{When }x=-1 \implies 1 & =A(0)+B(0)+C(-1) \implies C=-1\end{aligned}[/tex]
Substitute the found values of A and C and expand the identity:
[tex]\begin{aligned}\implies 5x^2+20x+16 & \equiv 16(x+1)^2+Bx(x+1)-x\\& \equiv 16x^2+32x+16+Bx^2+Bx-x\\& \equiv (16+B)x^2+(31+B)x+16\\\end{aligned}[/tex]
Compare the coefficients of the x² term to find B:
[tex]x^2 \textsf{ term } \implies 16+B =5\implies B & =-11[/tex]
Replace the found values of A, B and C in the original identity:
[tex]\dfrac{5x^2+20x+16}{x(x+1)^2} & \equiv \dfrac{16}{x}-\dfrac{11}{(x+1)}-\dfrac{1}{(x+1)^2}[/tex]
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Verify that y=e^xy is an implicit solution of the differential equation (1-xy)y'=y^2
Yes, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
Here,
The differential equation (1-xy)y' = y^2
And, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2.
What is Differential equation?
A differential equation is a mathematical equation that relates some function with its derivatives.
Now,
To show y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2, we have to find the solution of differential equation.
The differential equation is;
[tex](1-xy)y'=y^2\\\\\\\\[/tex]
[tex](1-xy) \frac{dy}{dx} = y^2[/tex]
[tex]\frac{dx}{dy} + \frac{x}{y} = \frac{1}{y^{2} }[/tex]
It is form of [tex]\frac{dx}{dy} + Px = Qy[/tex],
Where, P is the function of y and Q is the function of x.
Hence, Integrating factor = [tex]e^{\int\limits {\frac{1}{y} } \, dy} = e^{lny} = y[/tex]
The solution is;
[tex]x y = \int\limits {\frac{1}{y^{2} }y } \, dy + c[/tex]
[tex]xy = lny + c[/tex]
Take c = 0, we get;
[tex]xy = lny\\\\y = e^{xy}[/tex]
Hence, y = e^xy is an implicit solution of the differential equation
(1-xy)y'=y^2
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Anna is buying tomatoes and jalapenos to make salsa. Tomatoes cost $2.99 per pound and jalapenos cost $1.33 per pound. Anna spent $12.65 buying tomatoes and jalapenos. The relationship between pounds of tomatoes, t, pounds of jalapenos, j, and the total cost is represented by the equation 2.99t+1.33j=12.65. Write an equation that makes it easy to find the number of pounds of jalapenos if we know the number of pounds of tomatoes purchased.
The equation that makes it easy to find the number of pounds of jalapenos is j = (12.65 - 2.99t)/1.33.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
Tomatoes cost $2.99 per pound and jalapenos cost $1.33 per pound. Anna spent $12.65 buying tomatoes and jalapenos.
2.99t + 1.33j = 12.65
Make the subject as j and solve the equation for j:
1.33j = 12.65 - 2.99t
j = (12.65 - 2.99t)/1.33
Thus, the equation that makes it easy to find the number of pounds of jalapenos is j = (12.65 - 2.99t)/1.33.
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la suma de los primeros n enteros positivos es un numero de tres digitos iguales. cual es la suma de los digitos de n?
The sum of n natural numbers is three digits number and all digits are the same. The same digits is 6 and the sum is 666.
A three-digit number with the same digits is the sum of n natural numbers.
Let's say the sum of n natural numbers is bbb.
Then,
n( n + 1) / 2 = bbb
n( n + 1) / 2 = b( 111 )
n( n + 1) / 2 = b ( 3 × 37 )
n( n + 1) = 6b × 37
Now, the left-hand side of the equation is the product of two consecutive natural numbers.
Therefore, the right-hand side of the equation is also the product of two consecutive natural numbers.
Hence, 6b = 36
b = 36/ 6
b = 6 and n = 36
As a result, 36 numbers have been added together, and their total is 666.
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What is the f(n) for -5?
A.4
B.1
C.-1
D.-6
write the equation of a parabola that has the same shape as y=6x^2 but with the vertex (-1,7) write in the form a(x-b)^2+k
450 divisible by 2,3,4,5,6,8,9
or 10 explain why ! EXPLAIN WHY !?
Answer: 450 is divisible by 2, 3, 5, 6, and 9
Step-by-step explanation: 450 is divisible by 2 because the last digit (0) is an even number.
Divisible by three because the sum of all the digits in 450 is a multiple of three: 4+5+0 = 9 which is 3*3.
