The rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
What is rational function equation?
A rational equation can be defined as an equation that involves at least one rational expression
A rational function is a function of the form f( x )=P( x ) / Q( x ) ,
f( x ) = P( x ) / Q( x ) , where P( x ) and Q( x ) are both polynomials.
A rational function f ( x )=P( x ) / Q( x )
f( x ) = P( x ) / Q( x ) may have a vertical asymptote
The domain is the set of all real numbers for which Q( x ) ≠ 0
Given data ,
The function has vertical asymptote at x = 5 and x = -5
So , the denominator of the fraction of rational function contains the terms (x - 5) and (x + 5)
The x intercept is at ( 2 , 0 ) and ( -1 , 0 )
The y intercept is at ( 0 , 4 )
So , the numerator of the fraction of the rational function contains the terms
( x- 2 ) and ( x + 1 )
So , the rational function is of the form
f ( x )=P( x ) / Q( x )
f ( x ) = A ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
Now , we have the y intercept at ( 0 , 4 )
So , f ( 0 ) = 4
Substituting the value of f ( 0 ) in the above equation , we have
4 = A ( 0 + 1 ) ( 0 - 2 ) / ( 0 - 5 ) ( 0 + 5 )
4 = A ( -2 ) / ( -25 )
4 = 2A / 25
Multiply 25 on both sides , we get
2A = 100
Divide by 2 on both sides , we get
A = 50
Therefore , the rational function becomes
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
Hence , the rational function is of the form
f ( x ) = 50 ( x + 1 ) ( x - 2 ) / ( x - 5 ) ( x + 5 )
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automotive homework i dont get it
The speed of the output shaft is 182 rpm.
Given:
Gear index i = 0.33
Input speed = 60 rpm.
Let output shaft speed is x.
we know that:
gear index = [tex]\frac{n_{in} }{n_{out} }[/tex]
i = 60/x
0.33 = 60/x
x = 60/0.33
= 60/033/100
= 60*100/33
= 6000/33
= 181.818 ≈ 182 rpm.
Therefore The speed of the output shaft is 182 rpm.
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7. Find the minimum value of the expression
4cosx–3sinx−4.
Give the smallest possible positive value of x for which this minimum value occurs.
The minimum value of the expression is -9
From the question, we have
the expression is 4cosx–3sinx−4.
minimum value of the expression =[tex]c- \sqrt{a^{2} +b^{2} }[/tex]
[tex]=-4- \sqrt{4^{2} +(-3)^{2} }\\=-4-5\\=-9[/tex]
Subtraction:
The act of deleting items from a collection is represented by subtraction. Subtraction is denoted by the minus sign. For instance, supposing there are nine oranges stacked together (as indicated in the above image), four oranges are taken out and put in a basket, leaving nine – four oranges, or five oranges, in the stack. Therefore, 9 minus 4 equals 5, or the difference between 9 and 4.
Different kinds of numbers can also use subtraction, which is not just applicable to natural numbers.
The symbol for subtraction is the letter "-". The three numerical elements that make up the subtraction operation are the minuend, the subtrahend, and the difference.
The minuend, from which we subtract another number, is the first number in a subtraction process.
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when you are interrogating the external validity of a sample, which is the most important question to ask?
when you are interrogating the external validity of a sample, option(b). how was the sample collected? is the most important question to ask.
What is External validity?
The concept of external validity is related to the concept of generalization. It's imperative to keep that in mind. It is important to remember that validity refers to the approximate truth of a proposition, an inference, or a conclusion. In other words, external validity refers to the relative truth of generalizations based on generalizations. The external validity of your study is the degree to which the conclusions are applicable to other people, places, and times.
An external validity threat is an explanation of how a generalization could be flawed. A study you conducted in a particular place, with certain types of people, at a particular time, can be generalized to another context (for instance, another place, with slightly different people, at a slightly different time). External validity can be compromised in three ways: people, places, and times.
Question
When you are interrogating the external validity of a sample, which is the most important question to ask?
a. how many people are in the sample?
b. how was the sample collected?
c. how were the participants measured?
d. how many people are in the population?
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Can someone help me please with these problems, please and thank you
1) If 7 donuts cost $6.09, how many donuts would you get for $20.88?
