The partial fraction expansion of the rational function
f(s) = 7s²+30s+27s/3+9s is 7s/9 - 164/81s + 27 + 164/27
In math the term partial fraction is defined as a method that is used to split the complicated fraction into a simpler form.
Here we have given the rational function f(s) = 7s²+30s+27s/3+9s.
And we have to find the partial fraction expansion for the function.
While we looking into the given rational function, for the given function we have to perform the partial fraction decomposition of
=> f(s) = 7s²+30s+27s/3+9s.
And it can be simplified as,
=> f(s) = 7s²+57s/3+9s.
Take s as common on the numerator, then we get
=> f(s) = s(7s + 57) / 3 + 9s
Since the degree of the numerator is not less than degree of the denominator, perform synthetic division, then we get the result as
=> f(s) = 7s/9 + 164/27 + [-164/9]/9s + 3
When we further simplify this expression, then we get,
=> f(s) = 7s/9 + 164/27 - 164/81s + 27
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Determine which ratio forms a proportion with 14/35 by writing the ratio in simplist form.
A) 2/7
B) 4/5
C) 3/8
D) 2/5
What expression is equal to x squared minus 6x
Answer:
Step-by-step explanation:
[tex]x^{2} -6x[/tex]
2. Determine the number of real solutions of the system
You HAVE to show your work to get full credit.
(y=x²-3
y = -2x +4
The number of real solutions of the system are 2 if y=x²-3, y = -2x +4
What is meant by system of solutions?An equation system's solution is a collection of values for the variable that concurrently fulfill each equation. Finding all of the possible sets of variable values that make up the system's solutions is necessary to solve an equation system. However, the second equation does not have a solution at (5, 4). There is often only one solution to a system of linear equations, however it is possible for there to be infinite or no solutions (parallel lines) on occasion (same line).
Given,
y=x²-3 -----(1)
y=-2x +4 -----(2)
Solving equations 1 and 2, we get
x²-3=-2x +4
x²+2x-3-4=0
x²+2x-7=0
We have to solve by using quadratic formula,
x= (-b±√b²-4ac)/2a
x= (-2±√2²-4(1)(-7))/2(1)
x= (-2±√4+28)/2
x= (-2±√32)/2
x= (-2±4√2)/2
x= -1±2√2
x= -1-2√2, -1+2√2
Thus, the system has two solutions.
Therefore, the number of real solutions of the system are 2.
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What is the inverse of 6?
The Multiplicative Inverse of the number 6 is "1/6" .
The Inverse (Multiplicative) of the number is the number that when multiplied by the original number gives the product as 1 .
which means the product of the number and its multiplicative inverse is 1 .
the number is given to be 6 .
So , let the multiplicative inverse of 6 be = x .
So , According to Definition of Multiplicative Inverse ,
we can write : x * 6 = 1
dividing both side by "6" .
we get ;
x = 1/6 .
Therefore , the multiplicative inverse is 6 .
The given question is incomplete , the complete question is
What is the Multiplicative Inverse of 6 ?
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Bethany collected 200 survey responses regarding recycling behaviors in her city. of those responses, 174 people responded that they participate in the city’s recycling program. use this information to complete the statement. round all answers to the nearest hundredth. the approximate sample proportion is____, which means that %___of the people surveyed do not participate in the city’s recycling program.
Answer:
the approximate sample proportion is 87%, which means that 13% of the people surveyed do not participate in the city’s recycling program.
32^1/25 x 2^x = 8^1/4. work out the exact value of x.
