The rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.
We know that the rate of change of a function is nothing but the slope of the line.
The slope of the line is given by;
Slope = Change in y-coordinate / change in x-coordinate
We are given;
[tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex]
We need to find the rate of change of function for x = 4 and x = 9.
Let us find the value of y or f(x) for the given value of x.
For x = 4, [tex]f(x) = \sqrt{4} - \frac{1}{\sqrt{4}}[/tex] = 2 - 1/2 = 4 - 1 / 2 = 3 / 2
For x = 9, [tex]f(x) = \sqrt{9} - \frac{1}{\sqrt{9}}[/tex] = 3 - 1/3 = 9 - 1 / 3 = 8 / 3
Put the values of x and y in the slope formula, we will get;
Slope = (8 / 3 - 3 / 2) / (9 - 4) = 7 / 6*5 = 7 / 30
So, the rate of change of function is 7 / 30.
Thus, the rate of change of function [tex]f(x) = \sqrt{x} - \frac{1}{\sqrt{x}}[/tex] for x = 4 and x = 9 is 7 / 30.
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The vertices of a triangle are p(-1,4) Q (8,-3) and R(2,-6) Name the vertices of R y-x (PQR)
The reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).
First, let us understand the reflection of a point:
The reflection of a point or set of points across the line y = x results in a point or set of points whose coordinates are the interchange of the x-value and the y-value of the original point or set of points.
We are given:
The vertices of a triangle are P(-1, 4), Q(8, -3) and R(2, -6).
We need to find the reflection of the points across the line y = x.
So,
P(-1, 4) = P'(1, -4)
Q(8, -3) = Q'(-8, 3)
R(2, -6) = R'(-2, 6)
Thus, the reflection of the points P(-1, 4), Q(8, -3) and R(2, -6) across the line y = x are P'(1, -4), Q'(-8, 3) and R'(-2, 6).
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i am trouble finding out what 2(-4)
Answer:-8
Step-by-step explanation:
You are basically adding -4+(-4)
Answer:
Step-by-step explanation:
2(-4)
2 x -4
answer: -8
What kind of relationship is expressed below?
5i+3=7
The relationship for the expressed value will be an equation, as there is equal sign in between the expression.
What is an equation?
Two or more expressions with an equal sign is called an equation.
As in given expressed value two expressions are equated with equal sign,
5i+3=7
Here, Left hand side is equal to Right hand side.
Also have Equal sign.
Whereas in expression, there will be no equal sign,
only - variables, operators and numeric values.
For Function, expression is equated to F(variable).
Hence, equation is the relationship for 5i+3=7.
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Simplify this expression. If the answer contains exponents, all exponents should be positive.
Answer:
below
Step-by-step explanation:
(7p^9)^-4 a negative exponent means move the number up or down in the fraction
= 1 / [ (7 p^9) ^4 ]
= 1 / ( 7^4 p^36) = 1/(2401 p^36) <===don't omit the parentheses!
NO LINKS!! Please help me with this symmetry. Select all that apply.
We are looking for the functions which are symmetric with respect to the y-axis.
This should be an even function with the vertex on the y-axis.
All functions of odd degree or restricted domain or range are excluded:
Lines, cubic functions, square root or exponent functions.Possible symmetric functions:
Quadratic, 4th degree etc., absolute value, circles with center on the y-axis.See the attached. Those with red cross are excluded, with green mark are correct choices.
Answer:
[tex]y=-7x^2[/tex]
[tex]y=8x^2-3[/tex]
Step-by-step explanation:
Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:
f(x, y) = f(-x, y)To determine if a graph is symmetric with respect to the y-axis, replace all the x's with (−x). If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.
Therefore, any function that includes the term x² will be symmetric with respect to the x-axis since (-x)² = x².
[tex]\begin{aligned}&\textsf{Given}: \quad& y&=-7x^2\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=-7(-x)^2\\&\textsf{Simplify}: \quad &y&=-7x^2\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.
[tex]\begin{aligned}&\textsf{Given}: \quad& y&=8x^2-3\\&\textsf{Replace $x$ for $(-x)$}: \quad& y&=8(-x)^2-3\\&\textsf{Simplify}: \quad &y&=8x^2-3\\\end{aligned}[/tex]
Therefore, since the resultant expression is equivalent to the original expression, it is symmetric with respect to the y-axis.
What is 247.968 rounded to the nearest cent
Answer: 247.97
Step-by-step explanation:
The nearest cent is two decimal places.
GD 1 What can be concluded about a line that passes through the points (1.-2) and (4.-2)? Check all that apply.