Divisible by 5 because it ends with a 0 (could also end in 5)
Divisible by 6 because it is divisible by both 2 and 3 (2*3=6)
Divisible by 9 because 45 is divisible by 9.
What is the solution to -3/4 X +2<-7
Answer:
Pretty sure it’s x>12
Step-by-step explanation:
Answer x > 12
thats the whole thing
Point B is on line segment AC. Given AB = 7 and BC = 11, determine the length
AC.
What does AC equal?
Answer:
AC = 18
Step-by-step explanation:
AC = AB + BC = 7 + 11 = 18
1. Find the sum.
76,749
5 565
23
+
The sum is
(Simplify your answer. Type a whole number.)
Answer:
82,337
Step-by-step explanation:
76,749
5565
+ 23
82,337
Hope it helps!!!
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List five tasks that a layer can perform. is it possible that one (or more) of these tasks could be performed by two (or more) layers?
Error control, flow control, segmentation and reassembly, multiplexing, and connection setup are five tasks that a layer can perform.
Flow control: It is the efficient management of data flow between two or more devices like computers or nodes of a network.
Error control: The identification and correction of errors that occur during the transmission of data is called error control.
Segmentation and reassembly: Data to be transmitted is divided into small parts or chunks for convenience. This process is called segmentation. The combining of these chunks to reform the original data is called reassembling.
Multiplexing: The process of combination of digital data streams in one signal over a shared medium is known as multiplexing.
Connection setup: Establishing a connection between two devices that are connected to the same network is called connection setup.
All these tasks can be duplicated at different layers.
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On Elvis’s map, the area of a park is of thearea of the same park on Belinda’s map. Elvis’s map uses a 1/4 scale of 1 inch to 100 feet. What scale does Belinda’s map use?
Using proportions, it is found that Belinda's map uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.
What is a proportion?A proportion is a fraction of a total amount, and the measures can be related using a rule of three, which derives from proportional relationships.
Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures, involving operations such as division and multiplication, as they involve unit rates.
Scale problems are solved using proportions. Elvis’s map uses a 1/4 scale of 1 inch to 100 feet, hence:
1 inch represents 100 feet in the entire scale.1/4 of that is that 1/4 = 0.25 inches represent 100 feet.Belinda's map has the same area, hence they use the same scale, hence she uses a scale of 0.025 inches : 100 feet = 0.00025 inches : 1 feet.
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Marcus owes Abdullah
$10. He also owes
$5 to Mariyah. Which
integer represents
Marcus' finances?
A. -15
B. -5
C. 5
D. 15
In a random sample of 200 engineers, 137 have a master's degree. what is the sample proportion, p-hat, of engineers who have master's degrees?
The sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
p-hat proportion:
In this proportion, "p" denotes the probability of a certain event occurring or a certain parameter being true for a certain population, but when a population is large, it may be impractical or impossible to measure it directly. So, we have used the proportion for that cases.
The general form for calculating p-hat proportion is,
[tex]\hat{p}=\frac{x}{y}[/tex]
where
x is the number of successes in the sample, and
y is the size of the sample.
Given,
In a random sample of 200 engineers, 137 have a master's degree.
Here we need to find the the sample proportion, p-hat, of engineers who have master's degrees
According to the question,
x = 137 (number of successes in the sample)
and y = 200 (size of the sample)
Now apply the value on the formula then we get,
[tex]\hat{p}=\frac{137}{200}[/tex]
So, the value of p-hat is
[tex]\hat{p}=0.685[/tex]
The results are usually reported as a percentage, which in this case would be
=> 0.685 x 100 = 68.5%
Therefore, the sample proportion, p-hat, of engineers who have master's degrees is 68.5% out of 200 engineers.
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The difference of a number squared and 6
The algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is x^2 - 6
What are expressions?
Expressions are mathematical statements that are represented by variables, coefficients and operators
How to determine the algebraic expression of the mathematical statement?The mathematical statement is given as
The difference of a number squared and 6
Represent the number with x
So, the mathematical statement becomes
The difference of a number squared and 6 ⇒ The difference of x squared and 6
x squared implies x^2
So, the mathematical statement becomes
The difference of a number squared and 6 ⇒ The difference of x^2 and 6
difference means minus (-)
So, the mathematical statement becomes
The difference of a number squared and 6 ⇒ x^2 - 6
Hence, the algebraic expression of the mathematical statement given as "The difference of a number squared and 6" is x^2 - 6
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What is (1 2/3) divided by (1/8)?