Answer:
The exact value of x is 2.Step-by-step explanation:
To find the exact value of x, we need to solve the given equation for x. The equation is:
32^1/25 x 2^x = 8^1/4
To solve this equation, we need to rewrite it in a form that allows us to isolate the variable x. We can start by using the properties of exponents to simplify the left-hand side of the equation. We can use the property that says that raising a number to a fractional power is the same as taking the square root of that number, raised to the power of the denominator of the fraction. So, we can write:
(32^1/25)^2 = (32^1/25)^25/25 = 32^1/25
This simplification allows us to rewrite the left-hand side of the equation as follows:
32^1/25 * 2^x = (32^1/25)^2 * 2^x
Next, we can use the property of exponents that says that the product of two numbers raised to the same power is equal to the product of the numbers, raised to that power. So, we can rewrite the left-hand side of the equation as follows:
(32 * 2)^1/25 * 2^x = (32^1/25)^2 * 2^x
Then, we can use the property of exponents that says that raising a product to a power is the same as raising each factor to that power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 + x) = (32^1/25)^2 * 2^x
Finally, we can use the property of exponents that says that the exponent of a power is equal to the product of the exponents of the base and the power. So, we can rewrite the left-hand side of the equation as follows:
(32^1/25) * 2^(1/25 * 25 + 1 * x) = (32^1/25)^2 * 2^x
Since the right-hand side of the equation is already in a form that allows us to isolate the variable x, we can now use the property of exponents that says that raising a number to a power and then taking the square root of that number is the same as
Tori and Matias work as jewelers. Tori has an hourly
wage of $24 and gets overtime for every hour she works over 40 hours. The
overtime pay rate is 150% of the normal rate. Matias makes 5% commission
on all jewelry he sells. Who earns more money in a week if Tori works
60 hours and Matias sells $21,000 worth of jewelry? Explain.
Divide the base for that period by the appropriate commission rate to determine your commission for that period. Mark earns more money.Since $1680 > $1080, Mark earns more.
Who makes the most money each week?This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.
Mark: $24/h; 150% OT
Calculate Mark's overtime (OT) pay
Convert OT rate to decimals --> 150% = 1.5
Mark's OT wage is 1.5*$24 = $36
Mark worked for 20h OT. (60h-40h = 20h)
(Regular pay X regular hours worked) + (OT wage X OT hours worked)
= ($24 X 40h) + ($36 X 20h)
= $1680
Joe: 5% commission
Convert 5% to decimals --> 0.05
(Jewelry sold) X (commission rate)
= $21000 X 0.05
= $1050
Since $1680 > $1080, Mark earns more.
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need help
please and thank you
Answer:
98 laps
Step-by-step explanation:
(5x 14) + (2 x 14)
70+ 28 =98
How do you prove two triangles are congruent to each other?
All three pairs of corresponding sides are equal. : Two pairs of corresponding sides and the corresponding angles between them are equal. : Two pairs of corresponding angles and the corresponding sides between them are equal.
Congruent Figures :
Those figures which covers each other/one another exactly then they are congruent Figures.
There are 4 ways by which we can prove any 2 triangles as congruent :
If they are having -
SSS : Side Side SideThree pairs of side are equal then the triangles are congruent.
ASA : Angle Side Angle / AAS : Angle Angle SideIf any 2 pairs of angles and 1 side are equal then the triangles are congruent.
SAS : Side Angle SideIf any two pairs of sides and the included angle are equal then the triangles are congruent.
RHS : Right Hypotenuse SideIf any right angle triangles are having their hypotenuse and a pair of sides equal then they are congruent.
So, all three pairs of corresponding sides are equal then are congruent to each other.
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In the first week of July, a record 1020 people went to the local swimming pool. In the second week, 100 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 198 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
The percent decrease in the number of people who went to the pool over these four weeks is 15%.
What is the percent decrease in the number of people who went to the pool over these four weeks?The number of people in each week will be recorded below:
First week = 1020
Second week = 1020 - 100 = 920
Third week = 920 + 145 = 1065
Fourth week = 1065 - 198 = 867
The percent decrease in the number of people who went to the pool over these four weeks will be:
= (1020 - 867) / 1020 × 100
= 153 / 1020 × 100
= 15%
The percentage decrease is 15%.
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What is Z set in math?
Therefore, the Z set represents the all integers numbers .
Describe integer.
An integer is a whole number, not a fraction, that can be negative, positive, or zero. The numerals set of 5, 1, 5, 8, 97, and 3, 043 are a few examples. Non-integer numbers include 1.43, 1 3/4, 3.14, and other numbers.
