Given the function f(x) = x^2-6x+4, determine the average rate of change of the function over the interval 1≤x≤4.
Answer:
The average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.
Step-by-step explanation:
We are given the function:
[tex]f(x)=x^2-6x+4[/tex]
And we want to determine its average rate of change over the interval:
[tex]1\leq x\leq 4[/tex]
The average rate of change is synonymous with the slope. So, to find the average rate of change, we simply need to find the slope between the two endpoints.
Evaluate each endpoint:
[tex]f(1)=(1)^2-6(1)+4=-1[/tex]
[tex]f(4)=(4)^2-6(4)+4=-4[/tex]
So, our endpoints are (1, -1) and (4, -4).
The slope between them is:
[tex]\displaystyle m=\frac{(-4)-(-1)}{(4)-(1)}=\frac{-3}{3}=-1[/tex]
So, the average rate of change of f(x) over the interval 1 ≤ x ≤ 4 is -1.
I need help on this one too. Please.
help please !!!!!!!!!
Answer:
24
Step-by-step explanation:
Help please I am struggling thank you
The answer is 904.8 yd³
Step-by-step explanation:
The formula for a sphere's volume is 4/3πr²
r in this case is 12/2 which is 6. That means that r=6 which gives us 904.78 which is rounded to 904.8.
Answer:
904.32
Step-by-step explanation:
v= [tex]\frac{4}{3\\}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
first cube the radius (6) (radius is half of the diameter 12)
6x6x6 = 216
multiply by pi
216 x 3.14 = 678.24
multiply by 4/3
[tex]\frac{678.24}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{2712.96}{3\\}[/tex] = 904.32
Kiera’s middle school is conducting a survey to determine the winter dance theme. Which of the following best describes a random sample?
1 point
A. All of the students in Mrs. Jackson’s class are surveyed
B. Fifty student’s names from each grade are drawn from a hat
C. Fifty randomly selected staff members are surveyed
D. Fifty randomly selected 7th graders are surveyed
The best description of a random sample for Kiera's middle school survey to determine the winter dance theme is option D: Fifty randomly selected 7th graders are surveyed.
What is random sampling?Random sampling is a technique for picking a sample from a population in such a manner that each possible sample has a preset probability of being chosen.
As per the question, the sample should be representative of the entire student population, so selecting fifty students from each grade (option B) or all the students in Mrs. Jackson's class (option A) may not be representative of the entire student population.
Similarly, selecting fifty randomly selected staff members (option C) may not be representative of the student population.
Therefore, option D is the best choice as it randomly selects students from the population of interest.
Learn more about random sampling here:
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there are 5 green balls, 1 yellow ball,and 4 red balls in a bag. what are the probabilities?
choosing a red:
not choosing yellow:
choosing a blue:
Answer:
it is green balls=5
red balls =4
red +green
5+9
=14
Does anyone know how to turn off downtime without knowing the password or is there something I can download that anyone knows about
What is m Please help me I’m willing to pay you for other problems just message me.
Answer:
56
Step-by-step explanation:
56
hope this helps
¬_¬ :)
please help, you can just slide the answer
Answer:
c is correct have a nice day
Step-by-step explanation:
Help please this iis due today
Answer:
B is the correct answer
since
a1/a2=b1/b2≠c1/c2
Four lines are shown in the graph below.
Which line has the slope with the greatest value?
A
line A
B
line B
C
line C
D
line D
Answer:
D
Step-by-step explanation:
A vertical line will have the steepest slope
I need help plssssss
Answer:
Yes
Step-by-step explanation:
2 sides are equal as well as one angle being equal, so we know that the other angles must be equal, along with the other side.
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Can you conclude from the figure that ABC is similar to DEF? Explain.
Answer:
Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.
Step-by-step explanation:
We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.
Triangle ABC:
Measure of angle A= 60°
Measure of angle C= 40°
Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°
Triangle DEF
Measure of angle E= 80°
Measure of angle F= 40°
Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°
The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.
The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.
Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.
#savesheikhjarrah
Let’s all pray for Palestine ♥️
Answer:
soi de perú NO INGLISH IS SPANISH
Step-by-step explanation:
JAJAJAJ
The statement below is a different way to say that the sides of these similar parallelograms are proportional.
Complete the equations that go with the statement.
The correct statement is [tex]\frac{a}{b}[/tex] = [tex]\frac{t}{s}[/tex] , [tex]\frac{b}{c}[/tex] = [tex]\frac{s}{r}[/tex] , [tex]\frac{c}{d}[/tex] = [tex]\frac{r}{q}[/tex].
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Similar figures are those figures whose ratio of the length of sides are proportional.
Similar figures only differ in size, their shape is equal.
The sides a, b, c and d in the larger parallelogram is similar to the sides t, s, r and q respectively in the smaller parallelogram.
So we get the ratio b / c equal to the ratio s / r and the ratio c / d equal to the ratio r / q.
Hence the equation that go with the statement two sides of a parallelogram have the same ratio as the corresponding two sides of a parallelogram is [tex]\frac{a}{b}[/tex] = [tex]\frac{t}{s}[/tex] , [tex]\frac{b}{c}[/tex] = [tex]\frac{s}{r}[/tex] , [tex]\frac{c}{d}[/tex] = [tex]\frac{r}{q}[/tex].
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Answer:The first one is 16 and the second one is 18
Step-by-step explanation:
Express 0.74 as a percentage
Answer:
74%
Step-by-step explanation:
0.74 × 100 = 74%
Answer:
74% (answer).