2) $20 is equivalent to 389.10 Mexican pesos. How many dollars would you get for 1500 pesos?
Answer:
1. 3 donuts
2.$76.90
Step-by-step explanation:
3) Determine the numbers of solutions for 4x + 8 = 12x.
A) No Solutions
B) One Solution
C) Infinite Solutions
150 decreased by 15 percent
Answer:127.5
Step-by-step explanation:
15% of 150 = 22.5
150-22.5=127.5
Answer:
Step-by-step explanation:
At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The Triangle Inequality says that the length of any side must be less than the sum of the lengths of the other two sides. For the triangle in part (a) to exist, all of these
statements must be true:
?
?
?
5<3+4, 3<4+5, and 4<5+3.
Yes, the triangle with the given side lengths exists because the triangle inequality holds true.
At first, students might think that the lengths of the sides of a triangle can be any three lengths, but that is not so. The triangle inequality says that the length of any side must be less than the sum of the lengths of the other two sides.
We are given a set of three side lengths. The side lengths are 3, 4, and 5. We need to check whether a triangle can be formed using the given three side lengths. We will use the triangle inequality.
The first inequality is 3 + 4 > 5. This inequality holds true because 7 is greater than 5. The second inequality is 4 + 5 > 3. This inequality holds true because 9 is greater than 3. The first inequality is 5 + 3 > 4. This inequality holds true because 8 is greater than 4. The triangle inequality holds true, so a triangle with the given side lengths exists.
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A cylinder has a radius of 1.2 meters. Its volume is 48 cubic
meters. Use 3.14 for pi. Find its height to the nearest tenth
of a meter.
Answer:
10.6m
Step-by-step explanation:
height of cylinder:
h= V/pie r^2
h= 48/3.14x1.2^2
h=48/3.14x1.44
h=48/4.5216
h=10.61meter
round to the nearest tenth
= 10.6m
Please mark as brainliest
a sample of 158 college students asked them if they liked statistics. 93% said yes. calculate a 89% confidence interval for the true population proportion of those who like statistics
We must find p′, q′ in order to calculate the confidence interval; the sample proportion is p′ = 0.842; This is the population proportion's point estimate. Since CL = 0.95 is the requested confidence level, = 1 – CL = 1 – 0.95 = 0.05 (2) (2) = 0.025.
For P, what is the confidence interval at 95 percent?
Since 95% of the area under the curve falls within this interval, the interval (-1.96, 1.96) serves as a 95% confidence interval for the standard normal distribution.
What is the 95 percent confidence interval for the population's proportion of smokers?
Standard Error for Proportion Calculating a 95% Confidence Interval for each group separately is another way to consider whether smokers and nonsmokers have significantly different proportions with wrinkles. For the smokers, we have a certainty time period ± 2(0.0394) or 0.63 ± 0.0788.
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Given that f(x) = x^4 +5,g (x) is the inverse of f (x), and g (6) = 1 find g' (6).
Select one answer
A 4
B 1/4
C 9
D 1/9
Answer:
B 1/4
Step-by-step explanation:
f(x) = y = x⁴ + 5
the inverse function is
y - 5 = x⁴
x = 4th root(y - 5)
now we rename y and x to make it a regular function definition :
g(x) = y = ±4th root(x - 5) = ±(x - 5)^(1/4)
because g(6) = 1 (positive), we have
g(x) = (x - 5)^(1/4)
and since we are using the positive branch, it means also that all the tangent slopes (= g'(x)) are positive.
g'(x) = 1/4 × (x - 5)^(-3/4) × 1 = 1/4 × (x - 5)^(-3/4)
because (x - 5)' = 1
g'(6) = 1/4 × (6 - 5)^(-3/4) = 1/4 × (1/1³)^(1/4) =
= 1/4 × 1^(1/4) = 1/4 × 1 = 1/4
please note, we are using only the positive root result in this case to get a positive result as tangent slope for g(x) as enforced by g(6) = 1.
What's the answer to 1 1/2 + 3/4
Refer to the table shown below to answer the following question.
Answer: It does not appear to show a function because the numbers are not multiples of each other
Step-by-step explanation: Hope this helps :-)
9/5 ÷ by 2/3 I need a answer for that.
Answer:
Step-by-step explanation:
Exact Form: 6/5
Decimal Form : 1.2
Mixed Number Form : 1 (whole number) 1/5
with explanation if possible.
part c and d
The coordinates to the intercepts of the functions are given as follows:
c - i) Point P: P(-4,0).
c - ii) Point Q: Q(0,2).
d - i) Point P: P(-3,0).
d - ii) Point Q: Q(0,9).
What is the x-intercept of a function?The x-intercept of a function is the value of x at which the function crosses the x-axis, that is, the value of x when y = 0.
For item c, the function is:
2y = x + 4.
Hence the x-intercept is obtained as follows:
x + 4 = 0
x = -4.
Then the coordinates of point P are:
P(-4,0).
For item d, the function is:
y = 3x + 9
Hence the x-intercept is obtained as follows:
3x + 9 = 0
3x = -9
x = -3.
Then the coordinates of point P are:
P(-3,0).
What is the y-intercept of a function?The x-intercept of a function is the value of y at which the function crosses the y-axis, that is, the value of y when x = 0.
For item c, the function is:
2y = x + 4.
Hence the y-intercept is:
2y = 4
y = 2.
The coordinates of Q are:
Q(0,2).
For item d, the function is:
y = 3x + 9.
Hence the y-intercept is:
y = 3(0) + 9 = 9.
The coordinates of Q are:
Q(0,9).
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Pre-calc word problem
You receive two sales job offers. One company offers a straight commission of 5% of sales. The other company offers a salary of $500 per week plus 2% of sales. How much would you have to sell in a week in order to make the straight commission job offer better? (Round your answer to the nearest cent.)
To make straight commission the better offer, you would have to sell (more than, less than, equal to) $____ per week.
Answer:
To make straight commission the better offer, you would have to sell more than $16666.67 per week.
Step-by-step explanation:
Set inequality, assuming the sales amount is x:
5% of x > 500 + 2% of x0.05x > 500 + 0.02x0.05x - 0.02x > 5000.03x > 500x > 500/0.03x > 16666.67 (rounded to the nearest cent)Answer:
More than $16,666.67.
Step-by-step explanation:
Define the variables:
Let x = Weekly sales (in dollars).Let y = Total salary (in dollars).Create an equation for each job offer using the defined variables and given information.
Job Offer 1
Straight commission of 5% of sales:
[tex]\implies y=0.05x[/tex]
Job Offer 2
A salary of $500 per week plus 2% of sales:
[tex]\implies y=500+0.02x[/tex]
For Job Offer 1 to be better, set the expression for this offer to be greater than the expression for Job Offer 2 and solve the inequality:
[tex]\implies 0.05x > 500+0.02x[/tex]
[tex]\implies 0.05x-0.02x > 500+0.02x-0.02x[/tex]
[tex]\implies 0.03x > 500[/tex]
[tex]\implies \dfrac{0.03x}{0.03} > \dfrac{500}{0.03}[/tex]
[tex]\implies x > 16666.66666...[/tex]
Therefore, to make straight commission (Job Offer 1) the better offer, you would have to sell more than $16,666.67 (nearest cent) per week.
Drag and drop each example to the property it is demonstrating.
Commutative Associative Distributive
The example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.
According to the question,
We have the following information:
1) 5*(2+5) = 10+25
2) (2+3)+6 = 2+(3+6)
3) 4*(3+6) = 12+24
4) 6*(7*3) = (6*7)*3
5) 12*8 = 8*12
We know that commutative property of multiplication states:
a*b = b*a
So, this applies to 5th one.
Associative property of addition:
(a+b)+c = a+(b+c)
Associative property of multiplication:
(a*b)*c = a*(b*c)
Now, this applies to 2nd and 4th one.
Distributive property:
a*(b+c) = a*b+a*c
This applies to 1st and 3rd one.
Hence, the example demonstrating the commutative property is 12*8 = 8*12, the examples demonstrating associative property are (2+3)+6 = 2+(3+6) and 6*(7*3) = (6*7)*3 and the examples for the distributive property are 5*(2+5) = 10+25 and 4*(3+6) = 12+24.
