The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
What is inverse of function?
To find the inverse of a function, write the function y as a function of x i.e. y = f(x) and then solve for x as a function of y.An inverse function is a function that undoes the action of the another function. A function g is the inverse of a function f if whenever y=f(x) then x=g(y).Change y in for the f(x) :
y = ∛5x + 5
Switch the x and y
x³ = 5y + 5
x³ - 5 = 5y
y = ( x³ - 5 ) / 5
f⁻¹ = ( x³ - 5 ) / 5
Hence, The inverse of f(x) = ∛5x + 5 is f⁻¹ = ( x³ - 5 ) / 5
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Find x and y -- if your answer is not a whole number, round to the tenths!
X=______
Y=_______
Answer:
x ≈ 10.6
y = 15
Step-by-step explanation:
The opposite angles in an inscribed quadrilateral are supplementary.
Therefore:
(4y+14) + (7y+1) = 180
=> 11y + 15 = 180
=> 11y = 165
=> y = 15
7x+1 + 105 = 180
=> 7x + 106 = 180
=> 7x = 74
=> x ≈ 10.6
Help i dont know how to do this problems.
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
10 and 2x - 8 are parallel lines.
10 = 2x - 8
10 + 8 = 2x
18 = 2x
x = 9 (black)
7 and -17 + 2x are the two parts of a line separated by a midpoint.
7 = -17 + 2x
7 + 17 = 2x
2x = 24
x = 12 (orange)
7 and x + 15 are two parts of a line separated by a midpoint.
7 = x + 15
7 - 15 = x
x = 8 (purple)
m∠2 = 4x + 8
one angle = 45°
Other angle = 180 - 104 = 76°
The sum of the triangles is 180.
45 + 4x + 8 + 76 = 180
4x = 180 - 129
4x = 52
x = 12.75 (green)
Thus,
The value of x = 9 (back)
The value of x = 12 (orange)
The value of x = 8 (purple)
The value of x = 12.75 (green).
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Find the value of B, Please.
[tex]\frac{-5x^3+2x+3}{x+2} = A+\frac{B}{x+2}[/tex]
A. -13
B. 39
C. -21
D. -33
Answer:
B) 39------------------------------
We need to find the remainder when -5x³ + 2x + 3 is divided by x + 2.
According to the remainder theorem, the remainder is the value of the polynomial when x = - 2:
-5(-2)³ + 2(-2) + 3 = - 5(-8) - 4 + 3 = 40 - 1 = 39The matching choice is B.
Answer:
B. 39
Step-by-step explanation:
Divide the polynomials using long division:
[tex]\large \begin{array}{r}-5x^2+10x-18\phantom{)}\\x+2{\overline{\smash{\big)}\,-5x^3\;\;\;\;\;\;\;\;\;\;\;+2x+3\phantom{)}}}\\{-~\phantom{(}\underline{(-5x^3-10x^2)\phantom{-b)))))))}}\\10x^2+2x+3\phantom{)}\\-~\phantom{()}\underline{(10x^2+20x)\phantom{)))}}\\-18x+3\phantom{)}\\-~\phantom{()}\underline{(-18x-36)\phantom{}}\\39\phantom{)}\\\end{array}[/tex]
The solution is the quotient plus the remainder divided by the divisor.
Solution
[tex]-5x^2+10x-18+\dfrac{39}{x+2}[/tex]
PLEASE SOLVE FOR X I REALLY NEED HELP
Answer:
Below
Step-by-step explanation:
The bisector divides the base into lengths proportionate to the two sides (Angle Bisector theorem)
x+ 2 = 15/(15+20) * 14
x = 4 units
A decade ago, the average class size at Newton Middle School was 30 students. Now it is 30% smaller. What is the average class size currently?
Answer: 21 students
Step-by-step explanation:
A number being 30% smaller means that it has reduced to 70% of its original size.
This means we can multiply the original value by its new percentage, 30x0.7=21 students.
I need help with this question.
Dude I am so sorry that I do not know this answer
line into slope-intercept form, simplifying all fractions y - x = 8
The equation of a line into slope is 1/2x+1
What is meant by slope intercept ?A method of formulating a line's equation that makes it simple to identify the slope and y-intercept is known as the slope-intercept form. The point where the line crosses the y-axis is known as the y-intercept, and the slope refers to how steep the line is.
