Answer:
Step-by-step explanation:
so to go forward we input x and get out y, to go backwards ( the inverse) we plug in y and get out x , so just solve the equation for x
f(x) = 8x - 5
remember that f(x) = y
so,
y = 8x - 5
now solve for x
y+5 = 8x
(y+5) / 8 = x
then remember that we want to swap x and y ,
(x+5) / 8 = y
now y = \(f^{-1}\)(x), it's kinda confusing.
\(f^{-1}\)(x)= \(\frac{x+5}{8}\)
An odometer show that a car has traveled 40,000 miles by January 1, 2020. The car travels 16,000 miles each year. Write an equation that represents the number y of miles on the car’s odometer x years after 2020.
y = __
The equation will be \(y=40000+16000*x\)
How do you resolve a two-variable equation?Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.
Two variables are used in what kind of equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
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Help!!!WHOEVER ANSWERS FIRST WITH A GOOD EXPLANATION GETS BRAINLIEST
Answer:
i believe 43
Step-by-step explanation:
correct me if im wrong..
How to calculate your bi-weekly paycheck based on 20 hour weeks at a rate of $9.00 per hour. Also, You will need to deduct Federal Income Tax (11.9%) , State Income Tax (3.6%), F.I.C.A (7.65%), and professional dues. Lastly you will need to look determine whether or not you will be able to pay your monthly car insurance bill of $200.00?
To calculate your bi-weekly paycheck, follow these steps:
Step 1: Calculate the gross earnings:
Multiply the number of hours worked per week by the hourly rate.
20 hours/week * $9.00/hour = $180.00/week
Step 2: Calculate the total earnings for two weeks:
Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.
$180.00/week * 2 weeks = $360.00
Step 3: Calculate the deductions:
Calculate each deduction separately and subtract them from the gross earnings.
Federal Income Tax: $360.00 * 11.9% = $42.84
State Income Tax: $360.00 * 3.6% = $12.96
F.I.C.A: $360.00 * 7.65% = $27.54
Professional Dues: Amount varies depending on the specific dues.
Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues
Step 4: Calculate the net earnings:
Subtract the total deductions from the gross earnings.
Net Earnings = Gross Earnings - Total Deductions
Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.
It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.
Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.
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A utility pole is 40 4/9 feet tall. If 5 8/9 feet is cutoff the top, find the height of the pole.
Absolute vale of x+2 if x is less than 2
Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).
Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).
evaluate cos(sin^-1 x0)
Answer:
Pull terms out from under the radical, assuming positive real numbers.
0
Step-by-step explanation:
Pls help I’ll brainlest ASAP
Answer:
x=24
Step-by-step explanation:
this is your question
Answer:
0.18
Step-by-step explanation:
probability adds to 1 so you do the stuff and get the answer
Translate the given statement into a linear equation in the form
ax + by = c using the indicated variable names. Do not try to solve the resulting equation.
The number of new clients (x) is 149% of the number of old clients (y).
On solving the provided question ,we can say that The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as: x = 1.49y
what is a sequence?A sequence is a grouping of "terms," or integers. Term examples are 2, 5, and 8. Some sequences can be extended indefinitely by taking advantage of a specific pattern that they exhibit. Use the sequence 2, 5, 8, and then add 3 to make it longer. Formulas exist that show where to seek for words in a sequence. A sequence (or event) in mathematics is a group of things that are arranged in some way. In that it has components (also known as elements or words), it is similar to a set. The length of the sequence is the set of all, possibly infinite, ordered items. the action of arranging two or more things in a sensible sequence.
The statement "The number of new clients (x) is 149% of the number of old clients (y)" can be written mathematically as:
x = 1.49y
-1.49y + x = 0
-149y + 100x = 0
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The linear equation in the required form is: x - 1.49y = 0
What is linear equation?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional plane. It is an equation of the form:
y = mx + b
Let's start by assigning variables to the given information. We are told that "the number of new clients (x) is 149% of the number of old clients (y)."
Using this information, we can write:
x = 1.49y
To write this equation in the form ax + by = c, we need to move all the variables to one side of the equation and simplify.
