Calculate the average rate of change of f(x) over the interval [-4, -1] using the formula [ BLANK ] The value of f(-1) is [BLANK] The value of f(-4) is .[BLANK] The average rate of change of f(x) over the interval [-4, -1] is .[BLANK]
First set of answers: A. [f(-4)-f(-1)]/[-5]
B.[f(-1)-f(-4)]/[-5]
C.[f(-1)-f(-4)]/[3]
D.[f(-4)-f(-1)]/[3]
Second set of answers: A.3 Third set: A.-4 Final set A.-2
B.2 B.-3 B.-1.5
C.-1 C.4 C.2
D.4
![Calculate The Average Rate Of Change Of F(x) Over The Interval [-4, -1] Using The Formula [ BLANK ] The](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/9Z0lFvnIL1mlP0tIg57Q6uVjy4bf6osV.jpeg)
Answers
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2
==============================================
Explanation:
For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval
In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank
-------------------------------------------
To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.
-------------------------------------------
Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4
This is why f(-4) = -3
-------------------------------------------
We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.
From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]
We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3
Doing those replacements and simplifying leads to...
[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2
So the average rate of change is 2
Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.
Related Questions
if I have 300 apples and eat 123 how many do I have left?
Answers
You have 177 apples left.
You will have 177 apples left.
Let ABCD be a cyclic quadrilateral. Let P be the intersection of AD and BC, and let Q be the intersection of AB and CD. Prove that the angle bisectors of angle DPC and angle AQD are perpendicular.
Answers
Cyclic quadrilateral ABCD.
Produce AD and BC to meet at P.
Produce AB and CD to meet at Q,
Angle bisector PJ of angle DPC divides angle DPC into two equal parts,x.
Angle bisector QI of angle AQD divides angle AQD into two equal parts,y.
Solution:
Construct segment PQ.
Name U= angle BPQ
Name V=angle BQP.
See attached figure.
Steps:
1. Consider triangle BPQ:
U+V=angle ABP (exterior angle)........................(1)
2. Consider triangle DPQ
U+2X+V+2Y = 180-angle PDQ (exterior angle)
= angle ABC (cyclic quad->opposite angles are supplementary)
=>
U+2X+V+2Y = angle ABC...................................(2)
3. Add (1) and (2)
U+V + U+2X+V+2Y = angle DPQ+angle ABC
=>
2(U+V+X+Y)=180 degrees (angles ABP and ABC lie on a straight lie)
=>
U+V+X+Y = 90 degrees = angle IKJ
4. angle bisectors PJ and QI are perpendicular.
X is a normally distributed random variable with a mean of 5 and a standard deviation of 2. the probability that x is greater than 10.52 is
Answers
A suitable calculator can help with this.
Final answer:
The probability that X is greater than 10.52 for a normal distribution with a mean of 5 and a standard deviation of 2 is found by calculating the z-score of 10.52. The z-score is 2.76, and the area to the right under the normal curve represents a very small probability, typically less than 0.003.
Explanation:
To find the probability that X is greater than 10.52, when X is a normally distributed random variable with a mean of 5 and a standard deviation of 2, we first need to calculate the z-score for 10.52. Using the formula:
Z = (X - mean) / standard deviation
Substitute the given values into the formula:
Z = (10.52 - 5) / 2 = 5.52 / 2 = 2.76
This z-score tells us how many standard deviations above the mean our value lies. In this case, X = 10.52 is 2.76 standard deviations above the mean.
The probability of X being greater than 10.52 corresponds to the area under the standard normal distribution curve to the right of the z-score 2.76. Using standard normal distribution tables or software, we can find this probability to be very small, typically less than 0.003.
A pet store has 26 rabbits and hamsters. The number of rabbits is 2 more than double the number of hamsters. How many hamsters does the pet store have?
Answers
[tex]3x26 \: maybe[/tex]
Let the number of rabbits in the pet store is x
And the number of hamsters in the pet store is y.
Now, we have been given that pet store has 26 rabbits and hamsters. Thus, we have the linear equation
[tex]x+y=26...........(1)[/tex]
Now, number of rabbits is 2 more than double the number of hamsters. Hence, we have
[tex]x=2+2y[/tex]
Substituting this value of x in equation 1, we get
[tex]2+2y+y=26\\ 3y=24\\ y=8[/tex]
Thus, there are 8 hamsters in the pet store.