Y equals mx plus b is actually the slope intercept form. Because it provides both a slope and an intercept, the form is known as a slope intercept form.
A line's slope and y-intercept are expressed in the following formula: y=mx+b. The y-intercept, which is usually represented in coordinate form as (0,b), is the point where the line crosses the y-axis.
y=1/2x+1
8y-4x=8
Add 4x to both sides.
8y=4x+8
Divide 8 (the one with y) by both sides.
y=1/2x+1
Therefore the equation of a line into slope is 1/2x+1
The complete question is : 8y−4x=8 Put the following equation of a line into slope-intercept form, simplifying all fractions.
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One year, the population of a city was 102,000. Several years later it was 110,160. Find the percent increase.
Answer:
8% increase
Step-by-step explanation:
Difference between the two populations: 110160 - 102000 = 8160
Difference ÷ Initial population: 8160 ÷ 102000 = 0.08
Find the mean and standard deviation of the sample data in the table. (Round your answers to two decimal places.) x = [1, 2, 3, 4, 5]
f(x) = [2, 13, 15, 11, 13]
The mean and standard deviation of the sample data in the table is 182 and 508 respectively.
To calculate the mean and standard deviation,
mean= E(x)
= ∑x*f(x)
= 1(2) + 2(13) + 3(15)+4(11) + 5(13)
=2+26+45+44+65
=182
Standard deviation = E(x²)
= ∑x²*f(x)) - E(x)
=1(2) + 4(13) + 9(15)+16(11) +25(13) - E(x)
= 2 +52+135+176+325 - E(x)
=690 - 182 - E(x)
=508
The mean is the average of the values in the given set. It indicates that values in a particular data set are distributed equally.
The three most frequently employed measures of central tendency are the mean, median, and mode.
The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean.
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Evaluate the expression below. (−4)2 + |−7 − (−5)| − 23
Answer:
-7
Step-by-step explanation:
(-4)2 | -7 - (-5)| -23
-4*2=-8
-7- -5=-2
|-2|=2
-8*2=16
16-23=-7
If there is a problem with this answer please feel free to tell me, thanks :)
Which of the following is an equivalent form of the compound inequality -33> -3x - 6 ≥
-36?
The equivalent form of the compound inequality is -9>-x≥-10.
What is a compound inequality?A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the simultaneous truth of both statements in the compound sentence. It is when the solution sets for the various statements cross over or intersect. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true. It consists of the union or combination of the solution sets for the various statements. A conjunction is a compound inequality that contains the word "and." Even though "and" and "or" are considered to be conjunctions of speech, their meanings in mathematics are distinct from their grammatical counterparts. The conjunction (part of speech) "or"—when used to demonstrate this point—is whenever used in a compound inequality, it creates a disjunction, as the name suggests. Simply keep in mind that "con" stands for "with another" and "dis" for "one OR the other."
Calculation:Given -33>-3x-6≥-36.
Dividing everything by 3 we get -11>-x-2≥-12.
Now adding to every side we get compound inequality as -9>-x≥-10.
The equivalent form of the compound inequality is -9>-x≥-10.
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which equation is in slope-intercept form?
Answer: y = 3/2x +-9
Step-by-step explanation:
The equation in slope-intercept form, y = mx + b, is the equation y = 3/2x +-9.
See attached for more information on slope-intercept form.
Assume that a sample is used to estimate a population mean
μ
. Find the 90% confidence interval for a sample of size 52 with a mean of 85.5 and a standard deviation of 12.3. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.
Confidence interval for given data is (82.156,88.843)
What is confidence interval?The confidence interval is the range of values that, if you repeated your experiment or resampled the population in the same manner, you would anticipate your estimate to fall within a specific proportion of the time.