Step-by-step explanation:
To convert from decimal to percent, just multiply the decimal value by 100. In this example we have: 0.74 × 100 =74%
Herbert has three lawn-mowing jobs. One lawn is shaped like a trapezoid,
one like a triangle, and one like a rectangle. The trapezoidal lawn has bases that are 90 feet and 126 feet and a height of 75 feet. The triangular lawn has a height of 80 feet and a base of 105 feet. The rectangular lawn has a length of 120 feet and width of 90 feet. If Herbert can cut a 160 ft × 70 ft lawn in 2 hours, how long will it take him to mow all three lawns?
Answer:
4.125 hours
Step-by-step explanation:
Trapezoid shaped lawn :
Bases : 90 ; 126 ; height = 90
Area of trapezium = 1/2(a+b) h ; a and B are the bases and h = height
Area of trapezium = 1/2(90 + 126) * 75
Area = 108 * 90 = 8100 feets
Triangular lawn :
Height = 80 feets ; Base = 105 feets
Area of triangle = 1/2 base * height
Area = 1/2 * 80 * 105 = 4200 feets
Rectangular lawn :
Length = 120 feets ; width = 90 feets
Area of rectangle = Length * width
Area = 120 * 90 = 10800 feet²
Area of all 3 lawns = (8100 + 4200 + 10800) = 23100
In 2 hours ; Herbert can now (160 * 70) = 11200 feets
23100 / 11200 = 2.0625
Tine required to mow all three lawns :
2 hours * 2.0625 = 4.125 hours
= 4 hours, 7 minutes, 30 seconds
Please helpppp
Extra points and brainleist
Answer:
B
Step-by-step explanation:
x² - 4x - 7 = 0
(x - 2)² = 11
Lucy is planting grass in her front yard and backyard. Her front yard is 20 ft. by 35 ft., and her backyard is 13 ft. by 17 ft. What is the total area of the space in which Lucy will plant grass?
In how many different ways can 3 people select seats at a
dining table having 8 seating positions if they can select any
seat?
2x + 2y = -4
3x - 2y = 9
Answer:
x = −y −2
Step-by-step explanation:
help help help i’ll kiss u
Answer:
I, J
Step-by-step explanation:
PLEASE HELP THIS IS OVERDUE!!
Answer:
y=1/2x-3
Step-by-step explanation:
Translate algebraic words to symbols.
Two times the sum of a and b
A. 2(a + b)
B. 2 + ab
C. 2ab
D. 2(a/b)
Answer:
Option A
Step-by-step explanation:
That is your answer
Answer:
a) 2(a+b)
Step-by-step explanation:
the sum of 2 numbers (or more) is always addition
so the sum of a and b would be (a+b)
then, 2 times of a and b;
2(a+b)
^the times sign between the bracket and the 2 isnt needed, whenever there is a bracket and a number next to it, it is automatically a multiplication.
what the sum of (2×105)+(3.8×105)=
Find the area of a circle with a circumference of 50.24 units.
Answer:
200.96
Step-by-step explanation:
have a good day:D
Sam volunteers at an animal shelter. He created a line plot to show the weights in pounds of the kittens at the shelter.
Line plot named as ALTDCWeights of Kittens in ShelterALTDC shows a number line from half to two and half. The number line is divided into 4 equal parts. 3 dots on half, 2 dots on 1 and 1 dot on one and half is given.
What is the total weight of the kittens in the shelter?
Answer:
The total weight is 5kg
Step-by-step explanation:
Given
See attachment for box plot
Required
Determine the total weight of the kitten
First, we represent the plot in the following table where the number of dots represent the frequency.
So, we have:
[tex]Weight \to Frequency[/tex]
[tex]\frac{1}{2} \to 3[/tex]
[tex]1 \to 2[/tex]
[tex]1\frac{1}{2} \to 1[/tex]
[tex]2 \to 0[/tex]
[tex]2\frac{1}{2} \to 0[/tex]
Multiply the weight by the frequency, then add up the result
So, we have:
[tex]Total = \frac{1}{2} * 3 + 1 * 2 + 1\frac{1}{2} * 1 + 2 * 0 + 2\frac{1}{2} * 0[/tex]
[tex]Total = 1\frac{1}{2} + 2 + 1\frac{1}{2} + 0 + 0[/tex]
[tex]Total = 1\frac{1}{2} + 2 + 1\frac{1}{2}[/tex]
Express as improper fraction
[tex]Total = \frac{3}{2} + 2 + \frac{3}{2}[/tex]
Take LCM
[tex]Total = \frac{3+4+3}{2}[/tex]
[tex]Total = \frac{10}{2}[/tex]
[tex]Total = 5kg[/tex]
What is the axis of symmetry of h(x) = –2x2 + 12x – 3?
a. x = –15
b. x = –3
c. x = 3
d. x = 15
We will see that the axis of symmetry is x = 3, so the correct option is c.
How to find the axis of symmetry of a quadratic function?
The axis of symmetry is a line of the form x = a, such that it divides the parabola in two halves.
Particularly, the axis of symmetry passes through the vertex, so the x-value of the vertex is equal to the value of the axis.
Then we only need to find the x-value of the vertex, remember that for a quadratic:
[tex]y = a*x^2 + b*x + c[/tex]
The vertex is at:
[tex]x = -b/2a[/tex]
Then in our case, the vertex is at:
[tex]x = -12/(2*-2) = -12/-4 = 3[/tex]
So the axis of symmetry is x = 3, then the correct option is C.
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How many pints are in 6 1/2 quarts?
Answer:
13
Step-by-step explanation:
f0llow me if you have time thanks
hope it helps
#carryonlearning
#ownanswer
Answer:
13 pints
Step-by-step explanation:
2 pints per quart
6.5 x 2 = 12 + 1 = 13 pints
If my answer is incorrect, pls correct me!
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-Chetan K