Hey can you please help me posted picture of question
Answers
So, now the expression graph will be - 3x²
Next, it is shifted to left by 4 units.
So, now the expression will be - 3(x - 4)²
Finally the graph is shifted up by 4 units,
So, now the graph will be: - 3(x - 4)² + 4
Thus, the answer is option D
Explain why a square is always a rectangle but a rectangle is not always a square.
Answers
therefore, because a square has 4 straight sides with 4 right angles, it is a rectangle.
and a rectangle can have unequal adjacent sides, so it is not always a square
Supposed a Visa card had a credit card number of 4162 0012 3456789a where a is the check number what is the check number? A) 0 B) 3 C) 9 D) 7
Answers
Answer:
Option B) 3
Step-by-step explanation:
we have the number
4162 0012 3456 789a
Find the value of a (check number)
step 1
Multiply every even-position digit (when counted from the right) in the number by two. If the result is a two digit number, then add these digits together to make a single digit
4162 0012 3456 789a
9(2)+7(2)+5(2)+3(2)+1(2)+0(2)+6(2)+4(2)
(18)+(14)+(10)+(6)+(2)+(0)+(12)+(8)
Remember that If the result is a two digit number, then add these digits together to make a single digit
so
(1+8)+(1+4)+(1+0)+(6)+(2)+(0)+(1+2)+(8)
(9)+(5)+(1)+(6)+(2)+(0)+(3)+(8)=34
step 2
add every odd-position digit
4162 00123456 789a
so
8+6+4+2+0+2+1=23
step 3
Adds the result in step 1 and the result in step 2
34+23=57
The check-digit is what number needs to be added to this total to make the next multiple of 10
In our case, we’d need to add 3 to make 60
therefore
The check number is 3
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Trapezoid K' is the image of trapezoid K after a series of transformations.
Bella and Marco described the sequence of transformations in different ways.Which sequence or sequences are correct and why?
Answers
Answer:
Option A
Step-by-step explanation:
From the graph attached, we will write the transformation as followed.
a. Trapezoid k is dilated by a scale factor of [tex]\frac{3}{2}[/tex]
[ Since scale factor = [tex]\frac{\text{Largest side of k'}}{\text{Largest side of k}}[/tex]
= [tex]\frac{12units}{8units}[/tex]
= [tex]\frac{3}{2}[/tex] ]
2. scaled trapezoid then rotated by 180°.
3. Then rotated trapezoid is shifted 1 unit down.
By these transformations Bella's sequence was correct.
Therefore, Option A is the answer.
x·\sqrt[4]{x}
Rewrite simplest radical form
Answers
1. You have the following expression given in the problem above:
x√(4x)
2. You must simplify it as below:
(x)(4x)^1/2
3. By the exponents properties, you have:
4x^3/2
√(4x^3)
4. Finally, you obtain:
2√(x^3)
5. Therefore, as you can see, the answer is: 2√(x^3)
Answer:
b
Step-by-step explanation:
asdf
How to round 4.288 to the nearest hundredth
Answers
4,288
round to the nearest hundredth means that we must rewrite the number using only 2 decimal places.
Therefore, we must rewrite the number as follows:
4.29
We observed that:
1) the third decimal disappears
2) the second decimal is rounded to the next number since the third decimal is greater than five.
Answer:
4.29
Isabel created the tree diagram to represent the different ways she could order a salad at her favorite restaurant.
According to the diagram, how many combinations of lettuce type, dressing, and topping are possible?
Answers
Answer: Option B
(B) 12
Step-by-step explanation:
Tim answered all the questions on his math test but got 101010 answers wrong. He received 444 points for every correct answer, and there was no penalty for wrong answers. His score was 767676 points.
Write an equation to determine the total number of questions (q)(q)left parenthesis, q, right parenthesis on Tim's math test.
Find the total number of questions on his math test.
questions
Answers
4(q -10) = 76 . . . . . Tim got 4 points for every right answer, for a score of 76. He answered correctly 10 fewer questions than were on the test.
b)
q = 10 +76/4
q = 29
The total number of questions on Tim's math test was 29.