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Analyze the steps taken to solve for x. Identify the error and explain why you think the error was made. Then, correctly solve for x. 4x + 9 = 16
divide both sides by 4 to get x + 9 = 4
then subtract both sides by 9 to get: x + -5
Answer:
see explanation
Step-by-step explanation:
4x + 9 = 16
the error being made is that on dividing both sides by 4 all terms must be divided by 4.
to obtain x + 9 = 4 from 4x + 9 = 16
the term 9 has not been divided by 4
correct solution is
4x + 9 = 16 ( divide through by 4 )
x + [tex]\frac{9}{4}[/tex] = 4 ( each term being divided by 4 )
x + [tex]\frac{9}{4}[/tex] = 4 ( subtract [tex]\frac{9}{4}[/tex] from both sides )
x = 4 - [tex]\frac{9}{4}[/tex] = [tex]\frac{16}{4}[/tex] - [tex]\frac{9}{4}[/tex] = [tex]\frac{7}{4}[/tex] = 1.75
or
4x + 9 = 16 ( subtract 9 from both sides )
4x = 7 ( divide both sides by 4 )
x = [tex]\frac{7}{4}[/tex] = 1.75
Find the logarithm of 5.238 with solution
The logarithm of 5.238 with solution is 0.71916549409.
= log(5.238)
= log(5238/1000)
= log(5238) - log(1000)
= 3.71916549409 - log([tex]10^{3}[/tex])
= 3.71916549409 - 3log10
= 3.71916549409 - 3
= 0.71916549409.
Therefore the logarithm of 5.238 with solution is 0.71916549409.
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The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 97% of the people who have a disease. However, it erroneously gives a positive reaction for 5% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease". What is the probability of type i error if the new blood test is used?.
The probability of a type I error is 0.022.
Given,
It is not always possible to identify rare diseases by screening. A blood test that has been created by researchers is thought to be reasonably dependable. In 97% of those who suffer from a sickness, it produces a favorable response. However, 5% of those tested receive an incorrectly positive response because they do not have the condition.
The null hypothesis is given as "the individual does not have the disease".
We have to find the probability of type l error if the new blood test is used;
Here,
A: The individual does not have the disease
B: The individual does have the disease
We know that,
Type I Error is rejecting the true null hypothesis
Then, probability;
P (Type I Error) = P(Positive reaction to an individual who does not have the disease) = 0.022
That is,
The probability of a type I error is 0.022.
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X+62+x+9=180 help please
Answer:
x=54.5
Step-by-step explanation:
x+62+x+9=180
2x+71=180
2x+71-71=180-71(subtract 71 from both sides)
2x=109
2x/2=109/2(divide both sides by 2)
x=54.5
Answer:
x=54.5
Step-by-step explanation:
1. Combine like terms
x+62+x+9=180
2x+71=180
You can only combine the x and 62 and 9 in this equation.
2. Subtraction property of equality
2x+71=180
-71 = -71
2x=109
Subtract 71 from both sides to isolate the variable, x.
3. Division property of equality
2x=109
/2 /2
x=54.5
Hope this helps!
Write an equation in slope-intercept form of the line shown. (3,1) (1,-3)
Answer:
[tex]y = 2x - 5[/tex]
Step-by-step explanation:
The first step in finding the equation of a line from a given set of points is to find its slope. The slope of a line is defined by the formula:
[tex]m = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
In this problem, we are given two points in the form [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex].
So, we can define the x's and y's as:
[tex]x_1 = 3[/tex], [tex]y_1 = 1[/tex], [tex]x_2 = 1[/tex], [tex]y_2 = -3[/tex].
Hence, the slope of the line can be solved for.
[tex]m = \dfrac{-3 - 1}{1 - 3}[/tex]
[tex]m=\dfrac{-4}{-2}[/tex]
[tex]m = 2[/tex]
So, the slope of the line is 2.
Now, we can plug this into the point-slope equation for a line where (a, b) is a point on the line and m is its slope.
[tex]y - b = m(x - a)[/tex]
I will use the point (3, 1):
[tex]y - 1 = 2(x - 3)[/tex]
and isolate y to put it into slope-intercept form.
[tex]y - 1 = 2x - 6[/tex]
[tex]y = 2x - 6 + 1[/tex]
[tex]y = 2x - 5[/tex]
So, the equation in slope-intercept form for the line that goes through the points (3, 1) and (1, -3) is [tex]y = 2x - 5[/tex].