According to the given question:
The set of integers represented here by Z is..., 2,..., 1, 0, 1, 2,... Q stands for the collection of rational numbers (the set of all possible fractions, including the integers).
The set of real numbers is designated as R. The group of complex numbers is designated as C.
Therefore, the Z set represents the all integers numbers .
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Use the Law of Cosines to find the values of x°and y°. Round to the nearest tenth.
The value of x° and y° are 26.8° and 86.2°.
What is rounding to tenth?
Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5.
The length of sides of the triangle are 8, 6, and 5.
Assume that AB = c = 6, BC = a = 5, and AC = b = 8
m∠A = x° and m∠B = y°.
Cosine law:
c² = a² + b² - 2ab cos C ....(i)
b² = a² + c² - 2ac cos B ....(ii)
a² = b² + c² - 2bc cos A ....(iii)
Putting a = 5, b = 8, c = 6, and A = x° in law (iii)
5² = 8² + 6² - 2×8×6 cos x
25 = 64 + 36 - 84 cos x
84 cos x = 75
cos x = 75/84
x = 26.76°
x = 26.8° (nearest tenth)
Putting a = 5, b = 8, c = 6, and B = y° in law (ii)
8² = 5² + 6² - 2×5×6 cos y
64 = 25 + 36 - 60 cos y
60 cos y = 4
cos y = 4/60
y =86.177°
y =86.2°
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2. The price of licorice is proportional to its length. It costs
$0.50 to buy 5 in. How much licorice can you get for $1.80?
The required length of licorice for $1.80 is given as 18 in.
What is proportionality?proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.
here,
The price of licorice is proportional to its length. It costs $0.50 to buy 5 in; it is uncertain how much licorice you can get for $1.80.
Let the price be y and the length be x,
according to the quesiton,
y = kx,
put y = 0.50 and x = 5
0.50 = 5k
k = 0.1
Now
y = 0.1 x
for
y = 1.8
1.8 = 0.1x
x = 18
Thus, the length of licorice necessary for $1.80 is specified as 18 in.
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The cafeteria at Midtown Middle School surveyed 575 students about their favorite food. Find the number of students that responded for each of the following.
Fruit = 24%
Write your answer like this
Answer __________
The correct answer is 138 students.
How did we figure this out?
x = .24 * 575
x = 138 students
Therefore, the correct answer is 138 students.
What is the formula of commutative property?
The formula of commutative property of addition is a + b = b + a and the formula of commutative property of multiplication is a × b = b × a.
The Commutative Property is derived from the word commute, which means to move. It states that the product or sum of two numbers do not change even if the places of numbers are changed or if the numbers move from one place to another.
The commutative property of addition states that a + b = b + a
The commutative property of multiplication states that a × b = b × a.
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it took oliva 2 hour to drive 240 miles. at this rate how long does it take to drive 80 miles
Answer:
40 minutes
Step-by-step explanation:
rate = distance/time = miles/hr
rate = 240 mi/2 hr = 120 mi/hr
time = distance / rate = (80 mi)/(120 mi/hr) = 0.67 hr = 40 minutes
(0.67 hr)(60 min/hr) = 40 minutes
A rocket-powered hockey puck moves on a horizontal frictionless table. The figure below shows the graphs of vx and vy, the x- and y-components of the puck’s velocity. The puck starts at the origin.
Part A
In which direction is the puck moving at t = 3 s ? Give your answer as an angle from the x-axis.
Express your answer using two significant figures.
On a frictionless horizontal table, the rocket-powered hockey puck moves at an angle of 61.9° above the horizontal in 3 seconds.
what are significant figures ?The significance of non-zero digits is constant. Between any two significant digits, there can be no zeros. Only the final or trailing zeros in the decimal section are important. Between any two non-zero digits, all zeros are important. Seven significant digits are seen in, for instance, 108.0097. There is never any significance for any zeros that are both to the right and left of the decimal point and a digit that is not zero.
given
Then, using the formula that relates the tangent of angle, vertical component of velocity, and horizontal component of velocity to find the direction in which the puck is moving.