The alpha value determines the confidence level, which is the proportion of times you anticipate being able to recreate an estimate between the top and lower boundaries of the confidence interval.
general form of a confidence interval is:
point estimate + Z SE (point estimate)
Formula for confidence interval is given by
[tex]X[/tex] ± [tex]Z\frac{s}{\sqrt{n} }[/tex]
Where:
X is the mean
Z is the chosen Z-value from the table above
s is the standard deviation
n is the number of observations
In given ques
X = 85.5, Z=1.960, s =+ 12.3, n= 52
confidence interval = 85.5± (1.960×12.3/√52)
(82.156,88.843)
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AolaksksmsmsmsmsO? A a a a a s sbhuaybua aybaybayabyaba
Answer: There are several statements that could be false if f(x) is continuous on [a, b] and differentiable on (a, b):
1 The function f(x) has a maximum or minimum value at some point in the interval [a, b].
2 The function f(x) is monotonic (either increasing or decreasing) on the interval [a, b].
3 The function f(x) has an inflection point (a point where the concavity of the function changes) in the interval [a, b].
4 The function f(x) has an asymptote (a line that the function approaches but never touches) in the interval [a, b].
5 Note that these statements are not necessarily false, but they could be false depending on the specific function f(x).
5) A woman wants to borrow $12,000 to buy a car. She wants to repay the loan by monthly installments
for 4 years. If the interest in the loan is 10.5% per year, compounded monthly, what is the amount of
each payment?
Answer:
to much money to buy a car I try to work it down to 10k
The height of a statue of a boy was 12 meters and the scale used was 4 meters: 1 foot. Find his actual height.
By using the unitary method the boy's actual height is 3 meters.
What exactly is the unitary method?The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is the unitary method's formula?The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.
Given:
12 meters is the height of a boy statue.
The scale used was 4 meters = 1 foot.
1 metre = 1/4 feet
Assume the boy's actual height = H foot
By using the unitary method of unit conversion.
According to the question,
The actual height of the boy = height of the statue× scale used for 1 meter.
H = 12 × ¼
H = 12/4
H = 3 meters
By using the unitary method the boy's actual height is 3 meters.
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By using the unitary method the boy's actual height is 3 meters.
What exactly is the unitary method?The unitary method is used to solve a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
What is the unitary method's formula?The unitary method's formula is to find the value of a single unit and then multiply that value by the number of units to get the required value.
Given:
12 meters is the height of a boy statue.
The scale used was 4 meters = 1 foot.
1 metre = 1/4 feet
Assume the boy's actual height = H foot
By using the unitary method of unit conversion.
According to the question,
The actual height of the boy = height of the statue× scale used for 1 meter.
H = 12 × ¼
H = 12/4
H = 3 meters
By using the unitary method the boy's actual height is 3 meters.
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the chart shows the number of points different players scored during a game. what is the ratio of marcus's points to scott's points? responses
The ratio of Marcus's point to Scott's point will be = 1 : 2
According to the table given attached below,
We can find the ratio of the squares,
First, let us know about the definition of Ratio and Proportion.
The ratio is defined as the comparison between the two similar quantities
The fraction can also be represented as a ratio using the ' : ' sign
For example, let us consider two numbers a and b
In fraction, we could write it as = [tex]\frac{a}{b}[/tex]
Writing it as a ratio = a : b
According to the table given below,
Marcus's points = 7
Scott's points = 14
The ratio of Marcus's points to Scott's points = [tex]\frac{Marcus}{Scott}[/tex]
14 / 7
2 / 1
2 : 1
Therefore, The ratio of Marcus's point to Scott's point will be = 1 : 2
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What is equivalent to 2
Answer:
4 6 8 10
Are the ans
Step-by-step explanation:
Plus 2 each time
Graph the linear equation by solving for y first.
4x+5y=-2
Solving for y, the linear equation is: y = -4/5x - 2/5.
The table showing the corresponding y-value for each x-value is:
x | -8 -3 2 7
y | 6 2 -2 -6
The graph is in the attachment.
How to Graph a Linear Equation?To graph the linear equation of 4x + 5y = -2, rewrite in slope-intercept form by solving for y.
4x + 5y = -2
5y = -4x - 2
y = -4/5x - 2/5
Complete the table given by plugging each value of x into the linear equation, y = -4/5x - 2/5.