The conclusions for the given points (1.-2) and (4.-2) are
(A) The slope is 0.
(B) The y-intercept is -2.
(D) The line is horizontal.
(E) The equation of the line is y = -2
Calculating the equation of a line:The formula used to calculate the equation of the line passing through the points (x₁, y₁) with slope m is given by
=> (y -y₁) = m(x - x₁)Where the formula for Slope is given by
=> m = (y₂ - y₁) /(x₂ - x₁)Here we have
Given points (1, -2) and (4, -2)
Let us check each point one by one
(A) The slope is 0.
To find the slope of the line with given points using the formula
=> m = (y₂ - y₁) /(x₂ - x₁)
=> m = (-2 - (2)) /(4 - (-2)) = 0/6 = 0
∴ The slope of the line = 0
(B) The y-intercept is -2
To find the y-intercept calculate the equation line using the formula
=> (y -y₁) = m(x - x₁)
=> [y - (-2) ] = 0 (x - 1)
=> y + 2 = 0
=> y = -2
On comparing with the slope-intercept form y = mx+c, we get
y-intercept = -2
∴ The y-intercept is -2.
(D) Here the line is in the form of y = a then the given line will be a Horizontal line.
(E) The equation of the line is y = -2
Therefore,
The conclusions for the given points (1.-2) and (4.-2) is
(A) The slope is 0.
(B) The y-intercept is -2.
(D) The line is horizontal.
(E) The equation of the line is y = -2
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The complete question:
What can be concluded about a line that passes through the points (1, -2) and (4, -2) Check all that apply.
The slope is 0.
The y-intercept is -2.
The line is vertical.
The line is horizontal.
The line has no y-intercept.
The equation of the line is y = -2
Suppose that a particular medical procedure has a cost that is normally distributed with a mean of $19,800 and a standard deviation of $2900. What is the maximum cost that a patient would pay if he is in the lowest 4% of all paying patients?
Select one:
A) $24,875
B) $19,684
C) $14,725
D) $792
The maximum cost that a patient would pay if he is in the lowest 4% of all paying patients is C) $14,725.
How to calculate the cost?Given that
mean = $19800
standard deviation = $2900
Using standard normal table ,
P(Z < z) = 4%
P(Z < z) = 0.04
P(Z < -1.75) = 0.04
z = -1.75
Using z-score formula,
x = z * standard deviation + mean
x = -1.75 * 2900 + 19800 = 14725
The maximum cost is $14725
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Find the slope of the table below.
Answer: 10
Step-by-step explanation:
To find the slope, we will take two points and find the change in y over change in x.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } = \frac{35-15}{3-1}=\frac{20}{2} =10[/tex]
The slope of the table is 10.
What do you know about the relationship between lines a and b? justify your conclusion with a theorem or postulate
Answer:
last answer.
Step-by-step explanation:
First of all, how did you get the second answer?
Line a has to be perpendicular to Line b.
Perpendicular transversal theorem:
In a plane, if a line is perpendicular to one of two parallel lines , then it is perpendicular to the other line also.
In this case, a||c, and line b is perpendicular to line c.
We can therefore use perpendicular transversal theorem to state that line a is perpendicular to line b.
Make a list of all possible rational zeros of f(x)=5x^3+7x^2−81x+45, and then use this list to find all of the functions’ rational zeros, if any exist.
Rational Zero Candidates: ±
Rational Zeros:
The zeroes of the polynomial are x=3, x=-5 and x=3/5
What are Zeroes of the polynomial?The locations where a polynomial becomes zero overall are known as the zeros of the polynomial. The term "zero polynomial" refers to a polynomial with a value of zero . The highest power of the variable x is referred to as a polynomial's degree. A linear polynomial is a polynomial with degree 1.
Given:
f(x)=5x³+7x²−81x+45.
let us take x= 3
5(27)+7(9)-81(3)+45
=135+63-243+45
= 243-243
=0
So, 3 is a root of polynomial and x-3 is factor of Polynomial.
Now, divide 5x³+7x²−81x+45 by x-3 we get 5x²+22x-15
Now, factorise 5x²+22x-15.
= 5x²+25x-3x-15
= 5x( x+ 5) - 3(x+ 5)
= (5x - 3)( x+ 5)
Then, x= 3/5 and 5
Hence, the zeroes of the polynomial are x=3, x=-5 and x=3/5
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Write 375 as the product of prime factors.
Give your answer in index form.
Answer:
375=5^3 * 3
Step-by-step explanation:
375/5 = 75
75/5 = 15
15/5 = 3
3/3 = 1
Nakeisha is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Nakeisha will earn $30 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. Nakeisha's songs were played on 2 more commercials than movies, and her total earnings on the royalties from all commercials and movies was $760. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Nakeisha's songs were played. Define the variables that you use to write the system. Please help this is due tonight!!!
Answer:
z = 30x + 110y
x = y + 2
z = royalties
x = no of commercial
y = no of movies
Please help I was sick and missed out on class.Thank you
Answer:
Y= -1.67x + 0.67
Step-by-step explanation:
Hope this was ok
ABC is a straight line. The length AB is five times the length BC . AC= 90CM. Work out the length AB
Answer:
AB = 75cm
Step-by-step explanation:
Let BC equal x. Then AB is 5x because it is 5 times as long.
The whole length is 90, that was given.
Add the pieces, 5x and x, and set them equal to 90.
Solve the equation. See image. Last, calculate AB.
see image.
The graphs below have the same shape. f(x)=x2².
What is the equation of the graph of g(x)?
O A. g(x)=x²+2
OB. g(x)=(x-2)²
O C. g(x)=x2²-2
OD. g(x) = (x + 2)²
According to the concept of translation, the function of g(x) = x² + 2.
Translation:
The concept of translation is defined by using the function f(x) then f(x + a) is a horizontal translation of f(x)
If the value of a > 0 then a shift to the left of a units
If the value of a < 0 then a shift to the right of a units
Given,
Here we have the function f(x) = x².
Now, we have to find the equation of the graph of g(x) and how it change in corresponds to f(x).
While we looking the graph, the function f(x) has curved on the origin (0, 0).
Where the function g(x) has curved the point (2,0).
Which tells the the graph is move left side by 2 units.
So, according to the rule of translation, the value of a is 2.
Then the function g(x) is written as,
=> g(x) = x² + 2.
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how many miles per gallon of gasoline would a car get if it gets 24 kilometers per liter?
Answer:
160.1 divided by 22.3 = 7.179 miles per litre.
This is 7.179 x 4.544 = 32.62 miles per gallon.
hope that will help
keeping in mind that there are about 1.609 Km in 1 mile and that there are about 3.78L in 1 gallon(US)
[tex]\cfrac{24~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{mile}{1.609~~\begin{matrix} Km \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\cdot \cfrac{3.78~~\begin{matrix} L \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{gallon(US)} \\\\\\ \cfrac{24(3.78)}{1.609}\cfrac{mile}{gallon(US)} ~~ \approx ~~ 56.38\frac{mile}{gallon}[/tex]
find a function whose graph is a parabola with vertex (-3,-9) and that passes through the point (-2,-6)
your answer is f(x)= ____
The function is y = 3(x+3)^2-9
The equation of a parabola is
y=a(x-h)^2+k
where (h,k) are the coordinates of the vertex and a, is a constant.
From the question, we have
(h,k)=(-3,-9)
⇒y=a(x+3)^2-9
To find a, substitute x=-2,y=-6
-6=a(-2+3)^2-9
⇒a=3
The equation, y=3(x+3)^2-9
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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Find the equation of the linear function represented by the table
below in slope-intercept form.
X 0,1,2,3,4 y 6,8,10,12,14
to get the equation of any straight line, we simply need two points off of it, let's use those two in red in the picture below
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{12}-\stackrel{y1}{6}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{ 6 }{ 2 } \implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 3}(x-\stackrel{x_1}{1}) \\\\\\ y-6=3x-3\implies {\Large \begin{array}{llll} y=3x+3 \end{array}}[/tex]
At a music store in New York City, 70 people entering the store were selected at random and were asked to choose their favorite type of music. Of the 70, 18 chose rock, 20 chose
country, 8 chose classical and 24 chose something other than rock, country, or classical.
a) Determine the empirical probability that the next person entering the store favors rock music.
b) Determine the empirical probability that the next person entering the store favors country music.
c) Determine the empirical probability that the next person entering the store favors something other than rock, country, or classical music
a) The empirical probability that the next person entering the store favors rock music is
(Simplify your answer.)
b) The empirical probability that the next person entering the store favors country music is
(Simplify your answer.)
c) The empirical probability that the next person entering the store favors something other than rock, country or classical music is
The probability of the person favoring rock music is 0.257, favoring country music is 0.285, and favoring something other than rock, country, or classical music is 0.342.