Displacement is the smallest distance between the two points.
The vector representation of velocity is,
s = 1/2at2
= 1 .80 m
The puck moves at an angle 61.9° above the horizontal.
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For what value of k are the roots of the quadratic equation 3x² 2kx 27/0 real and equal?
The value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
The given equation 3x²+2kx+27=0
Here, a=3,b=2k,c=27
It is given that roots are real and equal.
b²-4ac=0
(2k)²-4(3)(27)=0
4k²-324=0
4k²=324
Divide both sides by 4
k²=81
Take square root on both sides
k=±9
Hence, the value of k is 9 for quadratic equation 3x²+2kx+27=0 whose roots are real and equal.
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What is the measurement of angle cbd
Given that:
Angle CBD=6x-40
Angle BFH=4x
From the given diagram, angle CBD=angle BFH ("corresponding angles")
Therefore 6x-40=4x,
6x-4x=40,
2x=40,
x=20
now Angle CBD= 6(20)-40
= 80
find the zeros
p(x)=5x3 −5x 2 −10x
and then place them on a graph
The polynomial function p(x) = 5x³ - 5x² - 10x have zeros of 0, -1 and 2
Zeros of a PolynomialThe zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial's graph. We will also see that they are directly related to the factors of the polynomial.
The polynomial function given is
p(x) = 5x³ - 5x² - 10x
The zeros of the function are 0, 2, -1
To test the zeros if they are the roots of the polynomial
p(0) = 5(0)³ - 5(0)² - 10(0)
p(0) = 0
p(2) = 5(2)³ - 5(2)² - 10(2)
p(2) = 0
p(-1) = 5(-1)³ - 5(-1)² - 10(-1)
p(-1) = 0
The zeros are 0, -1, and 2 to the polynomial
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How high above the water is the roadway in meters? Round to the nearest hundredth. (199 ft)
199 feet in meters
1 foot = 0.3048 meters
[tex]0.3048(meters)\times199(feet)[/tex]
[tex]=\fbox{60.66}[/tex]
What is the mode of the distribution 3 5 7 4 2 1 4 3 4?
Mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is 4.
As per the question the data given is 3, 5, 7, 4, 2, 1, 4, 3, 4.
Now we have to determine the mode of the given distribution.
Mode: A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.
The simple way to determine the mode is the most repeated data.
The number or the value which is "repeated more number of times compared to the other values".
From the data given:
3 repeated two times.
5 repeated one time.
7 repeated one time.
4 repeated three times.
2 repeated one time.
1 repeated one time.
Therefore the value of mode is 4.
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f(x)=x^3+8g(x)=4x^3−5x−8
find (f+g)(x)
A.
5x³-5x
B.
5x³-5x+16
C.
5x³-5x-16
The value of the sum of the functions f(x) and g(x), (f + g)(x) is 5x³ - 4x.
What is a function?The outputs for a certain set of inputs can be referred to as a function.
A function's inputs are referred to as its independent variables, while its outputs are referred to as its dependent variables.
Given, f(x) = x³ + 8 and g(x) = 4x³ - 5x - 8.
Let, f(x) = x³ + 0x + 8.
We know, (f + g)(x) = f(x) + g(x).
Therefore, (f + g)(x) = (x³ + 0x + 8) + (4x³ - 5x - 8).
(f + g)(x) = x³ + 4x³ + 0x - 4x + 8 - 8.
(f + g)(x) = 5x³ - 4x.
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What is the standard deviation for the set of numbers 2 4 6 8 10 12 14?
We calculated standard deviation 4 for the given set of numbers.
What means standard deviation?
In the statistics, standard deviation is an estimation that implies how far each data value apart from the mean value. A high standard deviation indicates that all data are dispersed around the mean. And a low score of standard deviation implies data values are close enough in relation to the mean.