Subtracting 1.49y from both sides, we get:
x - 1.49y = 0
So the linear equation in the required form is:
x - 1.49y = 0
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Sara bought a 24-ounce can of tomato sauce for $6. What is the unit price per ounce? *
Answer: 25 cents
Step-by-step explanation:
24 ounces = 6 dollars. Divide 24 by itself to get 1 ounce. Then, divide 6 by 24 to get 25 cents.
The unit price per ounce is 25 cents.
It is required to find the unit price per ounce.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
We know that,
24 ounces = 6 dollars.
Divide 24 by itself to get 1 ounce.
1 ounces = 6/24 dollars.
1 ounces = 1/4 dollars.
1 ounces = 1/4*100 cents
1 ounces =25 cents.
Therefore, the unit price per ounce is 25 cents.
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13 A young girl standing on a cliff is throwing stones up into the air so that they land in the ocean below. The height h, in meters, of each stone above the ocean is related to the
time 1, in seconds, after it has been thrown by the function
h = -21? + 21 + 40. What is the maximum height reached by
each stone?
The maximum height reached by each stone is 40.5 meters.
The height of each stone above the ocean is given by the function:
h = -2t² + 2t + 40
This is a quadratic function in standard form, with a = -2, b = 2, and c = 40.
The maximum height reached by the stone occurs at the vertex of the parabolic curve described by this function.
The t-coordinate of the vertex is given as:
t = -b / 2a
Substitute the values of a and b,
t = -2 / (2×(-2)) = 0.5
So the maximum height is reached 0.5 seconds after the stone is thrown.
To find the maximum height, substitute the value of t into the function:
h = -2(0.5)² + 2(0.5) + 40 = 40.5 meters
Therefore, the maximum height reached by each stone is 40.5 meters.
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The expression (4k + 8)/4 simplifies to an expression of the form ak+b where a and b are integers. find a/b.
If the expression (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2
The expression is (4k + 8) / 4
The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.
The given expression is (4k + 8)/ 4
Solve the expression
(4k + 8) / 4 = 4k/4 + 8/4
Divide the terms
=k + 2
The result is in the form of ak + b
The value of a = 1
The value of b = 2
The value of a/b = 1/2
Therefore, the value of the expression a/b is 1/2
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5 divided by 7.25 plz show me how you got that answer step by step
Answer: 1.45
Step-by-step explanation:
tanx(1+cos2x)=sin2x prove the identity
Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).
What is the prove of the given identity?To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.
Starting with the left-hand side (LHS):
tan(x)(1 + cos(2x))
We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:
LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))
Next, we can simplify the expression by expanding and combining like terms:
LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)
Simplifying further:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
Now, let's work on the right-hand side (RHS):
sin(2x)
Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).
Now, let's compare the LHS and RHS expressions:
LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)
RHS = 2sin(x)cos(x)
To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:
LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)
Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:
LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)
= [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)
= 2sin(x) - 2sin³(x) / cos(x)
Now, using the identity 2sin(x) = sin(2x), we can simplify further:
LHS = sin(2x) - 2sin³(x) / cos(x)
Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.
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A single filer had a taxable income of $90,725. Base on table, what is is the tax?
The amount that the taxpayer is owing in taxes is $2,691.05.
We have,
Income tax payable refers to a business organization's tax liability to the government in the jurisdiction in which it operates. The amount of liability will be determined by the company's profitability over a given time period and the applicable tax rates. Tax payable is considered a current liability rather than a long-term liability because it must be settled within the next 12 months.
Based on the table, we are using the tax rate of 15% for the taxable income of $11,757.
The tax payable will equals to:
= 15%*$11,757 + $927.50
= $1,763.55 + $927.50
= $2,691.05
Hence, The amount that the taxpayer is owing in taxes is $2,691.05.
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complete question:
Based on this table, if someone had a taxable income of $11,757, how much would they owe in taxes?
Find the domain and range of the relation. Also determine whether the relation is a function.
{(6,3), (8,5), (-4,-4), (5,5)}
The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
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0-(-5) what is the answer
Answer:
The answer is positive 5, or 5
(b) Suppose CG = 3 in., CH = 2 in. and GE = 5 in. Is it possible to find the length of DH? If so, show how
to find the length. If not, explain why not.