Answers:
Equation: [tex]q=\frac{76}{4} +10[/tex]
Questions: [tex]29[/tex]
Also, the verified Tutor above is in fact correct, but this answer is way more simple and easier to understand, thank you for your time :D
Explanation:
First, we need to find out the questions, even though the first question is, "What is the equation?". So, to the find the answer to how many questions there are in total we need to grab the total points "[tex]76[/tex]" and divide that by "[tex]4[/tex]" because that'll tell us how many questions that he answered correct. Especially since the "[tex]10[/tex]" questions he got wrong didn't affect his points.
So [tex]\frac{76}{4} =19[/tex]. Now we must add 10 to 19. [tex]10+19=29[/tex]. And so [tex]29[/tex] is the total amount of questions. Now we must write down how we found out. We found out by dividing [tex]76[/tex] and [tex]4[/tex], then we added [tex]10[/tex]!
Conclusion:
As simple as that, we found out how many questions there were in total and how we found out! Thank you for sticking with me♥!
Given rectangle PQRS with PQ=QR, PQ=SP, and SQ=6√2. Find SR. a)√2. b) 6. c) 5√2 d) not enough information
Answers
SQ is the diagonal of the square: [tex]SQ = 6 \sqrt{2} [/tex], but we know that in a square, the diagonal is equal to square root of 2 times the length of the side:
[tex]d = \sqrt{2} L [/tex]
where d is the diagonal and L the length of the side. Since in our square the length of the diagonal is [tex]d= 6 \sqrt{2} [/tex], the length of the side must be
[tex]L= \frac{d}{ \sqrt{2} } = \frac{6 \sqrt{2} }{ \sqrt{2} }=6 [/tex]
so, the correct answer is b) 6.
Where does the graph of y=sin x from x=0 to x=2pie start.
A- at its minimum
B- at an x intercept
C- at its maximum
D- between an x intercept and its maximum
Answers
A- at its minimum
B- at an x intercept
C- at its maximum
D- between an x intercept and its maximum
The correct answer is;
A- at its minimum
When a function is graphed. it usually start at its minimum. Considering the plot for the sine function, the Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°).
It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to -1.
Two quantities are related as shown in the table below:
x. y
2. 3
4. 4
6. 5
8. 6
Which equation best represents the relationship?
Answers
y-y
——
x-x
The y with the greatest value goes first and then the lowest. Same thing with x.
Choose two coordinates from the table
Ex: (4,4) & (2,3)
4-3=1
——-
4-2=2
The slop is 1/2 or 0.5
There is a y intercept which is 2. You get 2 when you divide 1 by 2
So the equation would be
y=1/2x+2 or y=0.5x+2
Hope this helped
A particular hybrid car travels approximately 204 mi on 4 gal of gas. Find the amount of gas required for a 714-mi trip.
Answers
The car needs 14 gallons of gas for the 714 mile trip.
To determine the amount of gas required for a 714-mile trip, we can set up a proportion based on the given information:
We know that the car travels 204 miles on 4 gallons of gas. We need to find the amount of gas needed for 714 miles. Let the gas required for 714 miles be X gallons
First, let us set up the proportion:
204 mi / 4 gal = 714 mi / X galNext, we solve for x (the amount of gas required for 714 miles):
204 mi × X gal = 714 mi × 4 gal204X = 2856X = 2856 / 204X = 14Therefore, the car requires 14 gallons of gas for a 714-mile trip.
A bank account earns interest at a rate of 3.5% per year ( in other words it increases in value by that percent) and starts with a balance of $350. Which of the following equations would give the account’s worth, W, as a function of the number of years, y, it has been gaining interest?
Answers
The account's worth, W, as a function of the number of years, y it has been gaining interest is given by the equation W = $350 + ($350 imes 0.035 imes y).
Explanation:The equation that gives the account's worth, W, as a function of the number of years, y, it has been gaining interest is:
W = $350 + ($350 imes 0.035 imes y)
Here's an example:
If the account has been gaining interest for 2 years, then W = $350 + ($350 imes 0.035 imes 2) = $364.70.
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Use part 1 of the fundamental theorem of calculus to find the derivative of the function. g(x) = x e2t2 − 4t dt 4
Answers
Using the Fundamental Theorem of Calculus Part 1, the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4 is ex2 - 4x where 'x' is the variable 't' from the integral.
Explanation:The subject of this question is the use of part 1 of the Fundamental Theorem of Calculus to find the derivative of a complex function. This theorem states that if f is a function that is continuous over the interval [a, b] and F is an antiderivative of f on the interval [a, b], then the definite integral of f from a to b is equal to F(b) - F(a).
In your specific question, you are asked to find the derivative of the function g(x) = ∫ (x e2t2 - 4t) dt from x=4.
The derivative of a definite integral, from a constant to a variable, of a function is simply the original function evaluated at the upper limit.
Therefore, the derivative of the given function g(x) is simply ex2 - 4x, treating 'x' as the variable 't' from the integral.
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(08.06 MC) Carly and Janiya put some money into their money boxes every week. The amounts of money (y), in dollars, in their money boxes after certain amounts of time (x), in weeks, are shown by the equations below: Carly y = 60x + 40 Janiya y = 50x + 80 After how many weeks will Carly and Janiya have the same amount of money in their money boxes and what will that amount be? (1 point) 5 weeks, $280 5 weeks, $340 4 weeks, $280 4 weeks, $340
Answers
y = 60x + 40
y = 50x + 80
Equaling both equations we have:
60x + 40 = 50x + 80
From here, we clear the value of x:
60x - 50x = 80 - 40
10x = 40
x = 40/10
x = 4 weeks
Substituting x = 4 in any of the equations we have:
y = 60 (4) + 40
y = 240 + 40
y = 280 $
Answer:
$ 280 4 weeks
Answer:
$ 280 4 weeks
Step-by-step explanation:
What are the correct coefficients (reading from left to right) when the chemical equation is balanced?__pbr3(l)+__h2o(l)→__h3po3(aq)+__hbr(aq)what are the correct coefficients (reading from left to right) when the chemical equation is balanced?________1, 3, 1, 31, 3, 3, 13, 5, 1, 81, 2, 1, 2?
Answers
1,3,1,3
The correct coefficients (reading from left to right) are chemical equation is balanced as 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq). which is the correct answer would be an option (A).
What is the rule of conservation of mass?Mass, according to the rule of conservation of mass, cannot be generated or destroyed. As a result, the mass of products must match the mass of reactants. Each element's atom count must be identical on the reactant and product sides. As a result, chemical equations are balanced.
According to the given question,
We have to substitute the coefficients (reading from left to right) are 1,3,1,3 in the given chemical equation
Thus, the correct coefficients (reading from left to right) are balanced chemical equation as :
⇒ 1PBr₃(l) + 3H₂O(l) → H₃PO₃(aq) + 3HBr(aq).
Hence, the correct answer would be option (A).
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What is the probability that a randomly thrown dart that lands within the rectangle lands within a shaded region? All of the circles are congruent, and the diameter of each circle is 100 cm. A. 39/200 B. 49/250 C. 98/125 D. 157/200
Answers
Which of the following is the graph of y=|x-1|-4y=∣x−1∣−4y, equals, vertical bar, x, minus, 1, vertical bar, minus, 4?
Answers
y = |x -1| -4
is show here.
Answer:
The graph of given function is shown below.
Step-by-step explanation:
The given function is
[tex]y=|x-1|-4[/tex] .... (1)
The vertex form of a absolute function is
[tex]y=a|x-h|+k[/tex] .... (2)
where, a is a constant and (h,k) is vertex.
On comparing (1) and (2), we get
[tex]a=1,h=1,k=-4[/tex]
The vertex of the function is (1,-4). The table of values is
x y
3 -2
2 -3
1 -4
0 -3
-1 -2
Plot these points on a coordinate plane. Draw a V-shaped curve by connecting these points with vertex at (1,-4).
Q9 Q4.) Write the augmented matrix for the system of equations to the right.
Answers
the first equation is x-y +8z = 7
so the first row in the matrix would be 1 ( there is 1x) -1 ( there is 1 negative y) 8 ( there are 8 z's) and then the answer is 7
then follow this step for the other 2 equations
see attached picture for answer:
In a school auditorium there are 33 seats in each row of seats. How many rows are needed for 528 students to each have a seat?
Answers
528/33 = 16 rows.