For x = -8:
y = -4/5(-8) - 2/5
y = 6
For x = -3:
y = -4/5(-3) - 2/5
y = 2
For x = 2:
y = -4/5(2) - 2/5
y = -2
For x = 7:
y = -4/5(7) - 2/5
y = -6
The complete table is:
x | -8 -3 2 7
y | 6 2 -2 -6
See the graph below.
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an employer agrees to pay $5,000 for medical insurance and contribute an additional 5% of the employees'
Answer: $5,250
Step-by-step explanation:
1) Half of 5000 is 2500. But that's 50%.
2) Divide the remaining value by 10. You now have 250, which is 5%.
It's a given rule in math that if you're working with the Powers of 10, by either multiplying or dividing them, all you need to do is add or remove some zeros.
Fill in the blanks so that the equation has infinitely many solutions. 12x + 2 -4x = _ (2x + _ )
Answer:
4 and 1/2
Step-by-step explanation:
left side must be ewual to right side. after you substract 12x-4x you get 8x+2 on right side. you than find a number on the left side, whit which you have to multiply 2x to get 8x(same number as on the other side) and you get 4. lastly you have to find a number that gives you 2 when multiplied with 4 and it is 1/2
List the elements of the following sets.
(a). {Vowels in the word "MATHEMATICS"}
(b). {The seven colours of the rainbow}
(c). {Multiples of 9 which are less than 50}
(d). {Even numbers which are between 10 and 23}
that's all pls I need it now asap
Answer:
a) {A,E,I}
b) {red, orange, yellow, green, blue, violet, indigo}
c) {9,18,27,36,45}
d) {12,14,16,18,20,22}
Lol I'm not sure if I did all of these correct :]
(Also what is this for? Like the coding class or something? (Just curious))
matie has 4 times as many stamps as arnav. if matie gives arnav 8 stamps, matie will have twice as many stamps as arnav. how many stamps does each boy have.
Answer: Mattie has 16 stamps and Arnav has 4 :)
Step-by-step explanation:
the system of equations used to solve it is
m=4a
m-8=2a
Martie have 48 stamps and Arnav have 12 stamps.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Let Matie has x stamps and Arnav has y stamps.
Given that,
Matie has 4 times as stamps as Arnav
Implies that,
x = 4y (1)
Also, If Matie gives 8 stamps to Arnav will have twice stamps to Arnav.
Implies that,
x - 8 = 2(y+8)
x - 8 = 2y + 16
x = 2y + 24 (2)
From equation (1) and (2),
y = 12
and x = 48
Matie and Arnav each have 48 and 12 stamps respectively.
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six pounds of potatoes cost 12.90 how much would 3.5 pounds cost
HELP
Answer:x=$7.31
Step-by-step explanation:6lbs
$12.90 x
6lbs x=($12.90 )(3.4 lbs)
6lbs x=43.86$lbs
6lbs x/6lbs=43.86$lbs/6lbs
Decide where the first digit of the quotient should be placed. Do not complete the
division.
The first digit in the quotient of 1, 592 64 is in the
Choose...
place.
The first digit in the quotient of 1, 592 64 should be placed in the; Hundredths place.
How to find the quotient with Long division?
When we carry out long division, it is pertinent to note that the first digit of the quotient usually appears over the least significant digit of the very first portion of the dividend that is now greater than or equal to the divisor.
In this question, when we perform long division, we compare;
64 vs 1 . . . no quotient digit
64 vs 15 . . . no quotient digit
64 vs 159 . . . the first quotient digit appears with the same place value as the 9 in 1.59. That is, the first quotient digit will be 0.02, with 2 being in the hundredths place.
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If 20% of an income of a man is Rs 4,800, find his income
The income of the man is 24000.
Step-by-step explanation:
income of man =24000
Let the income of man be x
According to the question,
20%*x = 4800
0.2x=4800
As a result, x =24000
(4800*10= 48000/2= 24000)
So the income of a man is 24000.
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Man's income is, 24000 rupees.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given, 20% of an income of a man is Rs 4,800.
To find the income:
Use percentage formula,
let m be the man's income.