Answer:
13 1/3
____
Work[tex]1\:2/3 = 5/3\\1/8 = 1/8\\\\5/3 \div 1/8\\=\frac{5\cdot8}{3\cdot1}\\= \frac{40}{3}\\= 13\:1/3[/tex]
When working with mixed numbers that are being divided, you know where to start. Start by converting mixed numbers to fractions, then multiply the fractions together to divide them. Simplify your improper fraction by counting how many times it surpasses the denominator.
what is the unit price for a 14.2- ounce bottle that costs $3.98
Answer:
28.028 cents per ounce
= 28.03 cents per ounce rounded to 2 decimal places
= 28.0 cents per ounce rounded to 1 decimal place
= 28 cents per ounce rounded to nearest cent
Step-by-step explanation:
[tex]\texttt{{Unit Price} = \ensuremath{\dfrac{\texttt{Total Price}}{\texttt{Quantity}}} }[/tex]
Here
Total Price = $3.98
Quantity = 14.2 ounce
[tex]\texttt{{Unit\;Price}\;=\;\ensuremath{\dfrac{\texttt{\$3.98}}{\texttt{14.2 oz}}} }[/tex]
Convert dollars in the numerator to cents for easier calculation
Since one dollar = 100 cents.
$3.98 = 3.98 x 100 = 398¢
Divide 398 by 14.2 to get
[tex]\ensuremath{\dfrac{\texttt{398}}{\texttt{14.2}}} } = \texttt{28.028 cents per ounce}[/tex]
which, you can round off as necessary
Rounding to 2 decimal places it becomes 28.03 cents per ounce
Rounding to 1 decimal place it becomes 28.0 cents per ounce
Rounding to nearest cent it becomes 28 cents per ounce
Please HELP ASAP!!!!
Solve negative a minus five eighths equals three fifths for a.
The solution of the expression for a is a = -1 9/40
How to solve the expression?The expression is given as:
negative a minus five eighths equals three fifths for a.
Rewrite the expression properly as:
-a - 5/8 = 3/5
Collect the like terms in the above expression
So, we have:
a = -5/8 - 3/5
Evaluate the like terms in the above expression
So, we have:
a = -1 9/40
Hence, the solution of the expression for a is a = -1 9/40
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Please Help!!
Complete the conjecture based on the pattern you observe in the examples below
1) Conjecture: The sum of any two odd numbers is…
1+1=2
1+5=6
7+9=16
9+11=20
13+21=34
101+103=204
2) Conjecture: The product of any two odd numbers is…
1*1=1
1*5=6
7*9=16
9*11=20
13*21=34
101*103=204
3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to…
3*5=4^2-1
4*6=5^2-1
5*7=6^2-1
7*9=8^2-1
8*10=9^2-1
Answer:
Hello,
Step-by-step explanation:
1) Conjecture: The sum of any two odd numbers is even
(2a+1)+(2b+1)=2a+2b+2=2(a+b+1) is even
2) Conjecture: The product of any two odd numbers is ODD
(2a+1)*(2b+1)=4ab+2b+2a+1=2(2ab+a+b)+1 is ODD
1*1=1
1*5=5
7*9=63
9*11=99
13*21=273
3) Conjecture: The product of a number (x-1) and the number (x+1) is always equal to the difference of the square of x between 1
(x-1)(x+1)=x²-x+x-1=x²-1
Which is equivalent to 6
41/4
Answer:
16 1/4
Step-by-step explanation:
4*10=40, add one more 1/4 and you get 41. So simplified, 41/4 = 10 1/4
Add the 6 and you get 16 1/4
8^x=2 find the value of x
Your answer is x=1/3
Good luck with your test!~ ^^
Is the function [tex]f(x)=\sqrt{x}[/tex] differentiable at x=0 and continuous over R?
Answer: No
Explanation:
Apply the derivative
[tex]f(x) = \sqrt{x}\\\\f(x) = x^{1/2}\\\\f'(x) = (1/2)x^{-1/2}\\\\f'(x) = \frac{1}{2x^{1/2}}\\\\f'(x) = \frac{1}{2\sqrt{x}}\\\\[/tex]
Though we run into a problem since f ' (0) is undefined, due to the zero in the denominator.
Therefore, f(x) is not differentiable at x = 0.
The function is continuous, but only on the interval [tex]x \ge 0[/tex] and not over the entire set of real numbers R.
i need help with plotting and answering bottom questions please
Assume $x is deposited into a savings account. Blank Bank offers an annual rate of r% for y years. Thank Bank offers a rate of ry% for 1 year. Which earns more interest?
Blank bank as well as Thank bank earn equal interest.
In this question, Blank Bank offers an annual rate of r% for y years.
and Thank Bank offers a rate of ry% for 1 year.
