Answers
The average rate of change of the function f(x) over the interval (-1, 2) is; 3.
What is the difference quotient of the function over the given interval?As evident in the task content; the given function is as represented by the graph of f(x).
Hence, the average rate of change of the function over the given interval; (-1, 2) is;
= ( f (2) - f (-1) ) / (2 - (-1))
where; f (2) = 5 and f (-1) = -4.
Therefore, the average rate of change is;
= (5 - (-4)) / (2 - (-1))
= 9 / 3.
= 3.
Ultimately, the difference quotient of f (x) over the given interval is; 3.
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Related Questions
Graph h(x)=−x2+3.
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answers
Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.
A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.
The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.
To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:
h(-2) = -(-2)^2 + 3
h(-2) = 4 + 3
h(-2) = 7
So the point (-2, 7) is also on the parabola.
With the vertex and one other point on the parabola, you can now graph the parabola.
Step-by-step explanation:
Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g. A. g(-13) = 20 B. g(0) = 2 C. g(7) = -1 D. g(-4) = -11
Answers
Answer: It is not possible to determine the truth of these statements without further information about the function g. The information given only provides the domain and range of the function and the values of g at two specific points, 0 and -9. To determine the value of g at other points, we would need to know the equation for the function g.
Step-by-step explanation:
Find the equation of the line L
Answers
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture above
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-3}-\underset{x_1}{(-1)}}} \implies \cfrac{1 +1}{-3 +1} \implies \cfrac{ 2 }{ -2 } \implies - 1[/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}{(-1)}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies y +1 = - 1 ( x +1) \\\\\\ y+1=-x-1\implies {\Large \begin{array}{llll} y=-x-2 \end{array}}[/tex]
what must be added to each term of the ratio 49:64 , so that it becomes 3:4 ?
Answers
Answer:
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.
Step-by-step explanation:
have a nice day.
I will give brainliest and ratings if you get this correct
Answers
The quotient rule is proved below.
What is derivative of a function?In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
Given is the expression -
Q(x) = F(x)/G(x)
Quotient rule -Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -
f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Proof -Now, let f(x) = u(x) and g(x) = v(x).
Q(x) = u(x)/v(x)
Q(x) = u(x) v⁻¹(x)
Using the product rule -
Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}
Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)
Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)
Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²
Therefore, the quotient rule is proved above.
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Select the graph of y = 2 sinz+2
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Answers
The graph of y = 2 sin(x) + 2 is given by the following option:
Graph A.
How to graph the sine function?The standard definition of the sine function is given as follows:
y = Asin(B(x - C)) + D.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: phase shift.D: vertical shift.The function in this problem has an amplitude of 2, meaning that before the vertical shift, it oscillates between -2 and 2.
Due to the vertical shift, the function is going to oscillate between 0 and 4, with a period of 2π and no phase shift, crossing the midline of y = 2 at the origin, hence Graph A is the correct graph.
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For 5days, Kareem put 4 into his savings account each day. His parents also added a certain amount of money to the account each day. In the end, there was a total of 40 in the account. How much money did Kareem's parents add each day?
Answers
Answer:
both Kareem and his parents added 4 each, to the ACC for five days
Jason wants to dine at five different restaurants during a summer getaway. If three of nine available restaurants serve seafood, find the number of ways that at least one
of the selected restaurants will serve seafood given the following conditions.
(a) The order of selection is important.
(b) The order of selection is not important.
(a) If the order is important, then the number of ways that at least one of the selected restaurants will serve seafood is
Answers
answer
C(9, 5) - C(6, 5) + C(3, 1) = 126 - 6 + 3 = 123
explanation
The first term, C(9, 5), represents the number of ways to select 5 restaurants out of 9, regardless of type. The second term, C(6, 5), represents the number of ways to select 5 non-seafood restaurants out of 6. To find the number of ways that at least one of the selected restaurants will serve seafood, we subtract the number of ways to select 5 non-seafood restaurants and add the number of ways to select exactly 1 seafood restaurant, represented by C(3, 1).
The result, 123, represents the number of ways that at least one of the selected restaurants will serve seafood.
please help as quickly as possible!
Answers
On solving the provided question we can say that the quadratic equation is 3x²+15x+9=0
What is quadratic equation ?A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.
the quadratic equation is 3x²+15x+9=0
by Shridhara Charya formula method, we have
x=−0.697224
x=−4.30278
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could you please help me find out how to add m+x
Answers
Answer:
i got u i have your email
Step-by-step explanation:
What is the value of r^2 for the following data yo three decimal places ?
Answers
The correlation coefficient of the data-set in this problem is given as follows:
C. r² = 0.931.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The points from the table in this problem are given as follows:
(3,2), (4,4), (5,5), (7,6), (10,20).
Inserting these points into a calculator, the correlation coefficient is obtained as follows:
r² = 0.931.
Meaning that the correct option is given by option C.
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Using The Distance Formula: What is the length of AB
With A(3,4) and B(-4,6)
A'B' = D2/3 (AB)
Answers
Multiply
-1/5. (-2/7)
Write answer in simplest form.
Answers
Answer:
2/35
Step-by-step explanation:
[tex](-\frac{1}{5})(-\frac{2}{7}) = \frac{2}{35}[/tex]
LEVEL 3
Record the letters
in your triangle from
left to right.
Example:
ABCDEFGHI
Enter the correct 9 letter sequence (no spaces) Use all capital letters *
Answers
Triangle is a polygon with 3 sides. The record of the letters in your triangle from left to right is EGFBIHDCA.
What is a triangle?A triangle is a polygon with 3 sides. Also, It has three vertices.
As the example is given to us, ABCDEFGHI is the record of the letters that are when seen from top to bottom, therefore, if we rotate the triangle such that the left side of the triangle is on the upper side, then the triangle we will get is given below.
Thus, the record of the letters in your triangle from left to right is EGFBIHDCA.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
Equations 4 and 5 are not equivalent to any of the other equations.
What is a equation in math?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
The equations that are equivalent are:
2 + x = 5
Negative 5 + x = negative 2
x + 1 = 4
Subtracting 2 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Adding 5 to both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
Subtracting 1 from both sides, we get x = 3. Therefore, the equation is equivalent to x = 3.
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1. Is Event 1 and Event 2 Mutually Exclusive of each other? Event 1: Pre- Schooler is a girl Event 2: Pre- Schooler prefers the color blue to the color pink Select one: a. No, A girl pre-schooler can prefer the color blue to the color pink. b. Yes, The gender of pre-schooler has no affect on color preference c. Yes, Girls prefer the color pink to the color blue 2. 70 preschoolers were asked whether they preferred blue or pink. 35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color. Assuming one of the pre-schoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
Answers
The probability of choosing a preschooler who is a girl and prefers the color blue is 0.3 or 30%.
The total number of preschoolers who were asked about their color preference is 70. Out of these, 35 girls chose pink, 15 girls chose blue, 5 boys chose pink, and 15 boys chose blue.
To find the probability of choosing a girl who prefers blue, we need to use the formula:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Here, the favorable outcome is choosing a girl who prefers blue. We can see that 15 girls chose blue as their preferred color. Out of these, we need to choose a girl, so the total number of favorable outcomes is 15.
The total number of outcomes is the total number of preschoolers, which is 70. Out of these, the number of girls is 35+15=50. Therefore, the total number of outcomes where a girl can be chosen is 50.
Putting these values in the formula, we get:
Probability = 15/50 = 0.3
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Complete Question;
70 preschoolers were asked whether they preferred blue or pink.
35 Girls chose pink as preferred color, 15 girls chose blue as preferred color, 5 boys chose pink as preferred color, and 15 boys chose blue as preferred color.
Assuming one of the preschoolers is chosen at random determine the probability of choosing a preschooler that is a girl that prefers the color blue. Round answer to 2 decimal places.
Rectangle A: 2 * 3 Rectangle B: 8 * 12 Rectangle C: 5 * 7 Rectangle D: 10 * 12 Which pair of rectangles is similar?
Answers
Answer: your mom
Step-by-step explanation:
Suppose you have $200 with which you can buy shares of stock from two companies:
ABC Hot Chocolate Company and XYZ Lemonade. Each company's stock currently sells for $100 per share. If the temperature next year is lower than average, the stock price for ABC will increase by $20, and the stock price for XYZ will not change.
If the temperature next year is higher than average, the stock price for XYZ will increase by $20, and the stock price for ABC will not change. There is a 50% chance that it will be colder than average next year, and a 25% chance that it will be warmer than average.
If you purchase two shares of ABC stock and no shares of XYZ stock, there is a _____ chance that your gain will be $40. Otherwise, your gain will be _____.
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
Answers
The chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and if it is not $40 the gain is:
1) 50%, $0
2) 25%, $20
3) 75%, $30
4) 50%, $20
So, the option (4) 50%, $20 is the correct option.
The given question is asking what the chances are that your gain will be $40 if you purchase two shares of ABC stock and no shares of XYZ stock, and what the gain will be if it is not $40.
Mathematically, this can be broken down as follows:
There is a 50% chance that the temperature will be lower than average, in which case the stock price for ABC will increase by $20. Thus, the expected gain from investing in ABC is 50% x $20 = $10.
There is a 25% chance that the temperature will be higher than average, in which case the stock price for XYZ will increase by $20. Since you are not investing in XYZ, your expected gain from this is 0.
Therefore, the expected gain from investing in ABC and not investing in XYZ is 50% x $10 + 25% x $0 = $10 + $0 = $10.
Since you are investing in two shares of ABC stock, your expected gain is 2 x $10 = $20. Thus, there is a 50% chance that your gain will be $40, and otherwise your gain will be $20.
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Subtract 5m + 11 and m + 8
Answers
The expression (m + 8) - (5m + 11) simplifies to -4m - 3.
How to subtract the expresisonsFrom the question, we have the following parameters that can be used in our computation:
Subtract 5m + 11 and m + 8
To subtract (5m + 11) from (m + 8), we need to distribute the negative sign to each term inside the first set of parentheses:
(m + 8) - (5m + 11)
Open the brackets
= m + 8 - 5m - 11
Evaluate the like terms
= -4m - 3
Hence, (m + 8) - (5m + 11) simplifies to -4m - 3.
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To encourage bulk buying, a company reduces the list price of $4,000 per unit by
three cents times the number of units bought. Write a function statement for the
company's revenue (R) from a particular distributor that buys x units.
R(x) =
Answers
The expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased and multiplying by x gives the total revenue from selling x units at that price.
What is revenue?
Revenue can be defined as the total amount of income generated by the sale of goods and services related to the primary operations of the business.
The revenue (R) from a particular distributor that buys x units can be calculated using the following function statement:
R(x) = (4000 - 0.03x) * x
Where
4000 is the original list price per unit 0.03 is the discount per unit per unit purchased x is the number of units purchasedThe expression (4000 - 0.03x) represents the discounted price per unit when x units are purchased, and multiplying by x gives the total revenue from selling x units at that price.
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Describe the transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4
A:The graph is vertically stretched by a factor of 1/3 and shifts up 4 units.
B:The graph is vertically stretched by a factor of 1/3 and shifts down 4 units.
C:The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
D:The graph is horizontally compressed by a factor of 1/3 and shifts down 4 units.
Answers
The transformation given to the parent function f(x)=sin(x) given the graph of the equation g(x)=sin(3x)-4 will be C. The graph is horizontally compressed by a factor of 1/3 and shifts up 4 units.
How to explain the transformationThe parent function f(x) = sin(x) has been transformed by replacing x with 3x in the argument of the sine function.
This results in a horizontal compression of the graph by a factor of 1/3. In addition, the graph of g(x) = sin(3x) is shifted upward 4 units, as indicated by the subtraction of 4 from the value of the sine function.
The correct option is C.
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18 What is the solution to the system of equations x - y = -1 and x-3y = - 13?
A. (5, 6)
B.
(6,5)
C. (7,8)
D.
(8,7)
Answers
Using elimination, subtract EQ.2 from EQ.1
When we subtract, we change the sign of EQ.2 and add
x - y = -1 Equation 1
- (x - 3y = -13) Equation 2
x - y = -1 Equation 1
-x + 3y = 13 Equation 2
__________
2y = 12
Divide both sides by 2 to solve
2/2 y = 12/2
y = 6
Substitute y value of 6 into EQ.1
x -6 = -1
Add 6 to both sides to solve for x
x -6 +6 = -1 +6
Simplify
x = 5
Solution: ( 5, 6 )
The angles of a triangle are in the ratio of 2 : 3 : 7. Find the measure of the two greatest angles of the triangle.
Answers
Answer:
Step-by-step explanation:
The measure of the two greatest angles is 105° and 45°
Let the angles be 2x, 3x and 7x ...... (i)
According to the 'Angle Sum Property' of triangle,
2x + 3x + 7x = 180°
12x = 180°
x = 15°
Now, put value of x in (i)
2x = 2 × 15 = 30°
3x = 3 × 15 = 45°
7x = 7 × 15 = 105°
so, the two greatest angles are 105° and 45°
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What else would need to be congruent to show that AABC= APQR by SSS?
B
A
A. AC = PQ
B. AB BA
C. BC= QR
D. ZAZP
C
Q
P
R
Given:
AC PR
AB=PQ
Answers
The condition which satisfy the congruency of the given triangle is
BC≈QR.
What is congruency of triangles?Two triangles are said to be congruent if all the corresponding sides are equal and all the corresponding angles are equal. The symbol of congruency is '≅'
To show that triangle ABC≈triangle PQR by SSS,
In this type of congruency, all the sides of the triangle ABC is equivalent to the all the sides of the triangle PQR.
Given, AC≅PR, AB≅PQ.
The another one condition is BC≅QR.
Hence, the condition which satisfy the congruency of the given triangle is BC≈QR.
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Find the average rate of change, problem in picture
Answers
The average rate of change of the function over the interval (-1, 2) is 3.
What is Average Rate of Change of a Function?Average rate of change of a function is defined as the rate at which the value of the function is changing with respect to the change in the input values.
Difference quotient of a function over an interval is also the same concept as the average rate of change of a function.
Average rate of change of a function f(x) over an interval (a, b) is [tex]\frac{f(b) - f(a)}{b-a}[/tex].
Given interval is (-1, 2).
From the graph, f(-1) = -4 and f(2) = 5
Average rate = [tex]\frac{f(2) - f(-1)}{2--1}[/tex] = (5 - -4) / (3) = 9/3 = 3
Hence the given function has an average rate of change over the interval (-1, 2) at 3.
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Identify true statements about set membership and subsets
Answers
The statement that are true are :
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
What is set?
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.
The following statements are true about the set
a. Z is an element {y,z}
b. {6,7,8 } is a subset of {1,2,3,4......}
c. 3 is an element of {2,3}
d. r is not an element of {s,t,u}
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find the value of each variable provide proofs
Answers
x= 19, y=19
There is a theorem with 45 degrees 45 degrees 90 degrees triangles, it is that the two legs are equal to a and the hypotenuse is equal to a√2
So, since we know the hypotenuse is 19√2, a=19
so x = 19and y = 19
Find the 66th
term in the following
arithmetic sequence
-92, -85, -78, -71, ...
Answers
Answer:
The [tex]66[/tex]th term is [tex]363[/tex].
Step-by-step explanation:
To find the [tex]n[/tex]th term, the formula is [tex]7n - 99[/tex]. Since we want to find the [tex]66[/tex]th term, we can plug [tex]n[/tex] for [tex]66[/tex]. So our expression is now [tex]7 \cdot 66 - 99 =[/tex] [tex]66[/tex]th term. Solving this we have
[tex]462 - 99 = 66\text{th term}\\363 = 66\text{th term}\\[/tex]. Therefore, the [tex]66[/tex]th term is [tex]\boxed{363}[/tex].
Answer:
a₆₆ = 363
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = - 92 and d = a₂ - a₁ = - 85 - (- 92) = - 85 + 92 = 7 , then
a₆₆ = - 92 + (65 × 7)
= - 92 + 455
= 363
Please help:) calculus asking about delta functions
Answers
The required solution of the given expression δ = 0.0002. as of the given conditions
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given |x - 3| < δ, we want to find a value of delta such that |5x - 15| < 0.001.
Starting with the inequality |x - 3| < δ, we can substitute x = 3 + delta or x = 3 - δ. Let's consider the case x = 3 + δ,
|5x - 15| = |5(3 + δ) - 15|
= |15 + 5δ- 15|
= |5δ|
Now, we want |5δ| to be less than 0.001. So, we can divide both sides of the inequality by 5,
|5δ|/5 < 0.001/5
|δ| < 0.001/5
Therefore, if the delta is less than 0.001/5, we have |5x - 15| < 0.001.
Similarly, if x = 3 - delta, we have:
|5x - 15| = |5(3 - δ) - 15| = |15 - 5δ - 15| = |-5δ|
|-5δ|/5 < 0.001/5
|δ| < 0.001/5
So, if δis less than 0.001/5, then |5x - 15| < 0.001 for both x = 3 + delta and x = 3 - δ.
Therefore, if |x - 3| < 0.001/5, then |5x - 15| < 0.001.
So, δ= 0.001/5 = 0.0002.
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PLEASE ANSWER QUICKLY!
For students majoring in Hospitality Management, it was determined that 5% have visited 1–10 states, 16% have visited 11–20 states, 45% have visited 21–30 states, 19% have visited 31–40 states, and 15% have visited 41–50 states. Suppose a Hospitality Management student is randomly selected. What is the probability that the student has visited 21 or more states?
A. 0.15
B. 0.21
C. 0.45
D. 0.79
Answers
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
from the given data we get,
The categories are mutually exclusive, so we have ...
P(≥21) = P(21-30) +P(31-40) +P(41-50)
= 45% +19% +15%
P(≥21) = 79%
=0.79
The probability is 0.79 that a randomly chosen student has visited 21 or fewer states.
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