When CG = 3 in., CH = 2 in. and GE = 5 in. the information made available in the question is not enough to solve for DH
What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Examining the figure, shows that lines GH and DE should be parallel to create similar triangles
For similar triangles the sides are proportional and this can be used to solve for DH using the equation below'
CG / CE = CH / CD
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The complete question is attached
write an equation in slope intercept form for the line that has a slope of 1/3 and passes through the point (3, -20)
y = 1/3x - 21 is the equation of the line in slope-intercept form.
What is a slope?
Slope is a measure of the steepness or incline of a line. It describes how much the dependent variable (usually y) changes for a given change in the independent variable (usually x).
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the slope is 1/3 and that the line passes through the point (3, -20). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes, and m is the slope. Plugging in the values we have:
y - (-20) = 1/3(x - 3)
Simplifying this equation:
y + 20 = 1/3x - 1
Subtracting 20 from both sides:
y = 1/3x - 21
This is the equation of the line in slope-intercept form.
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ZA and ZB are vertical angles. If mZA= (2x + 26)° and mZB = (3x + 21)',
then find the measure of ZB.
Answer:
m<ZB is 36 degrees
Step-by-step explanation:
Since they are vertical angles, they are congruent. U set up the equation like this “2x+26=3x+21” and solve for x
subtract 2x from both sides and you’ll get “26=x+21”
subract 21 from both sides and you’ll get “5=x”
now we substitute x for 5!
3(5)+21=
15+21=
36
So m<ZB is 36 degrees!
ur welcome :)
hope i helped
brainliest please?
Question One:
If a raw score corresponds to a z-score of 1.75, what does that tell you about that score in relation to the mean of the distribution?
Question Two:
What if the raw score corresponds to a z-score of -0.85?
Question One:A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two: , the raw score is relatively lower than the mean.
If a raw score corresponds to a z-score of 1.75, it tells us that the raw score is 1.75 standard deviations above the mean of the distribution. In other words, the raw score is relatively higher than the mean. The z-score provides a standardized measure of how many standard deviations a particular value is from the mean.
A positive z-score indicates that the raw score is above the mean, while a negative z-score indicates that the raw score is below the mean.
Question Two:
If a raw score corresponds to a z-score of -0.85, it tells us that the raw score is 0.85 standard deviations below the mean of the distribution. In other words, the raw score is relatively lower than the mean. The negative sign indicates that the raw score is below the mean.
To understand the meaning of a z-score, it is helpful to consider the concept of standard deviation. The standard deviation measures the average amount of variability or spread in a distribution. A z-score allows us to compare individual data points to the mean in terms of standard deviations.
In the case of a z-score of -0.85, we can conclude that the raw score is located below the mean and is relatively lower compared to the rest of the distribution. The negative z-score indicates that the raw score is below the mean and is within the lower portion of the distribution. This suggests that the raw score is relatively smaller or less than the average value in the distribution.
By using z-scores, we can standardize and compare values across different distributions, allowing us to understand the position of a raw score relative to the mean and the overall distribution.
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What value of x is in the solution set of 2(3x-1) ≥ 4x-6?
O-10
-5
-3
0-1
Mark this and return
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer: D
Step-by-step explanation: -135
3x + y = 4
8x + 2y = 10
Answer:
I take it that we solve for x and y, so we have
3x + y = 4, so we have y = 4 - 3x
and plug that in to
8x + 2y = 10
8x - 6x + 8 = 10
so
2x = 2
x = 1
y = 4 - 3
y = 1
According to a 2011 publication, the average monthly expenditure of college students on coffee is $100. Given a standard deviation of $20, but with no confirmation of a normal distribution, what is the probability that the mean coffee expense of a randomly selected sample of 42 college students is greater than $90?
The Central Limit Theorem states that, given a sufficiently large sample size, the sampling distribution of the mean for a variable will approximate a normal distribution regardless of the underlying distribution of the variable. In this case, we have a sample size of 42, which is large enough for the Central Limit Theorem to apply.
The mean of the sampling distribution of the mean is equal to the population mean, which is $100. The standard deviation of the sampling distribution of the mean is equal to the population standard deviation divided by the square root of the sample size, which is $20 / sqrt(42) ≈ $3.08.