Assuming $x is deposited into a savings account, we need to determine which bank earn more interest.
We know that, Interest = principal × rate × time
Now we convert the rates to decimals and to do that we divide by 100.
So, the annual rate of the Blank bank = 0.0r
And the annual rate of the Thank Bank = 0.0ry
Using above formula of interest,
For Blank bank, the interest would be,
I_B = x × 0.0r × y
I_B = xy(0.0r)
I_B = 0.0rxy ....................(1)
here, we find the interest for 'y' years
And for the Thank Bank, the interest would be,
I_T = x × 0.0ry × 1
I_T = I_B = 0.0rxy ....................(2)
From (1) and (2),
I_B = I_T
Both the banks earn equal interest.
Therefore, Blank bank as well as Thank bank earn equal interest.
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Write an equation and solve.
For a ride on a rental scooter, Justin paid a $2 fee to start the scooter plus 12 cents per
minute of the ride. The total bill for Justin's ride was $20.84. For how many minutes did
Justin ride the scooter?
Answer:
2+0.12x=time on scooter bill
x is minutes and x is 157 minutes on the scooter
Step-by-step explanation:
Brad's father asked an engineer to survey the field behind their house. He wanted to plant some orange and
tangerine trees there. According to the survey, the field is 32 feet long and 6 yards wide. What is the perimeter
of the yard in feet?
Francesca us making a scale drawing of the mural on a wall in her schools hallway.the mural is 12 ft high and 135 ft long.she is using a scale of 3 cm for every 4 ft.what is the dimensions of her scale drawing?
The dimensions of her scale drawing is 9 centimeters high and 101.25 centimeters long.
As we are informed from the question -
Measurement in real = measurement on scale
The 4 feet height measures 3 centimeters on scale
So, height of 12 feet on scale will be = (3/4) × 12
Performing multiplication and division to find the height of scale drawing
Height 12 feet on scale = 9 centimeters
The length of 135 feet will measure on scale = (3/4) × 135
Performing multiplication and division to find the height of scale drawing
Length 135 feet on scale = 101.25 centimeters
So, the dimensions of scale drawing will be 9 centimeters high and 101.25 centimeters long.
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an exterior angle of a triangle is 105 degree and one of its interior opposite angle is 35 degree less than the other .calculate the measure of both interior angle
The value of both the interior angles of the triangle is calculated as 70° and 35°.
What is the exterior angle property?If a triangle side is formed, the exterior angle made is equal to the sum of a 2 interior opposite angles.
When an equivalent angle is chosen to take at each vertex of the triangle, this same exterior angles always add up to 360°.Each exterior angle equals 180° minus the interior angle. If the relating interior angle is given, this formula can be used. Exterior angle = Sum of opposite angles on the inside. When the exterior angle's distant interior opposite angles are given, this formula can be used to find it.Now, as per the given question;
The exterior angle of a triangle is 105°.
Let one of the interior angle is 'x'.
Then, the other interior angle is 35 degree less; x - 35°.
By the exterior angle property.
Sum of interior angles = exterior angle
x + x - 35° = 105°
2x = 105° + 35°
2x = 140°
x = 70°
The other interior angle is; x - 35°
= 70° - 35°
= 35°
Therefore, the two interior angles of the triangles are estimated as 70° and 35°.
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Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by _____ random variables.
Experimental outcomes that are based on measurement scales such as time, weight, and distance can be described by Continuous random variables.
What is Continuous Random Variable ?
A continuous random variable is one which takes an infinite number of possible values. Continuous random variables are usually measurements. Examples include height, weight, the amount of sugar in an orange, the time required to run a mile.
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1. You opened a new business. Your first year you earned $18,000. Your goal is to
increase your sales by 3% each year. With this goal, what will be your sales after 15
years of business? (rounded to the nearest hundredth)
Answer:The final balance is $28,043.4.
The total compound interest is $10,043.4.
Step-by-step explanation:
https://www.omnicalculator.com/finance/compound-interest?c=USD&v=var1:1,subject:1138535033,var2:1,subject2:1,FinalBal:20000,FinalBal_adj:20000,apy:1.95!perc,infl:0,PeriodicDep:50,q:1000!!l,type:1,DepositBal:0,PrincipalBal:0,g:0!perc,first_day:19255,select1:1,TableFreq:111,InitialDep:18000,r:3!perc,t:180!yrsmos,m:1,ct1:1,ct2:0,compound_frequency:21,ct3:3,represent:13
Continuation of Qn on part ii)
Answer:
Step-by-step explanation:
