The inverse of the function y equals x squared - 10x (y = x² - 10x) is 5 ±√(x + 25).
What is an inverse function?An inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
First of all, we would translate the given word sentence into a function as follows:
y equals x squared - 10x ⇒ y = x² - 10x
In order to determine the inverse of this function f(x) = x² - 10x, we would interchange both the input value (x) and output value (y) as follows:
y = x² - 10x
x = y² - 10y
Next, we would add (half the coefficient of the y-term)² to both sides of the function as follows:
x + (-10/2)² = y² - 10y + (-10/2)²
x + 25 = y² - 10y + 25
x + 25 = (y - 5)²
±√(x + 25) = y - 5
Adding 5 to both sides of the function, we have:
5 ±√(x + 25) = y - 5 + 5
y = f⁻¹(x) = 5 ±√(x + 25)
Read more on inverse function here: https://brainly.com/question/4242416
#SPJ1
Evaluate the following function for the given value.
f(x)=-x-2; find f(-7).
Answer: f(-7)=-9
Step-by-step explanation:
Examine angle ABC below.
Which of the following equations correctly represent the relationships between the segments?
A) AG= 2GD
B) GC= 1/2FG
C) BE= 2BG
D) GA= 1/2AD
Answer:
A
Step-by-step explanation:
The centroid cuts the median in a 2:1 ratio from vertex to side.
NEED HELP.... Tom is planning a trip to three different cities this summer. When looking at amap, Tom has drawn in two of the distances between these cities. Which of youranswer choices is the correct way to represent the potential range for how manymiles City B is away from City C?- 3
we have that
the distance city B to city C is equal to
405+401=806 miles4
therefore
the answer is
3 < x < 807 -----> because is a potential range (Its not exact)
A student claimed that 0.045 m and 0.0045 m have the same number of significant digits. Do you agree or disagree?
Agree
Disagree
Please help I’ll mark you as brainliest if correct !!
47 had a finished basement with 0 three-car garage .
What is reasoning ?Thinking and cognition are related to reasoning, which requires using one's intellect. The study of logic focuses on how people can construct logically sound arguments using formal reasoning. Deductive, inductive, and abductive reasoning are three examples of logical reasoning that can be used to further break down reasoning. Aristotle distinguished between logical discursive reasoning (reason proper) and intuitive reasoning, noting that the former may lean toward the subjective and the personal, despite being correct. While logical and intuitive styles of reasoning might clash in certain social and political circumstances, in others they are considered as complimentary rather than competitive.
Calculationall the values are given that how many houses had a finished basement with no 3-car garage.
the no. of houses are = 47 .
learn more about reasoning here :
brainly.com/question/24573215
#SPJ13
Find a formula for the nth term in this
arithmetic sequence:
a1 = 7, a2 = 4, a3 = 1, a4 = -2, ...
an
Answer:
an = 7 -3(n -1)
Step-by-step explanation:
You want the formula for the n-th term of the arithmetic sequence 7, 4, 1, -2, ....
Arithmetic sequenceAn arithmetic sequence has a first term (a1) and a common difference (d) found by subtracting the previous term from the current term.
In the given sequence, the first term is a1=7, and the common difference is d=(a2 -a1) = 4 -7 = -3.
The n-th term of the given arithmetic sequence is ...
[tex]a_n=a_1+d(n-1)\\\\\boxed{a_n=7-3(n-1)}[/tex]
__
Additional comment
The formula can be simplified to ...
an = 10 -3n
Adam has 18 counters.
He gives 10 of the counters to Lesley.
a) What fraction of the 18 counters does Lesley get?
Give your answer in its simplest form.
b) What fraction of the 18 counters does Adam have now?
Give your answer in its simplest form.
The fraction of counters Lesley get if Adam gives 10 counters out of 18 counters is 5/9.
The fraction of counters Adam have now is 4/9.
FractionThis is an expression which consists of a numerator and a denominator
A numerator is the upper of top value of a fraction
A denominator is the lower or bottom value of a fraction
Number of counters Adam has = 18Number of counters Adam gave to Lesley = 10Number of counters Adam has left = Number of counters Adam has - Number of counters Adam gave to Lesley
= 18 - 10
= 8
Fraction of the 18 counters Lesley get = Number of counters Adam gave to Lesley / Number of counters Adam has
= 10/18
= 5/9
Fraction of the 18 counters Adam have now = Number of counters Adam has left / Number of counters Adam has
= 8 / 18
= 4/9
In conclusion, the fraction of counters Adam have now after giving out 10 counters to Lesley is 4/9
Read more on fraction:
https://brainly.com/question/11562149
#SPJ1
what is the geometric mean of 14 and 6 (just need answer)
9.16
1) Considering 14, and 6 the data. Let's calculate the Geometric Mean of it
[tex]X_G=\sqrt[]{14\cdot6}\Rightarrow X_G\approx9.16[/tex]2) To do that we just need to multiply those numbers, and since there are two of them take the square root of that product, between those 2 numbers
3) So the Geometric mean is 9.16 (approximately).
3^x-3^y=234,find the value of x and y
Value of x =5 and value of y =2
The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. It could be an integer, a fraction, a negative integer, or a decimal. Exponents are necessary since, without them, it is highly challenging to express the product when a number is repeated several times by itself. For instance, it is much simpler to write 5^7 than it is to write 5 5 5 5 5 5.
[tex]3^{x}-3^{y}=234\\ 3^{x-y}.3^{y}-3^{y}=234\\ 3^{y}(3^{x-y}-1)=234\\ 3^{y}(3^{x-y}-1)=3^{2}.26\\[/tex]
Now, by comparison, we get:
[tex]3^{y}=3^{2}\\ y=2\\ Also, \\3^{x-y} -1=26\\ 3^{x-y}=27\\ 3^{x-y}=3^{3}\\ x-y=3\\ x-2=3\\x=5[/tex]
Learn more about exponents:
https://brainly.com/question/15993626
#SPJ9
Write an equation of the line passing through (4,-3) and perpendicular to x+3y=-15
The equation of line passing through(4,-3) and perpendicular to x+3y=-15 is y = 3x - 15.
How do you determine a line's equation?Using the slope formula, determine the slope.
To find the y-intercept, use the slope and one of the points (b).
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of the line (y = mx + b).
Given,
coordinates = (4,-3)
equation of line = x+3y=-15
equation of line in standard form
⇒ y = -1/3x -5
Slope of line = -1/3
The slope of the line passing through (4,-3) and perpendicular to line x+3y=-15 is 3.
The equation of line becomes
(y + 3) = 3 (x - 4)
y + 3 = 3x - 12
y = 3x - 15
To learn more about equation of line from given link
https://brainly.com/question/18831322
#SPJ10
a. 161b.16c. -16116d.e.5
64 ^ (-2/3)
Rewrite 64 as 4^3
(4^3) ^ (-2/3)
Using the power rule a^b^c = a^(b*c)
4 ^(3*-2/3)
4^ -2
We know that a^ -b = 1/ a^b
1 / 4^2
1/16
1b. Below is a graph of the equation x + y = 500. Change it so that itrepresents solutions to the inequality representing this situation. Statewhat line you will use (dashed or solid line) and which side you will shade(A or B). **
Given:
The equation of the graph is x + y = 500.
The objective is to change the equation as inequality and to choose the correct region for shading.
Explanation:
As the equation is given as x + y = 500, the sum of the values of x and y lies within the 500. As its total sum is also equal to 500, the graph must lie with in the maximum range of 500 that is at A along with solid line. (If sum is not equal to 500, the graph will contain dotted line).
Representation of inequality:
The given equation can be represented in the form of inequality as,
[tex]x+y\le500[/tex]Graph:
Then, the graph of the inequality will be,
Hence, the inequality is x + y ≤ 500 and the graph contains solid line with shaded region in A.
how many groups of 1/2 are in 8
i think 16? 1/2+1/2=1 so 8*2=16
What is the sum of all the numbers less than 496 that divide evenly into 496?
Based on the numbers that are all less than 496 and yet divide evenly into 496, the sum is 496
How to find the sum?The numbers that are less than 496 and yet are able to divide evenly into it are known as the factors of 496. These numbers will not leave a reminder when they divide 496.
The factors of 496 include:
1, 2, 4, 8, 16, 31, 62, 124, 248, 496.
The sum of these numbers that are less than 496 is:
= 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248
= 496
In conclusion, the sum of all the numbers less than 496 that are able to divide it evenly is 496.
Find out more on sum at https://brainly.com/question/24612438
#SPJ1
f(x)=4x^4−19x^3−10x^2+35x−50 and g(x)=x−5, find (f/g)(x) and (f/g)(1)
Answer:
(f/g)(x) = 4x^3 +x^2 -5x +10(f/g)(1) = 10Step-by-step explanation:
You want to find the rational function (f/g)(x) and its value for x=1 when f(x) = 4x^4−19x^3−10x^2+35x−50 and g(x) = x-5.
Polynomial divisionThe ratio function is the ratio of the given functions, found by dividing f(x) by g(x). Since g(x) is a binomial with a leading coefficient of 1, synthetic division is recommended. The attachment shows the result.
[tex](f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{4x^4-19x^3-10x^2+35x-50}{x-5}\\\\\boxed{(f/g)(x)=4x^3+x^2-5x+10}[/tex]
The value of this function when x=1 is ...
(f/g)(1) = 4·1³ +1² -5·1 +10 = 4 +1 -5 +10
(f/g)(1) = 10
what is the percent value of 5/8
Answer: The correct answer is 62.5% and not 67.5 %
Step-by-step explanation: Yes you do 5 divided by 8 and then you move the decimal point two places to the right.
Hope this helped!!!!
A population forms a normal distribution with a mean of μ = 55 and a standard deviation of σ = 12. For each of the following samples, compute the z-score for the sample mean. a. M = 58 for n = 4 scores b. M = 58 for n = 16 scores c. M = 58 for n = 36 scores
It should be noted that the z-score for the sample mean that's given is 0.5.
What is the z score!A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
The following can be seen from the information illustrated:
Mean ( u ) =55
Standard Deviation ( sd )=12
Number ( n ) = 4
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)
Z = (58-55)/12/ Sqrt ( 4 )
Z = 3/6= 0.5
Therefore, the z score is 0.5.
Learn more about z score on:
https://brainly.com/question/25146622
#SPJ1
help me
look at the picture
The zeros of the quadratic are (1 and 3), the vertex is (2, -1). Draw the parabola with a "solid" line. Shade the "interior" of the parabola.
What is defined as the inequality?Inequalities are mathematical representations in which neither side is equal. Unlike equations, we consider the two values in inequality.When inequalities are connected together, it is possible to jump so over middle inequality.If, p < q and q < d, then p < dIf, p > q and q > d, then p > dFor the given question;
The inequality of the function is given as;
= x² - 4x + 3
Find the factors;
(x - 3)(x - 1) = 0
x = 1 and x = 3 are the zeros of the equation.
Now, to graph the equation find the point;
Put x = 0; y = 3
Put x = 1; y = 0
Put x = 2, y = -1
Plot the points on the graph and join the points with solid line.
The vertex of the parabola is found at (2, -1).
Thus, the graph of the parabola is plotted.
To know more about the inequality, here
https://brainly.com/question/25275758
#SPJ13
what is 40 divided by 50
Answer:
See below
Step-by-step explanation:
40 ÷ 50 = 40/50 = 4/5 = .8
The distance between 4 7/10 and -8 9/10
Answer: 68/5
Hope this helps! :)
write an equation of the line that passes the through point (0, 9) and has slope m=2/3
An equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
What is point-slop equation of a line?
The point-slope equation of a line is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
The equation is useful when we know:
one point on the line: ( [tex]x_{1}[/tex],[tex]y_{1}[/tex]) andthe slope of the line: m,and want to find other points on the line.
Given that,
slope , m = [tex]\frac{2}{3}[/tex] and passing through the point is (0,9)
An equation of a line given the slope and a point is
y - [tex]y_{1}[/tex] = m ( x -[tex]x_{1}[/tex] )
or y - 9 = [tex]\frac{2}{3}[/tex] (x - 0)
or y - 9 = [tex]\frac{2}{3}[/tex] x
or y = [tex]\frac{2}{3}[/tex] x + 9
or y = [tex]\frac{2x + 27}{3}[/tex]
or 3y = 2x + 27
or 3y - 2x - 27 = 0
Hence, an equation of the line that passes the through point (0, 9) and has slope m = [tex]\frac{2}{3}[/tex] is 3y-2x-27=0
To learn more about equation of line from the given link
https://brainly.com/question/18831322
#SPJ9
Find the quotient of (+22)÷(+2)
3. Disney on Ice is traveling to Chicago to perform. The revenue from their ticketsales is a function of the ticket price, x, and can be modeled with (x - 8)(450 – 3x).What are the ticket prices at which Disney on Ice would make no money at all?Type Here: They would earn no money when the function is equal oExplain or show your reasoning.Type Here: (x-3)(450-3x) = 0
the price of the ticket which Disney on ice would make no money at all is:
[tex](x-8)(450-3x)=0[/tex]and here, are two posible solutions:
[tex]\begin{gathered} 1)x-8=0 \\ 2)450-3x=0 \end{gathered}[/tex]for the first one 1)
[tex]x=8[/tex]for the second one 2)
[tex]\begin{gathered} 450=3x \\ \frac{450}{3}=x \\ 150=x \end{gathered}[/tex]and in this problem the realistic answer is the first one, so the solution is $8 dollars
HELP! ALgebra 2!
A rectangular swimming pool is twice as long as it is wide. The pool has an area of 450 feet. What are the dimensions of the pool?
======================================================
Explanation:
x = width
2x = length, since it is twice as long as it is wide
area = length*width = 2x*x = 2x^2
Set this equal to the area of 450 sq ft and solve for x
2x^2 = 450
x^2 = 450/2
x^2 = 225
x = sqrt(225)
x = 15 feet is the width
2x = 2*15 = 30 feet is the length
Check:
area = length*width = 30*15 = 450
The answers are confirmed.
help me!!! Write an equation of the line passing through the point (2, 8) that is perpendicular to the line 2x - 3y = 7
Answer:
y = -3/2x +11
Step-by-step explanation:
First you have to change the equation from standard form to slope form.
y = mx + b
2x-3y=7 --> subtract 2x from both sides
-3y = -2x + 7 --> now divide both sides by -3 to get y by itself
y = 2/3x - 7/3 --> the reason 2/3x is positive is because when there are two negatives it turns to a positive.
now you have to use point slope form y - y1 = m (x - x1)
x1 and y1 would be your point. 2 is x1 and 8 is y1
y - 8 = -3/2 (x - 2) --> the reason that m is -3/2 is because a perpendicular equation is the opposite reciprocal of the original slope
next distribute the -3/2
y-8 = -3/2x + 3 --> and now add 8 to 3 to get why by it self
now you have y = -3/2x + 11
The revenue for selling x units of a product is R = 113.95 x. The cost of producing x units is C = 93 x + 750. In order to obtain a profit, the revenue must be greater than the cost. For what values of x will this product produce a profit? (Enter a number. Round your answer up to the nearest whole unit.)
For profit with the revenue of R=113.95x and cost of C=93x + 750 the value of x is 36units.
As given in the question,
Revenue for selling x units of a product is R = 113.95 x
Cost of producing x units is C = 93 x + 750
For profit, the revenue must be greater than the cost.
R > C
113.95x > 93x +750
Subtract 93x from both the sides
113.95x -93x >93x-93x +750
⇒20.95x > 750
Divide by 20.95
⇒x > 750/20.95
⇒x>35.7995
Nearest whole number is 36.
Value of x to produce a profit is 36units
Therefore, to make a profit with the revenue of R=113.95x and cost of
C =93x + 750 the value of x is 36units.