So, m x 20 / 100 = 4800
Rearranging,
m = 4800 x 100 / 20
m = 24000
Therefore, the income is, 24000 Rs.
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Are your finances, buying habits, medical records and phonecalls really private? A real concern for many adults is thatcomputers and the Internet are reducing privacy. A survey conductedby Peter D Hart Research Associates for the Shell Poll was reportedin USA Today. According to the survey, 37% of adults are concernedthat employers are monitoring phone calls. Use the binomialdistribution formula to calculate the probability that:
a. out of 5 adults, none is concerned that employers aremonitoring phone calls.
b. out of 5 adults, all are concerned that employers aremonitoring phone calls.
c. out of 5 adults, exactly 3 are concerned that employers aremonitoring phone calls.
As per binomial distribution the probability of the following conditions are as follow:
a. probability for out of 5 none is concerned is 0.09924.
b. probability for out of 5 all are concerned is 0.02825
c. probability for out of 5 three are concerned is 0.4669.
As given in the question,
Percent of adults are concerned = 37%
p = 0.37
Percent of adults are not concerned = (100 -37)%
= 63%
1 - p = 0.63
Total number of adults 'n' = 5
Probability using binomial distribution
= ⁿCₓ pˣ ( 1- p)ⁿ⁻ˣ
a. Out of 5 none is concerned
here x = 0
⁵C₀( 0.37)⁰(0.63)⁵⁻⁰
= 0.09924
b. Out of 5 all are concerned
here x = 5
⁵C₅( 0.37)⁵(0.63)⁵⁻⁵
= 0.02825
c. Out of 5 three are concerned
here x = 3
⁵C₃( 0.37)³(0.63)⁵⁻³
= 0.4669
Therefore , using binomial distribution the probability of the given percent of adult data is equal to as follow:
a. probability for out of 5 none is concerned is 0.09924.
b. probability for out of 5 all are concerned is 0.02825
c. probability for out of 5 three are concerned is 0.4669.
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(4) The following question is from a New York State Algebra Common Core Exam.
Graph y=f(x) and y= g (x) the set of axes below.
f(x)=2 x²-8 x+3
g(x)=-2 x+3
State all paints that make both equations true.
The points that make both equations true are, (0,3) and (-3,3).
What is an 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.
A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.
A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
The graph of the equations is attached with the answer below. The points are (0,3) and (-3,3).
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WRITE THE EQUATION OF THE LINE IN SLOPE-INTERCEPT FORM.
The equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
To write the equation of a line in slope-intercept form (y = mx + b), we need to find the slope of the line (m) and the y-intercept (b).
To find the slope of the line, we can use the slope formula:
m = (y2 - y1)/(x2 - x1)
We have given the line passes through the points(0, 3) & (3, 0),
so, m = (0-3)/(3-0)
= -3/3
m = -1
The y-intercept is the point where the line intersects the y-axis. This point is (0, b), where b is the y-intercept.
Since the given line passes through the point (3, 0), we can substitute these values into the slope-intercept form of the equation to find the y-intercept:
y = mx + b
0 = -1 * 3 + b
b = -3
Solving for b gives us:
b = -3
Therefore, the equation of the line that passes through the point ((0, 3) & (3, 0) is y = -1x - 3.
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Let f(x)= 4x2-3 and let g(x)= 2x+3. Find (fg)(3).
(f+g)(3)=
The value of (f . g) (3) is 594 and (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
i) (f . g) (3)
(f . g) (x) = f(x) . g(x)
(f . g) (3) = f(3) . g(3)
= 4(3)² - 3 * 2(3) + 3
= 36 - 3 * 6 + 3
= 33 * 18
(f . g) (3) = 594
The value of (f . g) (3) is 594 when function is f(x) = 4x² - 3 and g(x) = 2x + 3
ii) ( f + g )( 3 )
( f + g )( x ) = f ( x ) + g ( x )
( f + g )( 3 ) = f (3 ) + g ( 3 )
= 4(3)² - 3 + 2(3) + 3
= 4(9) + 6
= 36 + 6
( f + g )( 3 ) = 42
The value of (f + g) (3) is 42 when function is f(x) = 4x² - 3 and g(x) = 2x + 3.
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