To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, divide the total number of students by the number of seats in each row. The answer is 16 rows.
Explanation:To find the number of rows needed for 528 students to each have a seat in a school auditorium with 33 seats in each row, we need to divide the total number of students by the number of seats in each row.
So, the number of rows needed would be:
Rows needed = Total number of students ÷ Number of seats in each row
Substituting the given values:
Rows needed = 528 ÷ 33 = 16
Therefore, 16 rows are needed for 528 students to each have a seat in the auditorium.
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Q7 Q26.) Find the quotient of the complex numbers and leave your answer in polar form.
Answers
(Where [tex]\text{cis}(\theta) = \cos(\theta) + i\sin(\theta)[/tex])
Then [tex]\dfrac{c_1}{c_2} = \dfrac{r_1}{r_2}\text{cis}(\theta_1-\theta_2)[/tex]
So then for your problem, that would be
[tex]\dfrac{z_1}{z_2} = \dfrac37\text{cis}\left(\dfrac\pi8-\dfrac\pi9\right)=\boxed{\dfrac37\text{cis}\left(\dfrac\pi{72}\right)}[/tex]
So that would be [tex]\boxed{\dfrac37\left(\cos\left(\dfrac\pi{72}\right)+i\sin\left(\dfrac\pi{72}\right)\right)}[/tex]
Hope this helps.
A television is 36 inches by 18 inches. What is the area?
Answers
hope this is helpful
Turtle and vicent combine their coins to find they have all dimes and quarters .They have 8 more quarters them dimes and the coins are worth a total of 5.15 .How many dimes and quarters do they have?
Answers
There are 9 dimes and 17 quarters.
Find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6
Answers
For 10/15 = x / 60
x = (10/15) * (60)
x = 40
For x / 108 = 4/9
x = (4/9) * (108)
x = 48
For 7/11 = x / 121
x = (7/11) * (121)
x = 77
For x / 144 = 2/6
x = (2/6) * (144)
x = 48
Final answer:
The missing numerators are found by creating equivalent fractions. By multiplying both the numerator and the denominator by the same factor that converts the original denominator to the new denominator, we find the missing numbers: 40, 48, 77, and 48 for each problem respectively.
Explanation:
To find the missing numerators, we need to use the concept of equivalent fractions. Equivalent fractions have different numerators and denominators but represent the same value.
a. 10⁄15 = ⁄60
We find the factor that converts 15 to 60, which is 4 (since 15 * 4 = 60), and multiply the numerator by the same factor (10 * 4 = 40). So, the missing numerator is 40.
b. ⁄108 = 4⁄9
To convert 9 into 108, multiply by 12 (since 9 * 12 = 108), and do the same with the numerator (4 * 12 = 48). Hence, the missing numerator is 48.
c. 7⁄11 = ⁄121
11 times 11 equals 121, so we multiply the numerator 7 by 11 as well (7 * 11 = 77), giving us 77 as the missing numerator.
d. ⁄144 = 2⁄6
To get from 6 to 144, multiply by 24 (since 6 * 24 = 144), so multiply the numerator 2 by 24 to get 48 as the missing numerator.
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle. The leg of the triangle labeled 4 inches passes through the center of the circle, O. The other two legs are labeled as 2 inches and 3 inches.
Which of the following expressions shows the area, in square inches, of the circle?
(π = 3.14)
3.14 ⋅ 2
3.14 ⋅ 3
3.14 ⋅ 22
2 ⋅ 3.14 ⋅ 22
Answers
Answer:
3.14 2^2
Step-by-step explanation:
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units. Then the correct option is C.
What is a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
The image below is a triangle drawn inside a circle with center O:
A triangle is shown inscribed inside a circle.
The leg of the triangle labeled 4 inches passes through the center of the circle, O.
The other two legs are labeled as 2 inches and 3 inches.
The expressions shows the area, in square inches, of the circle will be
Area of circle = (π/4) d²
The diameter of the circle is passing through center. Then the length of the diameter is 4.
Then the area of circle will be,
Area = (π/4) 4²
A = 3.14 × 4
A = 3.14 × 2² square units
The expressions shows the area, in square inches, of the circle will be 3.14 × 2² square units.
Then the correct option is C.
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simplify the expression 11x-(2x^2+8x).