How to calculate standard deviation for the given data?Let, X be the list of data value, X² be the square of the data value.
X X²
2 4
4 16
6 36
8 64
10 100
12 144
14 196
we add all the data value and get ∑X = 56
We add all the squared value and get ∑X² = 560
Standard deviation is calculated by using the formula
SD =
√ [∑X²/N - (∑X/N) ²]
where N is the number of data present N= 7
SD = √[560/7 - (56/7)²]
= 4
Hence, calculated standard deviation is 4
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Determine the domain of the following graph:
Answer: see below
Step-by-step explanation:
The domain of a graph consists of all the input values shown on the x-axis
We want to find the left-most x value and the right-most x value.
-8, 3
since there is a hole at the point where x=3 we will use a paratensesis
D:xE[-8,3)
What is the use of median?
Median is the only average to be used while dealing with qualitative data which cannot be measured quantitatively but still can be arranged in ascending or descending order of magnitude,
e.g., to find the average intelligence among a group of people.
It is to be used for determining the typical value in problems concerning wages, distribution of wealth, etc.
It helps us to identify if the distribution is symmetric or not.
The mean and median of a symmetric distribution are close together.
If the distribution is exactly symmetric, the mean and median are exactly the same.
In a skewed distribution, the mean is farther out in the long tail than the median.
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Are all equilateral triangles similar and congruent?
Yes, All equilateral triangles are similar to each other.
No, All equilateral triangles are not congruent to each other.
How all equilateral triangles are similar?The fact that every angle in an equilateral triangle is equal to 60 degrees is one of its characteristics.
According to the AAA Triangle Similarity Postulate, two triangles are similar if all of their angles are identical to their corresponding angles in another triangle.
According to the AAA Postulate, all equilateral triangles are similar because their angles are all 60 degrees.
why all equilateral triangle are not congruent?The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .
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Geometry book page 599
Answer:
Can you make another post showing us a picture of the Geometry book page 599? I may be able to help :-)
Two balls are to be pulled from a vase that contains 7 red balls, 9 green balls, and 2 black balls. After the first ball is drawn, it is
not replaced. What is the probability that two red balls are chosen from the vase?
The probability that two red balls are chosen from the vase would be = 1/9
What is probability?Probability is defined as the concept that proves that an event may occur or not.
The number of red balls = 7
The number of black balls = 2
The number of green balls = 9
The total number of balls in the vase = 18
The probability of getting 2 red balls = 2/18 = 1/9
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Answer two questions about Equations AAA and BBB: \begin{aligned} A.&&5x-2+x&=x-4 \\\\ B.&&5x+x&=x-4 \end{aligned} A. B. 5x−2+x 5x+x =x−4 =x−4 1) How can we get Equation BBB from Equation AAA
(Choice A) A Add/subtract a quantity to/from only one side
(Choice B) B Add/subtract the same quantity to/from both sides
(Choice C) C Rewrite one side (or both) using the distributive property (Choice D) D Rewrite one side (or both) by combining like terms
2) Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
(Choice A) A Yes
(Choice B) B No
The given equation A) 5x -2 + x = x - 4 and B) 5x + x = x - 4 are not equivalent.
The term equation in math refers the mathematical statement that is made up of two expressions connected by an equal sign.
Here we have given that the tow equations are
A) 5x -2 + x = x - 4
B) 5x + x = x - 4
And we need to find if they are equivalent or not.
While we looking into the given question, we have given the following equations,
A) 5x -2 + x = x - 4
B) 5x + x = x - 4
In order to find if they are equivalent or not, we have to simplify each of then then we get,
=> A) 6x - 2 = x - 4
=> A) 6x - 2 - x + 4
=> A = 5x + 2
Now, we have to do the same to simplify the equation (B), then we get
=> B) 6x = x - 4
=> B = 6x - x + 4
=> B = 5x + 4
Now, we compare the two solved equation,
=> A = B
=> 5x + 2 = 5x + 4
Here the variable part is equal but the constant value is not same.
Therefore, we have identified the the two equation are not equivalent.
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