Given that:
Total people = 70
Chose rock = 18
Chose country = 20
Chose classical = 8
Chose something other than rock, country, or classical = 24
a) The empirical probability that the next person entering the store favors rock music is = Total people choosing rock music/ Total people
= 18/70 = 9/35 = 0.257
b) The empirical probability that the next person entering the store favors country music is = Total people choosing country music/ Total people = 20/70 = 2/7 = 0.285
c) The empirical probability that the next person entering the store favors something other than rock, country, or classical music is = Total people choosing something other than rock, country, or classical music/ Total people = 24/70 = 12/35 = 0.342.
Hence, the empirical probability that the next person favors rock music is 0.257, favors country music is 0.285, and favors something other than rock, country, or classical music is 0.342.
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i thought of a two-digit number.the digits of my number are different. the units digit f my number is the tens digit raised to the third power. what is my number?
Answer:
28
Step-by-step explanation:
[tex] {2}^{3} = 8[/tex]
The units digit (8) is the tens digit (2) raised to the third power.
Shirley buys a piece of remnant fabric that is triangular in shape with a base length of 2 yd and a height measuring one half yd. If the fabric sells for $4.50 per square yard, how much does Shirley pay for the piece of fabric?
Answer:
the 2 x 0.5 triangle fabric piece cost $2.25
Step-by-step explanation:
Area of a triangle = 1/2 x base x heightbase: 2 yardsheight: 0.5 yards Area of fabric: 1/2 x 2 x 0.5 = 0.5 yards squaredPrice per square yard: $4.50Actual price: $4.50 / 2 = $2.25What is the quotient of 7.2x10^8 and 3.6x10^5 expressed in scientific notation
Answer:
2.0 x 10^3
Step-by-step explanation:
7.2x10^8/3.6x10^5= 2000= 2.0 x 10^3
will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest will give brainiest
Answer:
28.26
Step-by-step explanation:
Hey can someone please explain why you got the answer and how? Thank you so much!
Answer: 25.12 in
Step-by-step explanation:
The circumference of a circle with a diameter of [tex]d[/tex] is [tex]\pi d[/tex].
So, the circumference is [tex]8\pi \approx 25.12[/tex] in.
a waste bin is in the shape of a cylinder. the diameter of the base is 20cm and the height is 25cm. what is the volume of the bin. please help me with the answer.
Answer:
[tex]250\pi[/tex] cm³
Step-by-step explanation:
If the radius is 20 cm, the diameter is 10 cm.
Thus, the volume is [tex]\pi(10^2)(25)=250\pi[/tex] cm³.
Question 30 of 50
The inequality x ≤ -2 would represent the values {-1, -2, -3}.
False
True
Answer:
False. -1 is more than -2, so the first value shows it is false.
I need h e l p
△ABC has a right angle at C, BC=9.2 centimeters, and m∠A=63∘.
What is CA ?
Enter your answer rounded to the nearest tenth in the box.
Answer:
17.8
Step-by-step explanation:
You have to add 9.2 and 63 and the subtract from 90. Hope this helped! <3
On 1/31/Y1, Bailey Company leased a new machine from Sussex Corp. The following data relate to the lease transaction at its inception:
Lease term 10 years
Annual rental payable at beginning of each lease year $50,000
Useful life of machine 15 years
Implicit interest rate 10%
Present value of an annuity of 1 in advance for 10 periods at 10% 6.76
Present value of annuity of 1 in arrears for 10 periods at 10% 6.15
Fair value of the machine $400,000
The lease has no renewal option, the possession of the machine reverts to Sussex when the lease terminates, and the machine does have alternative uses. The first lease payment of $50,000 is paid at the inception of the lease. What is the amount of the first year's lease expense attributable to the interest component?
A. $0. It is an operating lease so there is no interest component.
B. $33,800
C. $25,750
D. $28,800
Answer:
the answer is 4
Step-by-step explanation:
the answer is 4
Suppose you sell 8,000 of the 3 pack of lenses described in question 3 above in one year. You cost on each 3 pack is $29.95 and you sell them for $59.95. If your operating expenses for the year total $144,080, what are your Net Income and Net Profit Margin Percentage?
Your net income and Net profit margin percentage, given the cost of the pack of lenses, and your operating expenses are:
Net income - $95, 920Net profit margin percentage - 19.3%How to find the net income?To find the net income, first find the revenue:
= Number of packs x selling price
= 8, 000 x 59.95
= $479,600
The cost of goods sold is:
= Cost of lenses x number of lenses
= 29.95 x 8,000
= $239, 600
The net income is:
= Revenue - cost of goods sold - operating expenses
= 479, 600 - 239,600 - 144,080
= $95, 920
The net profit margin percentage is:
= Net income / total revenue
= 95, 920 / 497, 600
= 19.3%
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