Learn more about profit here
brainly.com/question/15740603
#SPJ1
Write the equation of the line described.
through
(−1, 2)
and perpendicular to
5x + 3y = 15
Answer:
[tex]y = \frac{3}{5} x + \frac{13}{5} [/tex]
Step-by-step explanation:
The equation of a line can be written in the slope-intercept form y= mx +c, where m is the slope and c is the y-intercept.
Let's rewrite the given equation into the slope-intercept form, so that we can identify its slope.
5x +3y= 15
3y= -5x +15
Divide both sides by 3:
[tex]y = - \frac{ 5}{3} x + 5[/tex]
Thus, the slope of the given line is [tex] - \frac{5}{3} [/tex]
The slope of a perpendicular line is the negative reciprocal of the given line. In simpler terms, the slope of the perpendicular line can be found by flipping the denominator and numerator, and by multiplying -1 afterwards.
Slope of perpendicular line= [tex] \frac{3}{5} [/tex]
Substitute the value of the slope into the equation:
[tex]y = \frac{3}{5} x + c[/tex]
To find the value of c, substitute a pair of coordinates the line passes through.
When x= -1, y= 2,
[tex]2 = \frac{3}{5} ( - 1) + c[/tex]
Solve for c:
[tex]c = 2 + \frac{3}{5} [/tex]
[tex]c = \frac{13}{5} [/tex]
Thus, the equation of the line described is [tex]y = \frac{3}{5} x + \frac{13}{5} [/tex].
To learn more about equation of perpendicular lines, check out: https://brainly.com/question/28106460
Match the vocab word with the definition:
Question 1 options:
Order of Operations
Operator
Equation
Constant
Numerical Expression
Exponent (Power)
Evaluate
Variable Expression
Variable
Open Sentence
Term
Coefficient
Grouping Symbol
Inequality
1.
Devices, such as parentheses, brackets, and fraction bars, used to set apart an expression that should be simplified before other operations are performed
2.
An expression that consists of numbers, operations, and sometimes grouping symbol.
3.
The order in which operations must be computed when more than one operation is involve.
4.
A number representing how many times the base number should be multiplied by itself.
5.
A Symbol that represents a value that can change.
6.
A single number or variable, or numbers and variables multiplied together.
7.
The numerical factor in a term. A number being multiplied by a variable.
8.
A number on its own, it has a fixed value.
9.
A combination of variables, numbers, and operations.
10.
You replace, or substitute, all the variables with numbers and then simplify.
11.
A statement that the values of two math expressions are equal (indicated by the sign =).
12.
The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.
13.
The symbol of a math operation.
plus, minus, times, divided by, equals
14.
An equation or inequality containing one or more variable.
Answer:
1 : Grouping Symbol
2 : Operator
3 : Order of Operations
4 : Exponent
5 : Variable
6 : Term
7 : Coefficient
8 : Constant
9 : Numerical Expression
10 : Variable Expression
11 : Equation
12 : Inequality
13 : Evaluate
14 : Open Sentence
−8+n3=6, what does the n equal?
Answer:
n=2.4
Step-by-step explanation:
The value of n is ∛14.
What is Equation?An equation is a mathematical statement that asserts the equality of two expressions. It consists of two sides, known as the left-hand side (LHS) and the right-hand side (RHS), connected by an equal sign (=).
To solve the equation −8 + n³= 6
Add 8 to both sides of the equation to isolate the term with n:
−8 + n³ + 8 = 6 + 8.
Simplifying the equation gives: n³ = 14.
Take the cube root of both sides to solve for n.
Taking the cube root of n³ = 14
∛(n^3) = ∛14.
Therefore, n = ∛14.
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ2
A large pepperoni pizza from Papa Johns costs $14.75. After tax, the pizza is $15.93. What is the sales tax rate?
Answer:
8%
Step-by-step explanation:
divide the after tax price by the before tax price
15.93/14.75=1.08
then subtract 1 from 1.08 (the 1 is the base price of the pizza) and convert the difference to percent to get the answer of 8% tax rate