Write an exponential function in the form y=ab^xy=ab x that goes through points (0, 9)(0,9) and (3, 576)(3,576).
What is the product of 3x(x2 + 4)?
x2 + 3x + 4
3x3 + 4
3x3 + 12x
3x2 + 12x
answer is c 3x3 + 12x
A farmer has 180 bushels of wheat to sell at her roadside stand.She sells an average of 14 5/8 bushels each day.Represent the total change in the number of bushels she has for sale after 5 days.
A farmer has 180 bushels of wheat to sell at her roadside stand. She sells an average of 14 5/8 bushels each day.
The total change in the number of bushels she has for sale after 5 days can be represented as [tex]\frac{117}{8} X 5[/tex].
Define average.
The average is defined as the mean value, which is equal to the ratio of the sum of the number of values in a given set to the total number of values present in the set.
In plain English, an average is a single number taken as representative of a list of numbers, typically the sum of the numbers divided by how many numbers are in the list. For instance, the average of the digits 2, 3, 4, 7, and 9 is 5.
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…………………………………………/,,/,,..,,.,…….
Answer:
…………………………………………/,,/,,..,,.,…….
Step-by-step explanation:
Answer:.
Step-by-step explanation: .
Rewrite x4y2 − 3x3y3 using a common factor.
A) 3xy(x3y − x2y)
B) 3xy2(x2 − x2y)
C) x2y(xy − 3xy2)
D) x2y2(x2 − 3xy)
Rewrite [tex]x^4y^2-3x^3y^3[/tex] using a common factor.
A) [tex]3xy(x^3y-x^2y)[/tex]
B) [tex]3xy^2(x2-x^2y)[/tex]
C) [tex]x^2y(xy-3xy^2)[/tex]
D) [tex]x^2y^2(x^2-3xy)[/tex]
option d
The point-slope form of the equation of a line that passes through points (8, 4) and (0, 2) is y - 4 = 1/4(x-8)
the slope-intercept form of the equation for this line?
The equation for the line that runs between the points (8, 4) and (0, 2) has the following slope-intercept form is : y = 1/4 x + 2
What is equation of line?The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
Here,
A line's equation can be written as y = mx + b in slope-intercept form.
slope = m and y-intercept = b.
You can rewrite the equation in point-slope form as y = mx + b.
Given,
y - 4 = 1/4 (x - 8)
Change the formula to y = mx + b.
So,
y - 4 = 1/4 x - 2
We have to add 4 on both sides,
y - 4 + 4 = 1/4 x - 2 + 4
y = 1/4 x + 2
As a result, the equation of the line passing through the points (8, 4) and (0, 2) has the slope-intercept form is y = 1/4 x + 2 .
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2 a. You have 400 turkeys on your farm and you decide to
shoot 25 each week. Determine the slope and y-intercept
for the situation. Then write an equation to determine t,
the total number of turkeys after w weeks.
The equation of the situation is t = 400 - 25w. The y-intercept and slope of the equation are 400 and - 25 respectively.
How to represent linear equation?You have 400 turkeys on your farm and you decide to shoot 25 each week. The slope and y-intercept for the situation can be represented as follows;
Using slope intercept form equation,
y = mx + b
where
m = slopeb = y-interceptt = 400 - 25w
where
t = the total number of turkeys after w weeksw = number of weeks.Therefore, the y-intercept is 400 and the slope is - 25.
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Find the quotient. Write fractions in simplest form. 1 4/9 divide by -2/9=
Answer: 0.865 to (1dp)
Step-by-step explanation:
Super confused! I have other questions that I also need help with… :(
A) Evaluate the expression when z=7 3z+8=
B) Evaluate the expression when x=20 and y=4 8y-x=
The value for expression 1 that is 3z+8 is 29 and for expression 2 that is 8y-x is 12 by substituting the values.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. A mathematical expression is a phrase that contains a minimum of two numbers or variables and at least one mathematical operation.
Here,
For expression 1,
3z+8 where z=7
3*7+8=29
For expression 2,
8y-x where x=20 and y=4
8*4-20=12
By substituting the values, the value for expression 1 ,(3z+8) is 29, and the value for expression 2, (8y-x) is 12.
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