We can standardize to find the z-score for a sample mean of $90: z = ($90 - $100) / $3.08 ≈ -3.25. Using a z-table, we find that the probability of getting a z-score less than -3.25 is approximately 0.0006. Therefore, the probability that the mean coffee expense of a randomly selected sample of 42 college students is greater than $90 is approximately 1 - 0.0006 = 0.9994.
What percentage mark up is $30 to $50?
Answer:
66.67%
Step-by-step explanation:
HELP ASAP, FIRST ANSWER GETS BRAINLIEST,
Polygon JKLM is drawn with vertices J(−4, −4), K(−4, −6), L(−1, −6), M(−1, −4). Determine the image coordinates of K′ if the preimage is reflected across y = −7.
K′(−4, −4)
K′(−4, −5)
K′(−4, 6)
K′(−4, −8)
The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)
How to determine the image of the coordinates KBased on the given question, we have certain variables that can be utilized for our calculations.
K = (-4, -6)
First, find the equation of the reflection line
The reflection line is y = -7.
This can be expressed as
y = a = -7
The image of the reflection is then calculated as
K' = (x, -(y + 2|a|))
Replace the given or established values in the equation mentioned earlier, resulting in the following expression
K' = (-4, -(-6 + 2 * 7))
Evaluate
K' = (-4, -8)
Hence, the image coordinates of K′ are (-4, -8).
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In 2005 an area vocational school had an enrollment of 325 men and 123 women. In 2006 there were 149 women. what was the percent increase of women students. The answer should be rounded to the nearest whole percent
The nearest Whole percent, the percent increase of women students is approximately 21%.
The percent increase of women students, we need to compare the number of women students in 2005 and 2006.
In 2005, the number of women students was 123.
In 2006, the number of women students was 149.
To find the increase, we subtract the initial value (2005) from the final value (2006):
Increase = Final Value - Initial Value
Increase = 149 - 123
Increase = 26
Next, we need to calculate the percent increase. The percent increase is given by the formula:
Percent Increase = (Increase / Initial Value) * 100
Plugging in the values:
Percent Increase = (26 / 123) * 100
Calculating the percent increase:
Percent Increase ≈ 21.14%
Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.
Therefore, the answer is 21%.
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Find a and b using the factor theorem.
\(f(x)=x^3+ax^2+bx-12\) has factor \((x-1), (x+1)\)
The values of a and b using the factor theorem for the polynomial f(x), we set f(1) and f(-1) equal to zero. Solving the resulting system of equations, we find that a = 12 and b = -1.
To find the values of a and b using the factor theorem, we need to use the given factors (x - 1) and (x + 1) and the fact that they are roots of the polynomial f(x).
The factor theorem states that if (x - c) is a factor of a polynomial, then f(c) = 0. Therefore, we can set x = 1 and x = -1 in the polynomial f(x) to get two equations.
First, let's substitute x = 1 into f(x):
f(1) = (1)^3 + a(1)^2 + b(1) - 12
f(1) = 1 + a + b - 12
Next, let's substitute x = -1 into f(x):
f(-1) = (-1)^3 + a(-1)^2 + b(-1) - 12
f(-1) = -1 + a - b - 12
Since (x - 1) and (x + 1) are factors, f(1) and f(-1) must equal zero. Therefore, we can set the two equations equal to zero and solve for a and b:
1 + a + b - 12 = 0
-1 + a - b - 12 = 0
Rearraning the equations, we have:
a + b = 11
a - b = 13
Now, we can solve this system of equations. Adding the two equations, we get:
2a = 24
a = 12
Substituting the value of a into one of the equations, we find:
12 - b = 13
b = -1
Therefore, the values of a and b are 12 and -1 respectively.
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What are the answers to these questions?
Step-by-step explanation:
the inside expression of an absolute value expression can be positive or negative, but the result is only the positive one.
therefore, for our example here the negative case would be
2.5x - 6.8 = -12.9
which gives us
2.5x = -6.1
x = -6.1/2.5 = -2.44
and the positive case would be
2.5x - 6.8 = 12.9
and that gives us
2.5x = 19.7
x = 19.7/2.5 = 7.88